Publications
206 results found
Boccia A, Falugi P, Maurer H, et al., 2013, Free time optimal control problems with time delays, 52nd IEEE Annual Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 520-525, ISSN: 0743-1546
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- Citations: 9
Palladino M, Vinter RB, 2013, When Does Relaxation Reduce the Minimum Cost of an Optimal Control Problem?, 52nd IEEE Annual Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 526-531, ISSN: 0743-1546
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- Citations: 2
Bettiol P, Frankowska H, Vinter R, 2013, Sensitivity interpretations of the co-state trajectory for opimal control problems with state constraints, 52nd IEEE Annual Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 532-537, ISSN: 0743-1546
Festa A, Vinter RB, 2013, A decomposition technique for pursuit evasion games with many pursuers, 52nd IEEE Annual Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 5797-5802, ISSN: 0743-1546
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- Citations: 8
Özelçi AC, Vinter R, 2012, The shifted Rayleigh filter for 3D bearings-only measurements with clutter, Pages: 1385-1391
Bearings-only tracking concerns the estimation of the position of a moving target from noisy measurements of the direction of the target relative to the sensor platform. We present an algorithm for bearings-only tracking, in which the measurements are in 3D space and are corrupted by clutter. In common with the earlier proposed shifted Rayleigh filter (SRF), the algorithm is based on exact calculations of the updated conditional mean and covariance of the state variable, under the assumption of a Gaussian prior. The presence of clutter on bearings measurements in 3D space adds considerably to the difficulty of performing these exact calculations. We report on simulations in a challenging scenario, aimed at comparing the performance of various trackers. In these simulations, the proposed tracking algorithm consistently outperforms other moment matching filters and the mean square tracking error compares favorably with the posterior Cramér-Rao lower bound (CRLB). © 2012 ISIF (Intl Society of Information Fusi).
Falugi P, Kountouriotis P-A, Vinter RB, 2012, Differential Games Controllers That Confine a System to a Safe Region in the State Space, With Applications to Surge Tank Control, IEEE Transactions on Automatic Control, Vol: 57, Pages: 2778-2788, ISSN: 1558-2523
Surge tanks are units employed in chemical processing to regulate the flow of fluids between reactors. A notable feature of surge tank control is the need to constrain the magnitude of the Maximum Rate of Change (MROC) of the surge tank outflow, since excessive fluctuations in the rate of change of outflow can adversely affect down-stream processing (through disturbance of sediments, initiation of turbulence, etc.). Proportional + Integral controllers, traditionally employed in surge tank control, do not take direct account of the MROC. It is therefore of interest to explore alternative approaches. We show that the surge tank controller design problem naturally fits a differential games framework, proposed by Dupuis and McEneaney, for controlling a system to confine the state to a safe region of the state space. We show furthermore that the differential game arising in this way can be solved by decomposing it into a collection of (one player) optimal control problems. We discuss the implications of this decomposition technique, for the solution of other controller design problems possessing some features of the surge tank controller design problem.
Clark JMC, Vinter RB, 2012, Stochastic exit time problems arising in process control, Stochastics-An International Journal of Probability and Stochastic Processes, Vol: 84, Pages: 667-681, ISSN: 1744-2516
This paper concerns the problem of controlling a stochastic system, with small noise parameter, to prevent it leaving a safe region of the state space. Such problems arise in flow control and other areas. We consider a formulation of the problem, in which a control is sought, to maximize a cost which is related to the expected exit time, but modified to reduce the probability of an early exit, according to a specified level of risk aversion (‘risk sensitive’ stochastic control). Formally letting the noise parameter tend to zero, we find that the optimal control strategy for this problem coincides with the optimal feedback control strategy for a differential game. We identify a class of differential games arising in this way, the so called decomposable differential games, for which the optimal control strategy can be easily obtained and illustrate the proposed solution technique by applying it to a flow control problem arising in process systems engineering.
