Optimal control for controllable stochastic linear systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 98

This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of stochastic linear systems is studied. Then the optimal control is explicitly obtained by considering a parameterized unconstrained backward LQ problem and an optimal parameter selection problem. A notable feature of our results is that, instead of solving an equation involving derivatives with respect to the parameter, the optimal parameter is characterized by a matrix equation.

DOI : 10.1051/cocv/2020027
Classification : 49N10, 93E20, 93E24, 93B05
Keywords: Linear-quadratic, optimal control, controllability, controllability Gramian, Lagrange multiplier, optimal parameter, Riccati equation 
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     author = {Bi, Xiuchun and Sun, Jingrui and Xiong, Jie},
     title = {Optimal control for controllable stochastic linear systems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     year = {2020},
     publisher = {EDP Sciences},
     volume = {26},
     doi = {10.1051/cocv/2020027},
     mrnumber = {4185058},
     zbl = {1459.49019},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/cocv/2020027/}
}
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Bi, Xiuchun; Sun, Jingrui; Xiong, Jie. Optimal control for controllable stochastic linear systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 98. doi: 10.1051/cocv/2020027

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