RICHARD VINTER

BSc(Eng), PhD(Eng), ScD(Math), FIEEE, FIEE

 

                                                                     

Head of Control and Power Research Group,

C&P homepage

Department of Electrical and Electronic Engineering
Exhibition Road

London SW7 2BT UK

Phone: +44 20 7594 6287
Fax:     +44 20 7594 6282
E-mail: r.vinter@imperial.ac.uk

Short Curriculum Vitae

  • Higher Education and Degrees

BSc (Engineering Science) Oxford University (First Class), 1969

                        PhD (Engineering) Cambridge University, 1972

ScD (Mathematics) Cambridge University, 1988

  • Current Appointment

Professor of Control Engineering, Electrical and Electronic Engineering (since 1991)

  • Fellowships

Fellow, Institute of Electronic and Electrical Engineers

Fellow, Institute of Electrical Engineers

Harkness Fellow

Leverhulme Fellow

  • Visiting Appointments

Massachusetts Institute of Technology, Univ. of Toronto, Univ. of Montreal, Univ. of British Columbia, Polish Academy of Sciences, Warsaw, Univ. of Paris IX, Univ. of Padua, Univ. of Florence, Purdue University, Univ. of Florence, SISSA, Trieste, Univ. of Lyon.

  • Editorships

Past Editor, SIAM J. Control and Optimisation

Past Editor, Automatica

Editor, IMA J. on Mathematics of Control and Information, Applied Mathematics and Computation, Set Valued Analysis.

  • Professional Bodies, etc

Chair, Science and Technology Board of Data and Information and Fusion Defence Technology Centre

Member, EPSRC Control and Instrumentation College

Member, Defence Scientific and Advisory Committee (DSAC)

External Examiner, Cambridge University Engineering Part I

 


Teaching

Selected Past Lecturing Experience:

 

Math. Programming and Optimal Control (M.Sc. Course, M.I.T.)

Linear Systems (Research Course, Imperial College)

Optimal Control (Research Course, Imperial College)

Measure and Probability (Research Course, Imperial College)

Identification (MSc Course, Imperial College)

Statistics (MSc Course, Imperial College)

Filtering and Stochastic Control (MSc Course, Imperial College)

Deterministic Optimal Control (3rd Yr. UG Course, Imperial College)

Control Engineering (2nd Yr. UG Course, Imperial College)

Discrete Time Systems (4th Yr. UG Course, Imperial College)

Convex Analysis and Optimisation (Research Course, Purdue Univ.)

Deterministic Optimal Control (Int. Centre for Pure and Applied Math., Nice)

Digital Signal Processing (3rd Yr. UG Course, Imperial College)

Non-smooth Analysis and Opt. Control (Research Course, Univ. de Lyon)

 

Current Teaching (Imperial College):

 

Control Engineering (3rd Year EEE undergraduate course)

Probability and Stochastic Processes (Ms and 4th Year undergraduate course)

 

Current Research Supervision, etc:

 

Current PhD students:

S. Robbiati, M. Underwood, M. Yaqoob, S. Rakovic

 

Current Postdoctoral students/research associates

I. Schvartsman, J M C Clark, D Q Mayne


Research Statement

Research Interests:

Control systems (optimal control of non-linear systems, non-linear feedback design, computation of optimal controls, distributed parameter control systems, hybrid control systems, differential games), estimation, calculus of variations, non-linear analysis.

 

Current Grants:

Control and Power (EPSRC Portfolio Partnership Grant) (£2.42M), 2003-2008

(Subsumes earlier EPSRC grants ‘Robust Optimal Control’ and ‘Robust Optimal Control’)

High Precision Target Tracking (Data and Information Fusion DTC) (£270K), 2003-2006

Fault Detection and Condition Monitoring (Data and Information Fusion DTC) (£270K), 2003-2006

Integrated Programme in Aeronautical Research (EPSRC and BAe Systems)(£375K), 2004-2007

 


Optimal Control

 

Optimisation features in engineering design

 

a)      Directly.  Optimisation is a design objective. (There is an unambiguous ‘index’ of performance to minimize -- economic cost (in OR), product yield in process control)

b)      Indirectly. Design specifications do not involve optimisation, but these can be achieved by minimizing some ‘artificial’ cost function. (LQG control, . .)

 

 

 

 

 

 

 

 

 
Indirect applications of optimisation are most common.

 

Example of ‘Direct Optimization’: Minimum Time Ascent Problem for an F-4 aircraft

 

Objective: Reach operational altitude in minimum time

 

Expected flight path:

Range

 
 

 

 

 

 

 

 

 

 

 

 


Surprisingly, substantial improvements can be achieved by using an altogether different flight path:

 

 

 

 

Moral: for nonlinear dynamics and several decision variables, intuitive solutions to optimization problems are seldom optimal.

 

Example. Maximal Orbit Transfer Problem

 

Transfer vehicle to circular orbit of maximal radius (total fuel constraint)

  

                                                           

 

 

Dynamic optimisation predicts bang-bang thrust, with continuously varying thrust angle.

 

Many much more complex problems arising in mission planning have been investigated (‘gravity assist’ in outer planets exploration, minimise atmospheric heating, etc.)

 

 

 

(Autonomous Underwater Vehicle) AUV control: maximise altitude, but reduce effects on trajectory of variable drag coefficient:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Theoretical Research

Degenerate Optimal Control: Derivation of new, refined optimality conditions that give information about optimal controls for problems where traditional necessary conditions fail to do so.

R. B. VINTER, “Optimal Control”, Birkhäuser, Boston, 2000.

F. RAMPAZZO and R. B. VINTER, “Degenerate Optimal Control Problems with State Constraints”, SIAM J. Control, and Optim., 39, (2000), pp. 989-1007.

