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DOI: 10.23952/cot.2024.36
Received September 25, 2023; Accepted January 3, 2024; Published online June 24, 2024
Abstract. A finite horizon multi-model stochastic linear-quadratic optimal control problem is considered. For this problem, we treat the case where the problem’s functional does not contain a control function. This means that the problem under consideration is a singular optimal control problem. The solution to this problem is defined. To solve the considered problem, it is associated with a new optimal control problem for the same multi-model system. The functional in the new problem is the sum of the original functional and an integral of the square of the Euclidean norm of the vector-valued control with a small positive weighting coefficient. Thus, the new problem is regular. Moreover, it is a multi-model stochastic cheap control problem. Using the solvability conditions, the solution of this cheap control problem is reduced to solution of the following two problems: (i) a terminal-value problem for an extended matrix Riccati type differential equation; (ii) a nonlinear optimization (mathematical programming) problem. Asymptotic behaviour of solutions to these problems is analyzed. Using this asymptotic analysis, the optimal value of the functional of the original multi-model stochastic singular optimal control problem is obtained and the solution to this problem is derived. An illustrative academic example is presented.
How to Cite this Article:
V. Y. Glizer, Robust solution of multi-model stochastic singular linear-quadratic optimal control problem: Regularization approach, Commun. Optim. Theory 2024 (2024) 35.