Publications
206 results found
JMC C, Vinter RB, Yaqoob MM, 2007, Shifted Rayleigh filter: A new algorithm for bearings-only tracking, IEEE T AERO ELEC SYS, Vol: 43, Pages: 1373-1384, ISSN: 0018-9251
A new algorithm, the "shifted Rayleigh filter," is introduced for two- or three-dimensional bearings-only tracking problems. In common with other ' moment matching" tracking algorithms such as the extended Kalman filter and its modern refinements, it approximates the prior conditional density of the target state by a normal density; the novel feature is that an exact calculation is then performed to update the conditional density in the light of the new measurement. The paper provides the theoretical justification of the algorithm. It also reports on simulations involving variants on two scenarios, which have been the basis of earlier comparative studies. The first is a "benign" scenario where the measurements are comparatively rich in range-relate information; here the shifted Rayleigh filter is competitive with standard algorithms. The second is a more "extreme" scenario, involving multiple sensor platforms, high-dimensional models and noisy measurements; here the performance of the shifted Rayleigh filter matches the performance of a high-order bootstrap particle filter, while reducing the computational overhead by an order of magnitude.
Salmond D, Clark M, Vinter R, et al., 2007, Ground target modelling, tracking and prediction with road networks, 10th International Conference on Information Fusion, Publisher: IEEE, Pages: 661-+
Arulampalam S, Clark M, Vinter R, 2007, Performance of the Shifted Rayleigh Filter in single-sensor bearings-only tracking, 10th International Conference on Information Fusion, Publisher: IEEE, Pages: 1761-+
Clark, J M C, Vinter R B, 2006, A New Class of Moment Matching Filters for Nonlinear Tracking and Estimation Problems
Caines P E, Clarke F H, Liu X, et al., 2006, A Maximum Principle for Hybrid Optimal Control Problems with Pathwise State Constraints
Shvartsman IA, Vinter RB, 2006, Regularity properties of optimal controls for problems with time-varying state and control constraints, NONLINEAR ANAL-THEOR, Vol: 65, Pages: 448-474, ISSN: 0362-546X
In this paper we report new results. on the regularity of optimal controls for dynamic optimization problems with functional inequality state constraints, a convex time-dependent control constraint and a coercive cost function. Recently, it has been shown that the linear independence condition on active state constraints, present in the earlier literature, can be replaced by a less restrictive, positive linear independence condition, that requires linear independence merely with respect to non-negative weighting parameters, provided the control constraint set is independent of the time variable. We show that, if the control constraint set, regarded as a time-dependent multifunction, is merely Lipschitz continuous with respect to the time variable, then optimal controls can fail to be Lipschitz continuous. In these circumstances, however, a weaker Holder continuity-like regularity property can be established. On the other hand, Lipschitz continuity of optimal controls is guaranteed for time-varying control sets under a positive linear independence hypothesis, when the control constraint sets are described, at each time, by a finite collection of functional inequalities.. (c) 2005 Published by Elsevier Ltd.
Mayne DQ, Rakovic SV, Vinter RB, et al., 2006, Characterization of the solution to a constrained H-infinity optimal control problem, AUTOMATICA, Vol: 42, Pages: 371-382, ISSN: 0005-1098
This paper obtains an explicit Solution to a finite horizon min-max optimal control problem where the system is linear and discrete-time with control and state constraints, and the cost quadratic; the disturbance is negatively costed, as in the standard H-infinity problem, and is constrained. The cost is minimized over control policies and maximized over disturbance sequences so that the Solution yields a feedback control. It is shown that, under certain conditions, the value function is piecewise quadratic and the optimal control policy piecewise affine, being quadratic and affine, respectively, in polyhedra that partition the domain of the value function. (C) 2005 Elsevier Ltd. All rights reserved.