D. N. BESSIS, Y. S. LEDYAEV, AND R. B. VINTER, “Dualization of the Euler and Hamiltonian Inclusions”, Nonlinear Analysis, 43, (2001), pp. 861-882.

I. CHRYSSOCHOOS and R. B. VINTER, “Optimal Control Problems on Manifolds: A Dynamic Programming Approach”, Journal of Mathematical Analysis and Applications, 287, (2003), pp. 118-140.

A. V. ARUTYUNOV and R. B. VINTER, “A Simple ‘Finite Approximations’ Proof of the Pontryagin Maximum Principle, Under Reduced Differentiability Hypotheses", J. of Set Valued Analysis, 12, (2004), pp. 5-24.

R. VINTER, “Mini-max Optimal Control”, SIAM J. Control and Optim., 44, (2205), pp. 939-968.

 

Regularity of Optimal Controls: Establish qualitative features of optimal controls (smooth, bang-bang, etc) that facilitate numerical solution and implementation

G. GALBRAITH and R. B. VINTER, “Lipschitz continuity of optimal controls for state constrained problems”, SIAM J. Control and Optim.,42, pp. 1727-1744 ( 2003).

 

Dynamic Programming:  New Dynamic Programming principles for problems with path-wise constraints and other non-standard features.

H. FRANKOWSKA and R. B. VINTER, “A Theorem on Existence of Neighbouring Feasible Trajectories: Applications to Dynamic Programming for State Constrained Optimal Control”, J. Optim. Theory and Applic., 104, (2000), 21-40.

 

Multi-stage Optimal Control: Optimality conditions and computational methods for dynamic optimization problems involving multistage dynamic models with inter-stage coupling (space trajectories for multistage rockets, inventory problems, etc.)

G. GALBRAITH and R. B. VINTER, “Optimal Control of Hybrid Systems with an Infinite Number of Discrete States”, Journal of Dynamical and Control Systems 9, (2002), pp. 563-584.

D. BEROVIC AND R. B. VINTER, “The Application of Dynamic Programming to Optimal Inventory Control”, IEEE Trans. Automatic Control, in press.

 


Target Tracking

Aims

 

The aim of this project is to develop and assess new, high precision algorithms for difficult tracking problems involving single and multiple targets, applicable in situations where traditional tracking algorithms perform badly or fail altogether. The algorithms are Bayesian; they are based on probabilistic modeling and the recursive construction of approximations to the evolving condition distribution of target motion, given the observations. The problems considered include such features as ill conditioned bearings only measurements, target models with unknown parameters and tracking in high clutter environments. Research efforts have centred on developing and assessing a new algorithm, called the shifted Rayleigh filter, for bearings-only tracking of a single target. It takes its name form the fact that certain coefficients appearing in the algorithm can be interpreted as moments of a shifted Rayleigh distribution. 

 

The Shifted Rayleigh Filter

 

In common with other moment matching algorithms, the shifted Rayleigh filter makes use of a normal approximation to the prior distribution of target motion. It is unusual, however, in incorporating an exact calculation of the updated distribution, to take account of a new measurement. Thus the only approximation introduced by the algorithm is to replace a conditional distribution by a matched normal distribution, at a single point in each iteration. The isolation of the approximation in this way is important because it simplifies the analysis of tracker performance and permits the construction of error bounds.

 

The new filter is the subject of one journal paper and two conference papers.

 

The journal paper, in which full details of the underlying analysis appear, supplies a theoretical justification of the algorithm. The paper also confirms that the algorithm is competitive with other moment matching algorithms and particle filters in a ‘benign’ scenario, which has been the basis of earlier comparative studies.

 

The conference papers provide an assessment of the shifted Rayleigh filter, applied to more challenging bearings only tracking problems where, according to earlier simulation studies reported in the literature, standard moment matching algorithms, such as the extended Kalman filter, fail to provide useful estimates. The first reports on a comparative study of a particle filter and the shifted Rayleigh filter, where the purpose is to estimate the position of a moving target from noisy, bearings only measurements taken by six drifting sonobuoys, whose positions are estimated from bearings only measurements taken by a stationary monitoring sensor. Simulation studies reveal that the shifted Rayleigh filter performs favourably compared with the particle filter, while reducing the computational burden by an order of magnitude. The second conference paper concerns the application of the shifted Rayleigh filter a high clutter variant on the preceding tracking problem. Here, the filter provides excellent estimates, even in scenarios in which the clutter probability is 67% and standard deviations on the bearings only measurements are in excess of 16 degrees.   

 

There are many tracking problems for which moment matching algorithms are not suitable, notably those when the distributions of interest are multi-modal. But moment matching algorithms offer such substantial computational savings over particle filters, that it is important to explore the range of applicability of such algorithms. Perhaps the most significant aspect of this research is to point to new classes of nonlinear filtering problems for which moment matching algorithms, appropriately applied, are the best available choice.

 

Collaborator: J M C Clark

 

 

Publications

 

1                    J M C Clark, R B Vinter and M Yaqoob, ‘The Shifted Rayleigh Filter: a New Algorithm for Bearings Only Tracking’, IEEE Trans on Aerospace and Electronic Systems (submitted).

2                    J M C Clark, S Maskell, R B Vinter and M Yaqoob, ‘Comparative Study Of the Shifted Rayleigh filter and a Particle Filter’, 2005 IEEE Aerospace Conference, Big Sky Montana (Special Session on Monte Carlo Methods).

3                    J M C Clark, R B Vinter and M Yaqoob, ‘The Shifted Rayleigh Filter for Bearings Only  Tracking’,  Fusion 2005 (to be presented).

4                     J M C Clark, R B Vinter and M Yaqoob, ‘On High Precision Target Tracking for Manoeuvring Targets ’, Proc. IEE 2004 Conference on Target Tracking: Algorithms and Applications, Sussex 2004.

