You, Yuncheng Synthesis of time-variant optimal control with nonquadratic criteria. (English) Zbl 0872.49015 J. Math. Anal. Appl. 209, No. 2, 662-682 (1997). Summary: Under the assumption of convexity of nonquadratic time-variant criteria for a linear time-variant control system, it is proved in this paper that the closed-loop synthesis of the optimal control is given by a nonlinear feedback \[ u(t)= -R^{-1}(t) B^*(t)P(t,x(t)), \] in which \(P(t,x)\) is the normal solution of a quasi-Riccati operator equation. It is also shown that the nonlinear feedback operator \(P(t,x)\) can be explicitly expressed by solutions of the associated nonlinear algebraic equation and nonlinear integral equations, respectively, in three cases corresponding to Mayer problems, Lagrange problems, and Bolza problems. Cited in 3 Documents MSC: 49N35 Optimal feedback synthesis Keywords:time-variant optimal control; closed-loop synthesis; Mayer problems; Lagrange problems; Bolza problems PDFBibTeX XMLCite \textit{Y. You}, J. Math. Anal. Appl. 209, No. 2, 662--682 (1997; Zbl 0872.49015) Full Text: DOI References: [1] Berkovitz, L. D., Optimal Control Theory (1971), Springer-Verlag: Springer-Verlag New York/Berlin · Zbl 0295.49001 [2] Berger, M. S., Nonlinearity and Functional Analysis (1977), Academic Press: Academic Press New York [3] Ekeland, I.; Temam, R., Convex Analysis and Variational Problems (1976), North-Holland: North-Holland Amsterdam [4] Lee, E. B.; Markus, L., Foundations of Optimal Control Theory (1967), Wiley: Wiley New York · Zbl 0159.13201 [5] You, Y., Nonquadratic optimal regulators and solutions of quasi-Riccati equations, Scientia Sinica Ser. A, 30, 249-261 (1987) [6] You, Y., A nonquadratic Bolza problem and a quasi-Riccati equation for distributed parameter systems, SIAM J. Control Optim., 25, 905-920 (1987) · Zbl 0632.49004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.