Clark, J M C, Vinter R B, et al., 2005, A Comparison of the Particle and Shifted Rayleigh Filters in their Application to a Multi-sensor Bearings-only Problem
Vinter R B, Allwright J C, 2005, Second order conditions for periodic optimal control problems, Control and Cybernetics, Vol: 34, Pages: 1-27
Clark JMC, Vinter RB, Yaqoob MM, 2005, The Shifted Rayleigh Filter for Bearings Only Tracking
Allwright J C, Vinter R B, 2005, Second order conditions for periodic optimal control problems, Control and Cybernetics, Vol: 34, Pages: 617-644, ISSN: 0324-8569
Vinter R B, 2005, The Role of Metric Regularity in State Constrained Optimal Control
Clark M, Maskell S, Vinter R, et al., 2005, A comparison of the particle and shifted Rayleigh filters in their application to a multi-sensor bearings-only problem, 2005 IEEE Aerospace Conference, Publisher: IEEE, Pages: 2142-2147, ISSN: 1095-323X
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- Citations: 5
Vinter RB, 2005, Minimax optimal control, SIAM J CONTROL OPTIM, Vol: 44, Pages: 939-968, ISSN: 0363-0129
This paper provides a framework for deriving necessary conditions, in the form of a maximum principle, for minimax optimal control problems. The distinguishing feature of these problems is that the data depends on a vector a of unknown parameters, and "optimality" is defined on a worst case basis, as a ranges over the parameter set A. The centerpiece, a minimax maximum principle, is a set of optimality conditions for such problems. Here, the parameter set A is taken to be an arbitrary compact metric space and the hypotheses imposed on the dynamics and endpoint constraints are of an unrestrictive nature. The minimax maximum principle captures as special cases necessary conditions for optimal control problems with minimax costs, for problems involving "semi-infinite" endpoint constraints, and also a maximum principle for state constrained optimal control problems.
Vinter RB, Clark JMC, James MR, 2004, The Interpretation of Discontinuous State Feedback Control Laws as Non-Anticipative Control Strategies in Differential Games, IEEE Transactions Automatic Control, Vol: 49, Pages: 1360-1365
Clark JMC, Vinter RB, 2004, On the interpretation of non-anticipative control strategies in differential games and applications to flow control, Optimal control, stabilization and nonsmooth analysis, Editors: De Queiroz, Malisoff, Wolenski, Berlin, Publisher: Springer, Pages: 29-48, ISBN: 9783540213307
Berovic DP, Vinter RB, 2004, The application of dynamic programming to optimal inventory control, IEEE T AUTOMAT CONTR, Vol: 49, Pages: 676-685, ISSN: 0018-9286
This paper concerns a class of deterministic impulse control problems, arising in inventory control. A notable feature of the problem formulation is the presence of an end-point constraint. In consequence, the value function may be discontinuous. Viability theory provides a characterization of the value function as the unique lower semicontinuous solution to a Bensoussan-Lions type quasi-variational inequality (QVI), suitably interpreted for nondifferentiable, extended valued functions. Yet there are few examples in the literature of the use of this analytical machinery. This paper provides such an example. The example, which concerns a problem for which the value function is neither everywhere finite valued nor continuously differentiable on the interior of its effective domain, illustrates what is involved in calculating subdifferentials and checking satisfaction of QVI (in a generalized sense). This paper also provides a summary of the underlying theory, and gathers in the Appendix proofs of key results.