5                    J M C Clark, S Robiatti and R B Vinter, The Shifted-Rayleigh Mixture Algorithm for Bearings-Only Tracking of Manoeuvring Targets, (submitted).

 

 


Differential Games and Robust Controller Design

Aims

The goal of this project is to develop new, practical approaches to the design of feedback controllers of nonlinear systems (such as flow control systems and dynamic telecommunications links), based on the theory of differential games. The approach takes account of ‘worst case’ disturbances and path-wise constraints (representing, for example, actuator saturation or the necessity to avoid ‘dangerous’ regions of the operational profile in an aeronautics or process control context).

What Are Differential Games?

Differential Games concern the balance of ‘optimal’ strategies applied by two opposing players, who have conflicting notions of ‘best’ performance of the dynamical system they are both trying to control. The field has its origins in pursuit-evasion games in a military context, but now has a much more important role in Robust Controller Design.

Relevance of Differential Games to Robust Controller Design

Robust Control concerns the design of control systems whose performance is not degraded by modelling inaccuracies or the presence of disturbances. It is linked to Differential Games, because disturbances and model changes can be interpreted as ‘strategies’ of an antagonistic player. The Differential Games approach provides controllers that deal with disturbances on a worst case basis.

1                    J. M. C. CLARK, M. R. JAMES and R. B. VINTER, “The Interpretation of Discontinuous State Feedback Control Laws as Non-Anticipative Control Strategies in Differential Games”, IEEE Transactions Automatic Control, in press.

2                    J. M. C. CLARK and R. B. VINTER, "A Differential Dynamic Games Approach to Flow Control", Proc. 42nd CDC, Hawaii (2003).

 

 

Robust Model Predictive Control

Objective

The broad objective of this research is the development, analysis, assessment and exploitation of a new form of model predictive control (MPC), Feedback MPC that is inherently robust in the face of uncertainty. Main objective is to devise a method, the complexity of which is considersbly less than that of dynamic programming, for achieving feedback model predictive control of constrained dynamic systems that is robust to a wide class of uncertainties (unknown disturbances, model error and state estimation error when output feedback is used).

What is model predictive control?

Model Predictive Control is an approach to controller design that involves on-line optimization calculations. The online optimization problem takes account of system dynamics, constraints and control objectives. Conventional model predictive control requires the solution of an open-loop optimal control problem, in which the decision variable is a sequence of control actions, at each sample time. Current control action is set equal to the first term of the optimal control sequence.

Model predictive control has a rich and unusual history. The main reason for the wide-scale adoption by industry of model predictive control is its ability to handle hard constraints on controls and states that arise in most applications. These constraints are particularly important in the petro-chemical industry where optimization of set points results in steady-state operation on, or close to, the boundary of the set of permissible states. Model predictive control is one of very few methods available for handling hard constraints, and it is precisely this fact that makes it so useful for the control engineer, particularly in the process industries where plants being controlled are sufficiently `slow' to permit its implementation.

Robust Model Predictive Control

Since uncertainty often has a significant effect on stability and performance. Robust model predictive control requires, in principle, on-line solution of a min-max optimal control problem in which the decision variable is a sequence of control laws , that provides the feedback necessary for robustness, and the adversary is uncertainty. Naive inclusion of feedback leads to a dynamic programming problem of overwhelming complexity. The real challenge is to devise a method, the complexity of which is considerably less than that of dynamic programming, for achieving feedback model predictive control of constrained dynamic systems that is robust to a wide class of uncertainties.

In order to overcome existing limitations of robust model predictive control, in our approach the predicted trajectory is replaced by a predicted tube in state space; the control policy (sequence of control laws) is linear in the tube, and the tube and the policy are chosen so that all realizations of the state lie within the tube. State and control constraints are easily handled.

The online optimal control problem requires is more complex than that for conventional model predictive control but the increase in complexity is relatively modest, permitting employment of this strategy in situations where robustness is required.

 

Survey Paper


 

'Optimal Control' 
(Link to Chapter 1)
by
 Richard Vinter
Publication Details:
Birkhäuser, Boston, May 2000, 507 pp, Price: $79.95 ISBN: 0-8176-4075-4
 
Abstract:
Since the 1980's, new ideas in Optimal Control have led to far-reaching extensions of the theory. These include generalizations of the Pontryagin Maximum Principle, a rigorous framework for Dynamic Programming based on novel concepts of 'solution' to the Hamilton Jacobi Equation, such as viscosity solutions, and new, unrestrictive, conditions for minimizer regularity. A key element has been new analytic techniques that give sense to 'gradients' of functions, that are not differentiable in the conventional sense (Nonsmooth Analysis).
 
Optimal Control brings together many of the important advances of the last two decades. The analysis is self-contained and incorporates many of the simplifications and unifying concepts revealed by recent research. Among other purposes, the book aims to meet the needs of readers with little prior exposure to modern Optimal Control, who seek quick answers to the questions: what are the main results, what were the deficiencies of the classical theory and to what extent have they been overcome? The book includes, for their benefit, a lengthy overview, in which analytical details are suppressed and emphasis is placed instead on communicating underlying ideas.
 
Notable features of the book are:
 
1) A self-contained and accessible exposition of Nonsmooth Analysis and its applications to the analysis of minimizing arcs.
2) A thorough investigation of necessary conditions, including nonsmooth maximum principles and Euler-Lagrange and Hamilton-type conditions for differential inclusion problems. 
3) Self-contained coverage of Dynamic Programming from a system-theoretic point of view, with an emphasis on discontinuous value functions.
4) Detailed consideration of minimizer regularity, free-end time problems involving data discontinuous in time and other topics not previously treated in book form.
 
