Abstract.
We consider a linear-quadratic problem of minimax optimal control for stochastic uncertain control systems with output measurement. The uncertainty in the system satisfies a stochastic integral quadratic constraint. To convert the constrained optimization problem into an unconstrained one, a special S-procedure is applied. The resulting unconstrained game-type optimization problem is then converted into a risk-sensitive stochastic control problem with an exponential-of-integral cost functional. This is achieved via a certain duality relation between stochastic dynamic games and risk-sensitive stochastic control. The solution of the risk-sensitive stochastic control problem in terms of a pair of differential matrix Riccati equations is then used to establish a minimax optimal control law for the original uncertain system with uncertainty subject to the stochastic integral quadratic constraint.
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Date received: May 13, 1997. Date revised: March 18, 1998.
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Ugrinovskii, V., Petersen, I. Finite Horizon Minimax Optimal Control of Stochastic Partially Observed Time Varying Uncertain Systems. Math. Control Signals Systems 12, 1–23 (1999). https://doi.org/10.1007/PL00009843
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DOI: https://doi.org/10.1007/PL00009843