Risk-sensitive control and dynamic games for partially observed discrete-time nonlinear systems

James, M. R.; Baras, John S.; Elliott, Robert J.

doi:10.1109/9.286253

Cited by 255 publications

(184 citation statements)

References 22 publications

(18 reference statements)

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“…uEUk.k A key observation for one of the results to follow is that the above results of [12] can be generalized for coping with the more general cost indices (10) simply by replacing exp(-) in the above equations (1 2)-(17) by f(. ).…”

Section: S(qk)= Inf E[s(s(u Yk+l)qk + L)]mentioning

confidence: 99%

“…As shown in [12], minimization of the risk sensitive control index is equivalent to the following (19) (2), and with the cost term (7) under (18).…”

Section: Dynamic Programmingmentioning

confidence: 99%

“…In risk sensitive optimal control theory as in [12], small noise limits of the controllers achieve optimal deterministic nonlinear control in the presence of 'worst case' deterministic noise. These can be viewed as nonlinear H~ controllers.…”

Section: <~ Small Noise Limitsmentioning

confidence: 99%

“…J.S. Baras/Systems & Control Letters 26 (1995) [223][224][225][226][227][228][229][230] A follow on result in [12] develops risk sensitive generalizations of the earlier risk neutral theory so as to tune robustness with a so-called risk sensitive parameter, and moreover in this setting, achieves limiting results as the noise variances become zero which give optimal nonlinear feedback controllers for deterministic nonlinear plants. The small noise limit optimizing algorithms are differential games which allow tuning for robustness, and indeed can be interpreted as optimal in a worst case deterministic noise setting.…”

Section: Introductionmentioning

confidence: 99%

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Finite-dimensional optimal controllers for nonlinear plants

Moore

Baras

1995

Systems & Control Letters

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Optimal risk sensitive feedback controllers are now available for very general stochastic nonlinear plants and performance indices. They consist of nonlinear static feedback of so called information states from an information state filter. In general, these filters are linear, but infinite dimensional, and the information state feedback gains are derived from (doubly) infinite dimensional dynamic programming. The challenge is to achieve optimal finite dimensional controllers using finite dimensional calculations for practical implementation.This paper derives risk sensitive optimality results for finite-dimensional controllers. The controllers can be conveniently derived for 'linearized' (approximate) models (applied to nonlinear stochastic systems). Performance indices for which the controllers are optimal for the nonlinear plants are revealed. That is, inverse risk-sensitive optimal control results for nonlinear stochastic systems with finite dimensional linear controllers are generated. It is instructive to see from these results that as the nonlinear plants approach linearity, the risk sensitive finite dimensional controllers designed using linearized plant models and risk sensitive indices with quadratic cost kernels, are optimal for a risk sensitive cost index which approaches one with a quadratic cost kernel. Also even far from plant linearity, as the linearized model noise variance becomes suitably large, the index optimized is dominated by terms which can have an interesting and practical interpretation.Limiting versions of the results as the noise variances approach zero apply in a purely deterministic nonlinear Ho~ setting. Risk neutral and continuous-time results are summarized.More general indices than risk sensitive indices are introduced with the view to giving useful inverse optimal control results in non-Gaussian noise environments.

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Section: S(qk)= Inf E[s(s(u Yk+l)qk + L)]mentioning

confidence: 99%

“…As shown in [12], minimization of the risk sensitive control index is equivalent to the following (19) (2), and with the cost term (7) under (18).…”

Section: Dynamic Programmingmentioning

confidence: 99%

Section: <~ Small Noise Limitsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite-dimensional optimal controllers for nonlinear plants

Moore

Baras

1995

Systems & Control Letters

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“…It easily follows from (17) and (24) that satisfies the following difference equation: (25) where the operators and are given by (26) The filter can now be obtained immediately from . We, however, will always use the unnormalized version of the filter given in (25).…”

Section: Quantum Filteringmentioning

confidence: 99%

Quantum Risk-Sensitive Estimation and Robustness

Yamamoto

Bouten

2009

IEEE Trans. Automat. Contr.

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Abstract-This paper studies a quantum risk-sensitive estimation problem and investigates robustness properties of the filter. This is a direct extension to the quantum case of analogous classical results. All investigations are based on a discrete approximation model of the quantum system under consideration. This allows us to study the problem in a simple mathematical setting. We close the paper with some examples that demonstrate the robustness of the risk-sensitive estimator.Index Terms-Quantum filtering, quantum probability, quantum systems, risk-sensitive estimation, robustness.

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Nonlinear Discrete-Time Risk-Sensitive Optimal Control

Campi

James

1996

Int. J. Robust Nonlinear Control

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Risk-sensitive control and dynamic games for partially observed discrete-time nonlinear systems

Cited by 255 publications

References 22 publications

Finite-dimensional optimal controllers for nonlinear plants

Finite-dimensional optimal controllers for nonlinear plants

Quantum Risk-Sensitive Estimation and Robustness

Nonlinear Discrete-Time Risk-Sensitive Optimal Control

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