Chapter Headings
 
Chapter  1: Overview. pp. 1-60
Chapter  2: Measurable Multifunctions an Differential Inclusions, pp. 61-108
Chapter  3: Variational Principles, pp. 109-125
Chapter  4: Nonsmooth Analysis, pp. 127-170
Chapter  5: Subdifferential Calculus, pp. 179-197
Chapter  6: The Maximum Principle, pp. 201-228
Chapter  7: The Extended Euler-Lagrange and Hamilton Conditions, pp. 233-252
Chapter  8: Necessary Conditions for Free End-Time Problems, pp. 285-318
Chapter  9: The Maximum Principle for State Constrained Problems, pp. 321-359
Chapter 10: Differential Inclusions with State Constraints, pp. 361-396
Chapter 11: Regularity of Minimizers, pp. 397-432
Chapter 12: Dynamic Programming, pp. 435-487
References
Index
 
Reviews:  Automatica 38, 8, 2002 by B. Piccoli ( SISSA, Trieste), Mathematical Reviews  2001c:49001by QJ Zhu
 

 

Publications

 

BOOKS

 

3                    M. H. A. DAVIS and R. B. VINTER, “Stochastic Modelling and Control”, Chapman and Hall, London (1985).

4                    R. B. VINTER, “Optimal Control”, Birkhauser, Boston, 2000.

 

REFEREED JOURNAL ARTICLES

 

(pre-1999)

 

5                    R. B. VINTER and F. FALLSIDE, “Minimum Time Control of a Class of Linear Fixed Domain Systems with Distributed Input”, Proc. IEE, 117, (1970), pp. 2294-2300.

6                    R. B. VINTER and F. FALLSIDE, “A Generalized Neustadt Algorithm for Minimum Time Control of Linear Systems with Norm Constraints on the Controls”, Proc. IEE, 119, (1972), pp. 743-752.

7                    R. B. VINTER, “Application of Duality Theory to a Class of Composite Cost Control Problems”, J. Optim. Theory and Applic., 13, (1974), pp. 426-460.

8                    R. B. VINTER, “Approximate Solution of a Class of Singular Control Problems”, J. Optim. Theory and Applic., 13,(1974), pp. 461-483.

9                    R. B. VINTER, “A Generalization to Dual Banach Spaces of a Theorem by Balakrishnan”, SIAM J. Control, 12, (1974), pp. 150-166.

10                R. B. VINTER and T. L. JOHNSON, “Optimal Control of Non-Symmetric Hyperbolic Systems in n Variables on the Half-Space”, SIAM J. Control and  Optim.,  15, (1977),  pp. 129-143.

11                R. B. VINTER, “Filter Stability for Stochastic Evolution Equations”, SIAM J. Control and Optim., 15, (1977),  pp.465-485.

12                R. B. VINTER, “Stabilizability and Semigroups with Discrete Generators”, J. Inst. Math. and its Applic., 20, (1977),  pp. 371-378.

13                G. I. STASSINOPOULOS and R. B. VINTER, “On the Dimension of the Chattering Basis for Relaxed Controls”, IEEE Trans. Aut. Control, AC-22,  (1977), pp. 470-471.

14                R. B. VINTER, “On the Evolution of the State of Linear Differential Delay Equations in M2 : Properties of the Generator”, J. Inst. Math. and its Applic., 21, (1978), pp. 13-23.

15                R. B. VINTER and R. M.  LEWIS, “The Equivalence of Strong and Weak Formulations for Certain Problems in Optimal Control”, SIAM J. Control and Optim., 16,  (1978),  pp. 546-570.

16                R. B. VINTER and R. M. LEWIS, “A Necessary and Sufficient Condition for Optimality of Dynamic Programming Type, Making no A Priori Assumptions on the Controls”, SIAM J. Control and Optim., 16, (1978), pp. 571-583.

17                G. I. STASSINOPOULOS and R. B. VINTER, “Conditions for Convergence of Solutions in the Computation of Optimal Controls”, J. Inst. Math.and its Applic., 22, (1978), pp.1-14.

18                G. I. STASSINOPOULOS and R. B. VINTER, “Continuous Dependence of Solutions of a Differential Inclusion on the Right Hand Side with Applications to Stability of Optimal Control Problems”, SIAM J. Control and Optim., 17,  (1979),  pp. 432-449.

19                R. M. LEWIS and R. B. VINTER, “New Representation Theorems for Consistent Flows”, Proc. London Math. Soc., 3, (1980), pp.507-526.

20                R. B. VINTER and R. M. LEWIS, “A Verification Theorem which Provides a Necessary and Sufficient Condition for Optimality”, IEEE Trans. Aut. Control, AC 25, (1980), pp. 84-89.

21                R. M. LEWIS and R. B. VINTER, “Relaxation of Optimal Control Problems to an Equivalent Convex Program”, J. Math. An. and its Applic., 74, (1980),  pp.475-492.

22                R. B. VINTER, “A Characterization of the Reachable Set for Nonlinear Control Systems”, SIAM J. Control and Optim., 18, (1980), pp. 599-610.

23                R. B. VINTER and R. H. KWONG, “The Infinite Time Quadratic Control Problem for Linear Systems with State and Control Delays: an Evolution Equation Approach”, SIAM J. Control and Optim., 19, (1981), pp. 139-153.

24                R. B. VINTER, “Weakest Conditions for Existence of Lipschitz Continuous Krotov Functions”,  SIAM J. Control  and Optim., 21, (1983), pp. 215-234.

25                R. B. VINTER, “New Global Optimality Conditions in Optimal Control Theory”, SIAM J. Control and Optim., 21, (1983), pp. 235-245.

26                R. B. VINTER, “The Equivalence of ‘Calmness’ and ‘Strong Calmness’ in Optimal Control Theory”, J. Math. An. and its Applic., 96, (1983), pp. 153-179.

