Abstract
Yong J [Acta Math. Appl. Sin. Engl. Ser. 28 (2012), 1–30] [Math. Control Relat. Fields 1 (2011), 83–118] studied a standard linear quadratic time-inconsistent optimal control problem via a cooperative and non-cooperative approach, respectively. The authors extend his results to a singular case. To handle the singularity, the authors prove the solvability of a generalized Riccati equation, and introduce a notion of \(\mathbb{M}\mathbb{P}\) of matrix. It is shown that the authors can obtain a family of parameter equilibrium controls in both cases. Another interesting outcome is that a new type of parameter forward-backward Volterra integral equations is derived.
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This research was supported by the Natural Science Foundation of China under Grant No. 11971334.
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Ma, B. A Singular Linear Quadratic Time-Inconsistent Optimal Control Problem. J Syst Sci Complex 36, 1024–1052 (2023). https://doi.org/10.1007/s11424-023-1173-5
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DOI: https://doi.org/10.1007/s11424-023-1173-5