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The Stochastic Linear Quadratic Optimal Control Problem on Hilbert Spaces: The Case of Non-analytic Systems

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Abstract

We derive the algebraic Riccati equation associated with the infinite dimensional linear quadratic stochastic optimal control problem on an infinite horizon, for stochastic control systems with non-analytic dynamics. The linear system under consideration is modeled by a linear stochastic differential equation with noise in the control, and with a \(C_{0}\)-semigroup driving the deterministic component of the dynamics, and unbounded control action satisfying a singular estimate. We derive the feedback relation for the optimal control in terms of the optimal state via an operator solving an Algebraic Riccati equation. We show that the algebraic Riccati equation is well posed and has a unique solution in an appropriate class. These systems are typically coupled systems of stochastic partial differential equations comprising both parabolic and hyperbolic components with point or boundary control.

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  1. Department of Mathematics and Statistics, American University of Sharjah, Sharjah, UAE

    Amjad Tuffaha

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Tuffaha, A. The Stochastic Linear Quadratic Optimal Control Problem on Hilbert Spaces: The Case of Non-analytic Systems. Appl Math Optim 87, 58 (2023). https://doi.org/10.1007/s00245-023-09969-1

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