27                R. B. VINTER, “Control of Linear Hereditary systems with control and output delays”, Annals of New York Academy of Sciences, 410, (1983),  pp. 121-128.

28                F. H. CLARKE and R. B. VINTER “Local Optimality Conditions and Lipschitzian Solutions to the Hamilton Jacobi Equation”, SIAM J. Control and Optim., 21,  (1983), pp. 856-870.

29                F. H. CLARKE and R. B. VINTER, “On the Conditions Under which the Euler Equation or Maximum Principle Hold”,  Appl. Math. and Opt., 12,  (1984),  pp. 73-79.

30                R. B. VINTER, “On Separation of Convex Sets and Reachability Criteria in Control Theory”, Math. Appl. and Comp., 3, (1984),  pp. 303-315.

31                F. H. CLARKE and R. B. VINTER, “Regularity Properties of Solutions to the Basic Problem in the Calculus of Variations”, Trans. Am. Math.Soc., 289, (1985),  pp. 73-98.

32                F. H. CLARKE and R. B. VINTER, “Existence and Regularity in the Small in the Calculus of Variations", J. Diff. Equations, 59, (1985),  pp. 336-354.

33                R. B. VINTER and L. A. MENDOZA, “Global Optimality Conditions for Nonnormal Control Problems”, IMA  J. Math. Control and Inf., 2, (1985), pp. 241-250.

34                F. H. CLARKE and R. B. VINTER, “Regularity of Solutions to Variational Problems with Polynomial Lagrangians”,  Bul. Polish Ac. Sci., 34, (1986),  pp.73-81.

35                F. PEREIRA and R. B. VINTER, “Necessary Conditions for Optimal Control Problems with Discontinuous Trajectories”, J. Economics Dyn. and Control, 10,  (1986),  pp. 115-118.

36                F. H. CLARKE and R. B. VINTER, “The Relationship Between the Maximum Principle and Dynamic Programming”, SIAM J. Control and Optim., 25, (1987), pp. 1291-1311.

37                P. D. LOEWEN and R. B. VINTER, “Pontryagin-type Necessary Nonditions for Differential Inclusion Problems”, Systems and Control Letters, 9, (1987), pp.263-265.

38                R. B. VINTER and F. PEREIRA, “A Maximum Principle for Optimal Processes with Discontinuous Trajectories", SIAM J. Control and Optim., 26, (1988), pp. 205-229.

39                R. B. VINTER, “New Results on the Relationship between Dynamic Programming and the Maximum Principle”, Mathematics of Control, Signals and Systems, 1, (1988), pp.97-105.

40                R. B. VINTER, “Optimality and Sensitivity of Discrete Time Processes”, Control and Cybernetics, 7, (1988), pp. 191-211.

41                F.  H. CLARKE and R.B.VINTER, “Optimal Multiprocesses”, SIAM J. Control and Optim., 27, (1989), pp. 1072-1091.

42                F. H. CLARKE and R.B.VINTER, “Applications of the Theory of Optimal Multiprocesses”, SIAM J. Control and Optim., 27, (1989), pp. 1048-1071.

43                F. H. CLARKE, P.D.LOEWEN and R.B.VINTER, “Differential Inclusions With Free Time”, Annales de L'Institute Henri Poincare (Analyse Nonlineaire), 5, (1989), pp. 573-1071.

44                M. S. BRIGGS and R. B. VINTER, “Linear Filtering for Time Delay Systems”, IMA J. of Math. Control and Info., 6, (1989), pp. 167-178.

45                 F. H. CLARKE and R. B. VINTER, “Regularity of Minimizers for Problems in the Calculus of Variations with Higher Order Derivatives”, Bull. Canadian Math. Soc., 33, (1990).

46                F. H. CLARKE and R. B. VINTER, “A Regularity Theory for Problems in the Calculus of Variations with Higher Order Derivatives”, Trans. Am. Math. Soc., 320,(1990), pp. 227- 251.

47                F. H. CLARKE and R. B. VINTER, “Regularity Properties of Optimal Controls”, SIAM J. Control and Optim., 28, (1990), pp. 980-997.

48                R. B. VINTER and P. WOLENSKI, “Hamilton Jacobi Theory for Optimal Control Problems with Data Measurable in Time”, SIAM J. Control and Optim., 6, (1990), pp. 1404-1419.

49                R. B. VINTER and P. WOLENSKI, “Coextremals and the Value Function for Control Problems with Data Measurable in Time”, J. Math. An. and its Applic., 153, (1990), pp.37-51.

50                J. ROSENBLUETH and R. B. VINTER, “Relaxation Procedures for Time Delay Systems”, J. Math. An. and Applic., 162, (1991), pp. 542-563.

51                J. D. L. ROWLAND and R. B. VINTER, “A Maximum Principle for Free Endtime Optimal Control Problems with Data Discontinuous in Time”, Trans. IEEE on Aut. Control, AC 36, (1991), pp. 603-608.

52                J. D.L. ROWLAND and R. B. VINTER, “Construction of Optimal Feedback Controls”, Systems and Control Letters, 16, (1991), pp. 357-367.

53                J. D. L. ROWLAND and R. B. VINTER, “Pontryagin Type Conditions for Differential Inclusions with Free Time”, J. Math. Anal.and Applic., 165, (1992), pp. 587-597.

54                G. SILVA and R. B. VINTER, “Optimal Impulsive Control of Nonlinear Systems”, Proc. IMA Conference on Mathematical Control, Manchester, (1992).

55                J. D. L. ROWLAND and R. B. VINTER, “Dynamic Optimization Problems with Free Time and Active State Constraints”, SIAM J. Control and Optim., 31, (1993), pp.677-697.