Bettiol P, Boccia A, Vinter R, 2012, Stratified Necessary Conditions for Unbounded Differential Inclusions with State Constraints, 51st IEEE Annual Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 7703-7707, ISSN: 0743-1546
Gavriel C, Lopes S, Vinter R, 2011, Regularity of minimizers for higher order variational problems in one independent variable, ANNUAL REVIEWS IN CONTROL, Vol: 35, Pages: 172-177, ISSN: 1367-5788
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- Citations: 5
Bettiol P, Frankowska H, Vinter RB, 2011, L∞ estimates on trajectories confined to a closed subset, Journal of Differential Equations, Vol: 252, Pages: 1912-1933, ISSN: 1090-2732
This paper concerns the validity of estimates on the distance of an arbitrary state trajectory from the set of state trajectories which lie in a given state constraint set. These so called distance estimates have wide-spread application in state constrained optimal control, including justifying the use of the Maximum Principle in normal form and establishing regularity properties of value functions. We focus on linear, L∞ distance estimates which, of all the available estimates have, so far, been the most widely used. Such estimates are known to be valid for general, closed state constraint sets, provided the functions defining the dynamic constraint are Lipschitz continuous, with respect to the time and state variables. We ask whether linear, L∞ distance estimates remain valid when the Lipschitz continuity hypothesis governing t-dependence of the data is relaxed. We show by counter-example that these distance estimates are not valid in general if the hypothesis of Lipschitz continuity is replaced by continuity. We also provide a new hypothesis, ‘absolute continuity from the left’, for the validity of linear, L∞ estimates. The new hypothesis is less restrictive than Lipschitz continuity and even allows discontinuous time dependence in certain cases. It is satisfied, in particular, by differential inclusions exhibiting non-Lipschitz t-dependence at isolated points, governed, for example, by a fractional-power modulus of continuity. The relevance of distance estimates for state constrained differential inclusions permitting fractional-power time dependence is illustrated by an example in engineering design, where we encounter an isolated, square-root type singularity, concerning the t-dependence of the data.
Vinter RB, Bettiol P, 2011, Trajectories satisfying a state constraint: improved estimates and new non-degeneracy conditions, IEEE Transactions on Automatic Control, Vol: 56, Pages: 1090-1096
For a state-constrained control system described by a differential inclusion and a single functional inequality state constraint, it is known that, under an `inward pointing condition', the $W^{1,1}$ distance of an arbitrary state trajectory to the set of state trajectories, which have the same left endpoint and which satisfy the state constraint, is linearly related to the state constraint violation. In this paper we show that, in situations where the state-constrained control system is described instead by a controlled differential equation, this estimate can be improved by replacing the $W^{1,1}$ distance on state trajectories by the Ekeland metric of the distance of the control functions. A counter-example reveals that a refinement of this nature is not in general valid for state constrained differential inclusions. Finally we show how the refined estimates may be used to establish new conditions for non-degeneracy of the state constrained Maximum Principle, in circumstances when the data depends discontinuously on the control variable.
Clark JMC, Kountouriotis PA, Vinter RB, 2011, A Gaussian Mixture Filter for Range-Only Tracking, IEEE TRANSACTIONS ON AUTOMATIC CONTROL, Vol: 56, Pages: 602-613, ISSN: 0018-9286
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- Citations: 17
Gavriel C, Vinter R, 2011, Regularity of Minimizers for Second Order Variational Problems in One Independent Variable, Discrete and Continuous Dynamical Systems. Series A, Vol: 29
Vinter RB, 2011, Game theoretic controllers that confine a system to a safe region in the state space, Pages: 2570-2576, ISSN: 1474-6670
This paper addresses the problem of controlling a system, subject to disturbances, to prevent exit from a safe region of the state space. Problems of this nature are encountered in many different contexts, for example in the control of tanks to avoid overflow and of operation of telecommunications systems to avoid the failing of a communications link. The proposed control methodology is based on solving a differential game, in which a feedback control is found that minimizes the disturbance energy to force the state out of the safe region. Such controls also have interpretations in terms of stochastic exit-time problems. We announce a new class of exit problems, including problems with high state dimension, for which the related game can be simply computed. The proposed solution technique involves the on-line solution of N optimal control problems where, typically, N is small. Accordingly, the computational effort is several times larger, but still of the same order of magnitude, as that involved in implementing a standard non-linear model predictive controller. © 2011 IFAC.
