Stability analysis of stochastic optimal control: the linear discounted quadratic case - Archive ouverte HAL
Article Dans Une Revue IEEE Transactions on Automatic Control Année : 2025

Stability analysis of stochastic optimal control: the linear discounted quadratic case

Mathieu Granzotto
Dragan Nešić
Andrew Teel

Résumé

We analyze the stability properties of stochastic linear systems in closed-loop with an optimal policy that minimizes a discounted quadratic cost in expectation. In particular, the linear system is perturbed by both additive and multiplicative stochastic disturbances. We provide conditions under which mean-square boundedness, mean-square stability and recurrence properties hold for the closed-loop system. We distinguish two cases, when these properties are verified for any value of the discount factor sufficiently close to 1, or when they hold for a fixed value of the discount factor in which case tighter conditions are derived as illustrated in an example. The analysis exploits properties of the optimal value function, as well as a detectability property of the system with respect to the stage cost, to construct a Lyapunov function for the stochastic linear quadratic regulator problem.
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Dates et versions

hal-04766631 , version 1 (05-11-2024)

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Mathieu Granzotto, Romain Postoyan, Dragan Nešić, Andrew Teel. Stability analysis of stochastic optimal control: the linear discounted quadratic case. IEEE Transactions on Automatic Control, In press, pp.Early Access. ⟨10.1109/TAC.2024.3490980⟩. ⟨hal-04766631⟩
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