56                R. B. VINTER, “Convex Duality and Nonlinear Optimal Control”, SIAM J. Control and Optim. 31, (1993), pp. 518-538.

57                J. KOTSIOPOULOS and R. B. VINTER, “Dynamic programming for free-time problems with endpoint constraints”, Math. of Control, Systems and Signals, Math. of Control, Systems and Signals, 6 (1993), pp. 180-193 .

58                H. BABAD and R. B. VINTER, “Sensitivity Interpretations of the Costate Function of Optimal Control”, IMA J. on Math. Control and Info., 10, (1993), pp. 21-31.

59                M. FERRIERA and R. B. VINTER, “When is the Maximum Principle for State Constrainted Problems Degenerate?”, J. Math. An. and Applic., 187 (1994), pp.438-467.

60                R. B. VINTER, “Uniqueness of Solutions to the Hamilton Jacobi Equation: a System Theoretic Approach”, Systems and Control Letters, Systems and Control Letters, 22 (1994), pp. 267-275.

61                H. MICHALSKA and R. B. VINTER, “Receding Horizon Control for General Nonlinear Systems: Stability and Robustness”, IMA J. on Math. Control and Info., 11 (1994), pp. 321-340.

62                G. TOUTSINOS AND R. B. VINTER, “Duality Theorems for Convex Problems with Time Delay”, J. Optim.  Theory and Applic., 36 (1995).

63                M. do R. de PINHO and R. B. VINTER, “An Euler Lagrange Inclusion for Optimal Control Problems”, IEEE Trans Aut. Control, 40 (1995), pp.1191-1198.

64                G. N. SILVA and R. B. VINTER, “Measure Differential Inclusions”, J. Math. Analysis and Applic., 202 (1996), pp. 727-746.

65                A. RAPAPORT and R. B. VINTER, “Invariance Properties of Time Measurable Differential Inclusions and Dynamic Programming”, J. of Dynamical and Control Systems, Journal of Dynamical Control Systems, 2, (1996), pp. 423-448.

66                R. B. VINTER and H. ZHENG, “An Extended Euler Lagrange inclusion for nonconvex variational problems”, SIAM J. Control and Optim., 35, (1997), pp. 56-77.

67                G. N. SILVA and R. B. VINTER, “Necessary Conditions for Optimal Impulsive Control Problems”, SIAM J. Control and Optim., SIAM J. Control and Optim., 35, (1997) pp. 1829-1846.

68                R. B. VINTER and P. WOODFORD, “On the Occurence of Intermediate Local Minimizers that are not Strong Local Minimizers”, Systems and Control Letters, 31, (1997), pp. 235-242.

69                M. do R. de PINHO and R. B. VINTER, “Necessary Conditions for Optimal Control Problems Involving Nonlinear Differential Algebraic Equations”, J. Math. Analysis and Applic., 202 (1997), pp. 493-516.

70                F. H. CLARKE, Y. LEDYAEV and R. B. VINTER, “Regularity properties of solutions to linear quadratic optimal control problems with state constraints”, Systems and Control Letters, 30, (1997), pp. 265-272.

71                R. B. VINTER AND H. ZHENG, “Necessary Conditions for Optimal Control Problems with State Constraints”, Trans. American Mathematical Society, 350, (1997) pp. 1181-12040.

72                M. L. BELL, R. W. H. SARGENT AND R. B. VINTER, “Existence of Optimal Controls for Continuous Time Infinite Horizon Problems”, Int. J. Control, 68, (1997), pp. 887-896.

73                R. PYTLAK and R. B. VINTER, “A Feasible Directions Type Algorithm for Optimal Control Problems with State and Control Constraints, SIAM J. Control and Optim., 36, (1998), pp.1999-2019.

74                F.RAMPAZZO and R.B.VINTER, “A Theorem on the Existence of Neighbouring Feasible Trajectories with Applications to Optimal Control”, IMA J. Math. Control and Systems, 16, (1999), 335-351.

75                R. PYTLAK and R. B. VINTER, “A Feasible Directions Type Algorithm for Optimal Control Problems with State and Control Constraints: Implementation”, J. Optim. Theory and Applic., 101, (1999), pp. 623-650.

76                M. M. A. FERREIRA, F. A. C. C. FONTES and R. B. VINTER, “Nondegenerate Necessary Conditions for Nonconvex Optimal Control Problems with State Constraints”, J. Math. Anal. Applic., 233, (1999), 116-129.

 

(2000)

 

77                F. RAMPAZZO and R. B. VINTER, “Degenerate Optimal Control Problems with State Constraints”, SIAM J. Control, and Optim., 39, (2000), pp. 989-1007.

78                H. FRANKOWSKA and R. B. VINTER, “A Theorem on Existence of Neighbouring Feasible Trajectories: Applications to Dynamic Programming for State Constrained Optimal Control”, J. Optim. Theory and Applic., 104, (2000), 21-40.

79                J. M. C. CLARKE and R. B. VINTER, “Flow Rate Control”, Electronics Letters 36, (2000), pp.1328-1329.

80                R. B. VINTER and H. ZHENG, “Necessary Conditions for Free End-Time, Measurably Time Dependent Optimal Control Problems with State Constraints”, J. Set Valued Analysis, 8,(2000), 1-19

 

(2001)

 

81                M. Do R. de PINHO, R. B. VINTER and H. ZHENG, “A Maximum Principle for Optimal Control Problems with Mixed Constraints”, IMA J. Math. Control and Info., 18, (2001), pp. 189-205.

82                D. N. BESSIS, Y. S. LEDYAEV, AND R. B. VINTER, “Dualization of the Euler and Hamiltonian Inclusions”, Nonlinear Analysis, 43, (2001), pp. 861-882.