Singh R, Pal BC, Jabr RA, et al., 2011, Meter Placement for Distribution System State Estimation: An Ordinal Optimization Approach, IEEE Transactions on Power Systems, Vol: 26, Pages: 2328-2335, ISSN: 0885-8950
This paper addresses the problem of meter placement for distribution system state estimation (DSSE). The approach taken is to seek a set of meter locations that minimizes the probability that the peak value of the relative errors in voltage magnitudes and angle estimates across the network exceeds a specified threshold. The proposed technique is based on ordinal optimization and employs exact calculations of the probabilities involved, rather than estimates of these probabilities as used in our earlier work. The use of ordinal optimization leads to a decrease in computational effort without compromising the quality of the solution. The benefits of the approach in terms of reduced estimation errors is illustrated by simulations involving a 95-bus UKGDS distribution network model.
Bettiol P, Bressan A, Vinter RB, 2011, ESTIMATES FOR TRAJECTORIES CONFINED TO A CONE IN R<i><SUP>n</SUP></i>, SIAM JOURNAL ON CONTROL AND OPTIMIZATION, Vol: 49, Pages: 21-41, ISSN: 0363-0129
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- Citations: 11
Ledyaev YS, Vinter RB, 2010, Discontinuous feedback in nonlinear control: Stabilization under persistent disturbances, PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, Vol: 268, Pages: 222-241, ISSN: 0081-5438
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- Citations: 2
Gavriel C, Vinter R, 2010, Second Order Sufficient Conditions for Optimal Control Problems with Non-unique Minimizers, American Control Conference, Publisher: IEEE, Pages: 756-761, ISSN: 0743-1619
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- Citations: 1
Bettiol P, Bressan A, Vinter R, 2010, ON TRAJECTORIES SATISFYING A STATE CONSTRAINT: W-1,W-1 ESTIMATES AND COUNTEREXAMPLES, Siam Journal on Control and Optimization, Vol: 48, Pages: 4664-4679
Bettiol P, Vinter RB, 2010, SENSITIVITY INTERPRETATIONS OF THE COSTATE VARIABLE FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS, SIAM JOURNAL ON CONTROL AND OPTIMIZATION, Vol: 48, Pages: 3297-3317, ISSN: 0363-0129
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- Citations: 24
Bettiol P, Vinter R, 2010, Existence of Feasible Approximating Trajectories Satisfying Multiple State Constraints, 49th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 3421-3426, ISSN: 0743-1546
JMC C, Kountouriotis PA, Vinter RB, 2009, A New Gaussian Mixture Algorithm for GMTI Tracking Under a Minimum Detectable Velocity Constraint, IEEE T AUTOMAT CONTR, Vol: 54, Pages: 2745-2756, ISSN: 0018-9286
This paper introduces a new methodology to account for Doppler blind zone constraints, arising, for example, in ground moving target indicator (GMTI) tracking applications. In such problems, target measurements are suppressed when the range rate (Doppler) of the target drops below a specified threshold in magnitude (the minimum detectable velocity). The proposed method, employing Gaussian mixture approximations to the filtering density, differs from earlier Gaussian mixture approaches in the way missed measurements are modelled. The distinctive feature of the algorithm, as compared with other Gaussian mixture filters, is that it is based on an exact calculation of the filtering density when a measurement is not recorded. Algorithms that result from applying this methodology are simple to implement and computationally undemanding. Simulation results indicate a uniform improvement in estimation accuracy over that of earlier proposed analytic techniques, and a tracking performance comparable to that of state-of-the-art particle filters.