Galbraith GN, Vinter RB, 2004, Regularity of optimal controls for state constrained problems, Meeting on Variational Analysis and Applications held at the 1st AMS-UMI Joint Meeting, Publisher: SPRINGER, Pages: 305-317, ISSN: 0925-5001
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- Citations: 3
Clark JMC, Vinter RB, Yaqoob MM, 2004, On high precision bearings only tracking for manoeuvring targets, Pages: 51-56, ISSN: 0537-9989
Arutyunov AV, Vinter RB, 2004, A simple 'finite approximations' proof of the Pontryagin maximum principle under reduced differentiability hypotheses, SET-VALUED ANALYSIS, Vol: 12, Pages: 5-24, ISSN: 0927-6947
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- Citations: 26
Clark JMC, Vinter RB, 2004, On the interpretation of non-anticipative control strategies in differential games and applications to flow control, Conference on Mathematical Control Theory (MCT 03), Publisher: SPRINGER-VERLAG BERLIN, Pages: 29-47, ISSN: 0170-8643
Shvartsman I, Vinter RB, 2004, On the regularity of optimal controls for state constrained problems, 43rd conference on decision and control; CDC 43, Nassau, Bahamas, Publisher: IEEE, Pages: 2285-2290
Papakos V, Vinter RB, 2004, A structured robust optimal control technique, New York, 43rd IEEE conference on decision and control, Nassau, Bahamas, DEC 14 - 17 December 2004, Publisher: IEEE, Pages: 2279-2284
Chryssochoos I, Vinter RB, 2003, Optimal control problems on manifolds: a dynamic programming approach, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, Vol: 287, Pages: 118-140, ISSN: 0022-247X
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- Citations: 10
Arutyunov AV, Vinter RB, 2003, A finite-dimensional approximation method in optimal control theory, DIFFERENTIAL EQUATIONS, Vol: 39, Pages: 1519-1528, ISSN: 0012-2661
Vinter RB, Zheng H, 2003, Some finance problems solved with nonsmooth optimization techniques, JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, Vol: 119, Pages: 1-18, ISSN: 0022-3239
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- Citations: 3
Galbraith GN, Vinter RB, 2003, Optimal control of hybrid systems with an infinite set of discrete states, J DYN CONTROL SYST, Vol: 9, Pages: 563-584, ISSN: 1079-2724
Hybrid control systems are described by a family of continuous subsystems and a set of logic rules for switching between them. This paper concerns a broad class of optimization problems for hybrid systems, in which the continuous subsystems are modelled as differential inclusions. The formulation allows endpoint constraints and a general objective function that includes "transaction costs" associated with abrupt changes of discrete and continuous states, and terms associated with continuous control action as well as the terminal value of the continuous state. In consequence of the endpoint constraints, the value function may be discontinuous. It is shown that the collection of value functions (associated with all discrete states) is the unique lower semicontinuous solution of a system of generalized Bensoussan-Lions type quasi-variational inequalities, suitably interpreted for nondifferentiable, extended valued functions. It is also shown how optimal strategies and value functions are related. The proof techniques are system theoretic, i.e., based on the construction of state trajectories with suitable properties. A distinctive feature of the analysis is that it permits an infinite set of discrete states.
Galbraith GN, Vinter RB, 2003, Lipschitz continuity of optimal controls for state constrained problems, SIAM J CONTROL OPTIM, Vol: 42, Pages: 1727-1744, ISSN: 0363-0129
This paper provides new conditions under which optimal controls are Lipschitz continuous for dynamic optimization problems with functional inequality constraints, a control constraint expressed in terms of a general closed convex set and a coercive cost function. It is shown that the linear independence condition on active state constraints, present in the earlier literature, can be replaced by a less restrictive, positive linear independence condition that requires linear independence merely with respect to nonnegative weighting parameters. Smoothness conditions on the data, imposed in earlier work, are also relaxed. The new conditions for Lipschitz continuity of optimal controls are obtained by a detailed analysis of the implications of first order optimality conditions in the form of a nonsmooth maximum principle.
Clark JMC, Vinter RB, 2003, A differential dynamic games approach to flow control, New York, 42nd IEEE conference on decision and control, Maui, HI, 9 - 12 December 2003, Publisher: IEEE, Pages: 1228-1231
Arutyunov A, Vinter RB, 2003, The method of finite approximations in optimal control theory, Differential Equations, Vol: 39, Pages: 1443-1451, ISSN: 0012-2661
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