 

(2002)

 

83                G. GALBRAITH and R. B. VINTER, “Optimal Control of Hybrid Systems with an Infinite Number of Discrete States”, Journal of Dynamical and Control Systems 9, (2002), pp. 563-584.

 

(2003)

 

84                G. GALBRAITH and R. B. VINTER, “Lipschitz continuity of optimal controls for state constrained problems”, SIAM J. Control and Optim.,42, pp. 1727-1744 ( 2003).

85                A. ARUTYUNOV and R. B. VINTER, “The Finite Dimensional Approximation Method in Optimal Control Theory”, Differential Equations, 39, 2003, pp. 1519-1528.

86                I. CHRYSSOCHOOS and R. B. VINTER, “Optimal Control Problems on Manifolds: A Dynamic Programming Approach”, Journal of Mathematical Analysis and Applications, 287, (2003), pp. 118-140.

87                R. B. VINTER AND H. ZHENG, “Some Finance Problems Solved with Nonsmooth Optimization Techniques”, Journal of Optimization Theory and Applications, 119, (2003), pp. 1-18.

 

(2004-5)

 

88                G. GALBRAITH and R. B. VINTER, “Regularity of Optimal Controls for State Constrained Problems”, Journal of Global Optimization, 28, (2004), pp. 305-317.

89                A. V. ARUTYUNOV and R. B. VINTER, “A Simple ‘Finite Approximations’ Proof of the Pontryagin Maximum Principle, Under Reduced Differentiability Hypotheses", J. of Set Valued Analysis, 12, (2004), pp. 5-24.

90                J. M. C. CLARK, M. R. JAMES and R. B. VINTER, “The Interpretation of Discontinuous State Feedback Control Laws as Non-Anticipative Control Strategies in Differential Games”, IEEE Transactions Automatic Control,  49, (2004), pp. 1360-1365.

91                D. BEROVIC AND R. B. VINTER, “The Application of Dynamic Programming to Optimal Inventory Control”, IEEE Trans. Automatic Control, 49, (2004), pp. 676-685.

92                R. B. VINTER, “Mini-Max Optimal Control”, SIAM J. Control and Optim., 44, (2005), pp. 939-968.

 

REFEREED ARTICLES IN CONFERENCE PROCEEDINGS

 

93                S. K. MITTER and R. B. VINTER, “Filtering for Linear Stochastic Hereditary Linear Systems”, in Control Theory , Numerical Methods and Computer Systems Modelling, (Ed A.Bensoussan), Lecture Notes in Economics and Math. Systems Ì, No.107, Springer Verlag (1974).

94                R. B. VINTER, “Filter Stability for Stochastic Evolution Equations (a summary)”,  Proc. 15th Conf. on Decision and Control,  Fort Lauderdale,  (1976).

95                R. B. VINTER, “Semigroups on Product spaces with Application to Initial Value Problems with Non-local Boundary Conditions”, Proc. Symp. on Control of Distributed Parameter Systems, Warwick,  (1977).

96                R. B. VINTER, “Dynamic Programming:  a Global Approach to Determining Necessary and Sufficient Conditions of Optimality”, Proc. 17th Conf. on Decision and Control, San Diego, (1978).

97                R. B. VINTER, “State Space Reduction in Quadratic Cost Control Problems Involving Delays in States and Controls”, Abstracts of ‘Optimization Days’,  Montreal  (1979).

98                R. H. KWONG and R. B. VINTER, ``On the Infinite Time Quadratic Cost Control Problem for Linear Systems with State and Control delays", Proc. 18th  Conf. on Decision and Control,  Fort Lauderdale, (1979).

99                R. B. VINTER, A New Global Optimality Condition in Control Theory", Proc. 19th Conf. on Decision and Control,  Albequerque, (1981).

100            R. B. VINTER and G.PAPPAS, “A Maximum Principle for Non-Smooth Optimal Control Problems with State Constraints”, J. Math. An. Applic., 89, (1982),  pp. 212-232.

101            F. PEREIRA and R. B. VINTER, “Optimal Control Problems with Discontinuous Trajectories”, Proc. 25th Conf. on Decision and Control,  Athens, (1986).

102            R. B. VINTER, “Is the Costate Variable the State Derivative of the Value Function?”,  Proc. 25th Conf. on Decision and Control, Athens,  (1986).

103            F. PEREIRA and R. B. VINTER, “Necessary Conditions for Impulsive Control Problems with State Constraints”,  Abstracts  13th IFIP TokyoÌ, (1987).

104            P. D. LOEWEN and R. B. VINTER, “Free Time Optimal Control Problems with Unilateral State Constraints”,  Proc. 8th International Conference:  Analysis and Optimization of Systems, Antibes (1988).

105            R. B. VINTER, “A Unified Treatment of Some Nonstandard Problems in Dynamic Optimization”, Proc. Conf. on Nonsmooth Optimization and Related Topics, Erice, Sicily,1988.

106            R. B. VINTER and P. WOLENSKI, “Hamilton Jacobi Theory for Optimal Control Problems with Data Measurable in Time (a Summary)”, Proc. 28th Conf. on Decision and Control, San Diego, (1989).

107            R. B. VINTER, “Relaxed Controls for Time Delay Systems”, Proc. 9th International Conference: Analysis and Optimization of Systems, Antibes, (1990).

108            J. D. L. ROWLAND and R. B. VINTER, “Free Time Optimal Control Problems with Active State Constraints”, Proc. 30th Conf. on Decision and Control, Brighton, (1991).

109            R. B. VINTER and H. MICHALSKA, “Receding Horizon Control of Nonlinear Time-Varying Systems”, Proc. 30th Conf.on Decision and Control, Brighton, (1991).