Singh R, Pal BC, Vinter RB, 2009, Measurement Placement in Distribution System State Estimation, IEEE Transactions on Power Systems, Vol: 24, Pages: 668-675, ISSN: 0885-8950
This paper introduces a technique for meter placement for the purpose of improving the quality of voltage and angle estimates across a network. The proposed technique is based on the sequential improvement of a bivariate probability index governing relative errors in voltage and angle at each bus. The meter placement problem is simplified by transforming it into a probability bound reduction problem, with the help of the two sided-Chebyshev inequality. A straightforward solution technique is proposed for the latter problem, based on the consideration of 2-$sigma$ error ellipses. The benefits of the proposed technique are revealed by Monte Carlo simulations on a 95-bus UKGDS network model
Clarke FH, Vinter RB, 2009, Stability analysis of sliding-mode feedback control, Conference on 50 Years of Optimal Control, Publisher: POLISH ACAD SCIENCES SYSTEMS RESEARCH INST, Pages: 1169-1192, ISSN: 0324-8569
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- Citations: 14
Bettiol P, Vinter R, 2009, Existence of feasible approximating trajectories for differential inclusions with obstacles as state constraints, Joint 48th IEEE Conference on Decision and Control (CDC) / 28th Chinese Control Conference (CCC), Publisher: IEEE, Pages: 8624-8629, ISSN: 0743-1546
Clark JMC, Kountouriotis PA, Vinter RB, 2008, A new algorithm for GMTI tracking problems, subject to a doppler blind zone constraint, Pages: 49-58
This paper introduces a new methodology to take account of the Doppler blind zone arising, for example, in GMTI tracking. Here, the measurements are suppressed, when the range-rate of the target drops below a specified threshold. Algorithms based on the new methodology are easy to implement, robust to choice of initial distributions and computationally efficient. Simulations have been conducted for a number of scenarios featuring in earlier comparative exercises. The new techniques exhibit a uniform improvement in estimation accuracy, as compared with earlier proposed approximate analytic techniques. © The Institution of Engineering and Technology.
Clark JMC, Kountouriotis PA, Vinter RB, 2008, A methodology for incorporating the Doppler blind zone in target tracking algorithms
The problem of tracking targets, where measurements may occasionally be masked by the Doppler blind zone of the sensor, arises in Ground Moving Target Indicator tracking and aerial surveillance. For such problems, no target return is registered when the range rate (Doppler) of the target falls below a sensor-specific threshold in magnitude. For this reason, possible missed detections provide kinematic information about the target, and it is of interest how to incorporate this information in tracker design. In this paper, we introduce a new methodology for tracking under Doppler blind zone constraints, based on Gaussian mixture approximations to the conditional density. The filter equations are based on analytic calculations of the posterior density, while the Gaussian mixture approximation step is carried out over a scalar variable and involves exact moment matching. The presence of clutter and the employment of jump Markov models to describe target motion are naturally covered by the new paradigm. Simulation results indicate performance improvements over other analytic techniques and comparable accuracy of estimation with high-order particle filters.
Bettiol P, Vinter R, 2008, Sensitivity Relations for Optimal Control Problems with State Constraints, 47th IEEE Conference on Decision and Control, Publisher: IEEE, Pages: 2404-2407, ISSN: 0743-1546
Clarke FH, Vinter RB, 2008, STABILITY ANALYSIS OF SLIDING MODE CONTOLLERS, Conference on Geometric Control and Nonsmooth Analysis, Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD, Pages: 164-+, ISSN: 1793-0901
Gelenbe E, Tilbrook A, Vinter R, 2007, Editorial: Introduction to the special issue, COMPUTER JOURNAL, Vol: 50, Pages: 630-631, ISSN: 0010-4620
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