Displaying similar documents to “Approximation, estimation and control of stochastic systems under a randomized discounted cost criterion”

Approximation and estimation in Markov control processes under a discounted criterion

J. Adolfo Minjárez-Sosa (2004)

Kybernetika

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We consider a class of discrete-time Markov control processes with Borel state and action spaces, and ℜ k -valued i.i.d. disturbances with unknown density ρ . Supposing possibly unbounded costs, we combine suitable density estimation methods of ρ with approximation procedures of the optimal cost function, to show the existence of a sequence { f ^ t } of minimizers converging to an optimal stationary policy f ∞ .

Adaptive control for discrete-time Markov processes with unbounded costs: Discounted criterion

Evgueni I. Gordienko, J. Adolfo Minjárez-Sosa (1998)

Kybernetika

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We study the adaptive control problem for discrete-time Markov control processes with Borel state and action spaces and possibly unbounded one-stage costs. The processes are given by recurrent equations x t + 1 = F ( x t , a t , ξ t ) , t = 0 , 1 , ... with i.i.d. ℜ k -valued random vectors ξ t whose density ρ is unknown. Assuming observability of ξ t we propose the procedure of statistical estimation of ρ that allows us to prove discounted asymptotic optimality of two types of adaptive policies used early for the processes with bounded...

Optimal control of a rotating body beam

Weijiu Liu (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we consider the problem of optimal control of the model for a rotating body beam, which describes the dynamics of motion of a beam attached perpendicularly to the center of a rigid cylinder and rotating with the cylinder. The control is applied on the cylinder via a torque to suppress the vibrations of the beam. We prove that there exists at least one optimal control and derive a necessary condition for the control. Furthermore, on the basis of iteration method, we propose...

Double-stepped adaptive control for hybrid systems with unknown Markov jumps and stochastic noises

Shuping Tan, Ji-Feng Zhang (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper is concerned with the sampled-data based adaptive linear quadratic (LQ) control of hybrid systems with both unmeasurable Markov jump processes and stochastic noises. By the least matching error estimation algorithm, parameter estimates are presented. By a double-step (DS) sampling approach and the certainty equivalence principle, a sampled-data based adaptive LQ control is designed. The DS-approach is characterized by a comparatively large estimation step for parameter estimation...