110            R. B. VINTER, “Free Time Problems with Endpoint Constraints”, Proc. 30th Conf.on Decision and Control, Brighton, (1991).

111            R. B. VINTER and M. FERRIERA, “On the Nontriviality of the Maximum Principle for Control Problems with State Constraints”, Proc. 31st Conf. on Decision and Control, Tucson, Arizona, 1992.

112            G. SILVA and R. B. VINTER, “Optimal Impulse Control Problems with State Constraints”, Proc. 32 Conf. on Decision and Control, San Antonio, Texas, (1993).

113            M. Do R. de PINHO, R.W.S.Sargent and R.B.VINTER, “Optimal Control of Nonlinear DAE Systems”, Proc. 32nd Conf. on Decision and Control, San Antonio, Texas, (1993).

114            R. PYTLAK and R. B. VINTER, A Feasible Directions Algorithm for Optimal Control Problems with Hard State and Control Constraints”, Proc. 32nd Conf. on Decision and Control, San Antonio, Texas, (1993).

115            L. KERSHENBAUM, D. Q. MAYNE, R. PYTLAK AND R. B. VINTER, “Nonlinear Model Predictive Control”, Proc.  Symp. Advances in Model Based Predictive Control , Oxford, (1993).

116            R. PYTLAK and R. B. VINTER, “An Algorithm for a General Minimum Fuel Problem”, Proc. 33 Conf. on Decision and Control, Orlando, Florida (1993), pp. 3613-3621.

117            M. do R. de PINHO, R. B. VINTER and H. ZHENG, “A Maximum Principle for Optimal Control Problems with State Dependent Control Constraints”, Proc. 1996 Portuguese Control conference, Porto, (1996).

118            P. MAVRIKIS and R. B. VINTER, “Trajectory Specific Model Reduction”, 37th Conf. on Decision and Control, San Diego, (1997).

119            G. SILVA and R. B. VINTER, “Optimal Impulse Control”, 37th Conf. on Decision and Control, San Diego, (1997).

120            P. D. LOEWEN, R. B. VINTER and H. ZHENG, “A Maximum Principle for Optimal Control Problems with Nondifferentiable Data”, 38th Conf. on Decision and Control, Tampa, (1998).

121            G. SILVA AND F. PEREIRA and R. B. VINTER, “Optimal Impulse Control of Differential Inclusions”, 38th Conf. on Decision and Control onference, Tampa, (1998).

122            H. FRANKOWSKA and R. B. VINTER, “Dynamic Programming for State Constrained Optimal Control Problems”, Proc. MTNS Conf., Perpignon, (2000).

123            J. M. C. CLARKE and R. B. VINTER, “A Differential Dynamic Games Problem Arising in Surge Tank Control”, Proc. UKACC Intern. Conf. on Control, Cambridge, 2000.

124            F. PEREIRA, G. SILVA and R. B. VINTER, “Necessary Conditions of Optimality for Vector-Valued Impulsive Control Problems with State Constraints”, Proc. European Control Conference, Porto, (2001).

125            I. CHRYSSOCHOOS and R. B. VINTER, “Dynamic Programming and Optimal Control Problems on Manifolds”, pp. (2001), Proc. European Control Conference, Porto, 2001,(2001).

126            G. GALBRAITH and R. B. VINTER, “Lipschitz Regularity of Optimal Controls”, Proc. 41st Conf. on Decision and Control, Las Vegas, (2002).

127            R. B. VINTER, “A Maximum Principle for Mini-Max Optimal Control Problems”, Proc. 41st Conf. on Decision and Control, Las Vegas, (2002).

128            J. M. C. CLARK and R. B. VINTER, "A Differential Dynamic Games Approach to Flow Control", Proc. 42nd CDC, Hawaii (2003).

 

REFEREED BOOK CHAPTERS

 

129            R. B. VINTER, “2Convex Functions Arising in Optimal Control and Ioffe's Global Optimality Condition”, in ‘Convex Analysis and Optimization’, (Eds. Aubin and Vinter), Pitmans Research Notes in Mathematics, No. 57, (1982), pp. 152-179.

130            R. B. VINTER, “Applications of Convex Analysis to Some Problems in Non-Linear Control Theory”, in ‘Differential Equations and Applications’, (Eds. Kappel and Schappacher), Pitmans Research Notes in Mathematics, No.68, (1983), pp. 259-273.

131            R. B. VINTER,  ``Dynamic Programming for Optimal Control Problems with Terminal Constraints", in Recent mathematical methods in dynamic programming", Ed. T. Zolezzi and W.H. Fleming, Springer Verlag,  (1985),  pp. 190-202.

132            F. H. CLARKE and R.B.VINTER, “On the Connection Between the Maximum Principle and the Dynamic Programming Technique”, in Mathematics for Optimization", Ed. J.-B. Hirriart-Urraty, Springer Verlag,  New York,  (1986),  pp.77-102.

133            R. B. VINTER, “Semigroup Models for Linear Distributed Systems with Boundary Control”, in Recent Advances in Communications and Control Theory”,  Eds. R.E. Kalman et al.,  New York: Optimization Software, Inc., Publications Division, (1987), pp. 287-307.

134            T. P. STADLER and R. B. VINTER, “On the Controllability and Observability Functions of Nonlinear Control”, in “Modelling and Control of Mechanical Systems”, Imperial College Press, London,(1997), pp. 65-73

 

EDITED CONFERENCE PROCEEDINGS

 

135            J.-P. AUBIN and R. B. VINTER (Eds.), “Convex Analysis and Optimization”, Pitmans Research Notes in Mathematics, 57, (1982).

136            A, ASTOLFI, D.J.N.LIMEBEER, C. MELCHIORRI, A.TORNAMBE and R. B. VINTER (Eds.), “Modelling and Control of Mechanical Systems”, 57, (1982).