Optimal Control Problems for Lipschitz Dissipative Systems with Boundary-Noise and Boundary-Control
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 HamiltonJacobiBellman equation under the general cost functional and obtain the optimal control in the feedback law.
lipschitz dissipative systems m-dissipativity kolmogorov operator stationary hamiltonjacobibellman equation stochastic control