10 results found
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.
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.
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.
Clark JMC, Robbiati SA, Vinter RB, 2006, The Shifted Rayleigh Mixture Filter for Bearings-only Tracking of Manoeuvering Targets, IEEE Trans Signal Processing, Vol: 55, Pages: 3218-3226, ISSN: 1053-587X
This paper introduces the shifted Rayleigh mixture filter (SRMF), which is based on jump Markov linear systems. The formulation permits the presence of clutter. For bearings-only tracking problems involving maneuvering targets, the conditional density of the target state given the available measurements evolves as a growing mixture of probability density functions associated with a history of manoeuvre "modes." Similar to other "mixture" algorithms, the SRMF approximates this conditional density by a Gaussian mixture of fixed order. Unlike the extended or unscented Kalman filters,, the shifted Rayleigh filter incorporates an exact calculation of the posterior density, when the prior is assumed to be Gaussian, given the latest bearings measurement. Computer simulations are provided to demonstrate the performance of the algorithm.
Clark JMC, Crisan D, 2005, On a robust version of the integral representation formula of nonlinear filtering, Probability and Related Fields, Vol: 133, Pages: 43-56
Vellekoop MH, Clark JMC, 2003, A Nonlinear Filtering Approach To Changepoint Detection Problems: Direct And Differential-Geometric Methods, SIAM Journal on Control and Optimization, Vol: 42, Pages: 469-494
Vellekoop MH, Clark JMC, 2001, Optimal speed of detection in generalized Wiener disorder problems, Stochastic Processes and their Applications, Vol: 95, Pages: 25-54
Meister B, Clark JMC, Shah N, 1996, Optimisation of oilfield exploitation under uncertainty, European Symposium on Computer Aided Process Engineering - 6 (ESCAPE-6), Publisher: PERGAMON-ELSEVIER SCIENCE LTD, Pages: S1251-S1256, ISSN: 0098-1354
DAVIS MHA, CLARK JMC, 1994, A NOTE ON SUPER-REPLICATING STRATEGIES, PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 347, Pages: 485-494, ISSN: 1364-503X
MAYNE DQ, ASTROM KJ, CLARK JMC, 1984, A NEW ALGORITHM FOR RECURSIVE ESTIMATION OF PARAMETERS IN CONTROLLED ARMA PROCESSES, AUTOMATICA, Vol: 20, Pages: 751-760, ISSN: 0005-1098
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