Minimax optimal control of stochastic uncertain systems with relative entropy constraints

Petersen, Ian R.; James, Matthew R.; Dupuis, Paul

doi:10.1109/cdc.1997.657107

Cited by 55 publications

(85 citation statements)

References 24 publications

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“…which defines a probability measure on the measurable space ðW; F T Þ: The class of input and disturbance processes considered in this paper comprises the processes w 11 ; v 11 that give rise to probability measures Q T whose relative entropy with respect to P T is finite [15,18] hðQ T jjP T Þ51 for all T51 ð4Þ…”

Section: Probabilistic Model Of An Uncertain Communication Channelmentioning

confidence: 99%

“…Indeed, from (17), inequality (15) follows. Furthermore, using the chain rule [20], the dependence structure of the probability measure Q T given by (9) and conditions (15), (14), we obtain…”

Section: Channels With a Gaussian Reference Modelmentioning

confidence: 99%

“…Definition 1 0 was originally introduced in Reference [18] as an extension of the corresponding definition given in Reference [15] to an infinite time interval case. A detailed discussion of Definition 1 0 in the context of ISI equalization has been given in Section 2.…”

Section: Problem Formulationmentioning

confidence: 99%

“…In this section we extend the minimax optimal control theory of References [15,18] to solve the minimax filtering problem (25) in a manner analogous to the solution to the continuous-time minimax filtering problem obtained in Reference [17]. The results presented in References [15,18] did not directly allow for error functionals of the form (24) due to the different form of the functional (24).…”

Section: Problem Formulationmentioning

confidence: 99%

“…The mathematical tractability of such a worst-case estimation problem depends to a great extent on how the uncertain perturbations, including parameter variations, are modelled and quantified. In this paper as well as in the earlier papers [14][15][16][17][18], we employ an uncertainty model which deals with probability distributions of input signals and disturbances rather than time-domain samples. In this model, the magnitude of the perturbations is quantified using the relative entropy between distributions of the non-Gaussian input signal and disturbances, and a reference probability measure corresponding to a 'nominal' Gaussian white noise input and a reference channel.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Robust ISI equalization for uncertain channels via minimax optimal filtering

Ugrinovskii

Petersen

2006

Int. J. Adapt. Control Signal Process.

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We consider a problem of equalization for intersymbol interference (ISI) occurring during data transmission through an imperfectly known channel. It is shown that this problem can be effectively addressed using the minimax filtering approach developed in the paper. This approach leads to a numerically tractable methodology for robust equalizer design which guarantees an optimal upper bound on the equalization error.

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Section: Probabilistic Model Of An Uncertain Communication Channelmentioning

confidence: 99%

Section: Channels With a Gaussian Reference Modelmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust ISI equalization for uncertain channels via minimax optimal filtering

Ugrinovskii

Petersen

2006

Int. J. Adapt. Control Signal Process.

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Robust tracking problem for continuous time stochastic uncertain systems

Yoon

Ugrinovskii

2008

Asian Journal of Control

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We propose a finite-horizon robust minimax tracking controller design method for time-varying continuous time stochastic uncertain systems. The uncertainty in the system is characterized by a set of probability measures under which stochastic noises, driving the system, are defined. A minimax optimal tracking controller is derived from the solution of a risk-sensitive linear quadratic Gaussian control problem. Also a numerical example is presented to illustrate the characteristics of proposed tracking controller.

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Risk-Sensitive, Minimax, and Mixed Risk-Neutral / Minimax Control of Markov Decision Processes

Coraluppi¹,

Marcus²

1999

Stochastic Analysis, Control, Optimization and Applications

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This paper analyzes a connection between risk-sensitive and minimax criteria for discrete-time, nite-state Markov Decision Processes MDPs. We synthesize optimal policies with respect to both criteria, both for nite horizon and discounted in nite horizon problems. A generalized decision-making framework is introduced, leading to stationary risk-sensitive and minimax optimal policies on the in nite horizon with discounted costs. We introduce the mixed risk-neutral minimax objective, and utilize results from risk-neutral and minimax control to derive an information state process and dynamic programming equations for the value function. We synthesize optimal control laws both on the nite and in nite horizon, and establish the e ectiveness of the controller as a tool to trade o risk-neutral and minimax objectives.

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Minimax optimal control of stochastic uncertain systems with relative entropy constraints

Cited by 55 publications

References 24 publications

Robust ISI equalization for uncertain channels via minimax optimal filtering

Robust ISI equalization for uncertain channels via minimax optimal filtering

Robust tracking problem for continuous time stochastic uncertain systems

Risk-Sensitive, Minimax, and Mixed Risk-Neutral / Minimax Control of Markov Decision Processes

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