Optimal Control Problems for Lipschitz Dissipative Systems with Boundary-Noise and Boundary-Control

Desheng Yang ()
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Desheng Yang: Central South University

Journal of Optimization Theory and Applications, 2015, vol. 165, issue 1, No 2, 14-29

Abstract: Abstract This paper studies the infinite-horizon optimal control problems for Lipschitz dissipative systems with boundary-control and boundary-noise of Neumann type. By introducing Sobolev spaces based on the invariant measure and using the m-dissipativity of the Kolmogorov operator, corresponding to the uncontrolled system, we prove the existence of a unique mild solution of the associated stationary Hamilton–Jacobi–Bellman equation under the general cost functional and obtain the optimal control in the feedback law.

Keywords: Lipschitz dissipative systems; Stationary Hamilton–Jacobi–Bellman equation; Kolmogorov operator; m-dissipativity; Stochastic control (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10957-014-0612-9

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