A constrained closed-loop optimal control problem is considered in a linear-quadratic framework. To solve the problem, a special type open-loop optimal control problem and a standard open-loop optimal control problem are introduced and carefully studied, via which the existence and uniqueness of the globally optimal closed-loop control is established by a synthesis method.
B. D. O. Anderson and J. B. Moore, Linear Optimal Control, Prentice-Hall, New Jersey, 1971.
View at: Zentralblatt MATH | MathSciNetL. D. Berkovitz, Convexity and Optimization in , Pure and Applied Mathematics (New York), John Wiley & Sons, New York, 2002.
View at: Zentralblatt MATH | MathSciNetP. Brunovský, “Regular synthesis for the linear-quadratic optimal control problem with linear control constraints,” Journal of Differential Equations, vol. 38, no. 3, pp. 344–360, 1980.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. Casti, “The linear-quadratic control problem: some recent results and outstanding problems,” SIAM Review, vol. 22, no. 4, pp. 459–485, 1980.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetL. Cesari, “Existence of solutions and existence of optimal solutions,” in Mathematical Theories of Optimization (Genova, 1981), vol. 979 of Lecture Notes in Math., pp. 88–107, Springer, Berlin, 1983.
View at: Google Scholar | Zentralblatt MATH | MathSciNetG. R. Chen, “Closed-form solutions of a general inequality-constrained LQ optimal control problem,” Applicable Analysis, vol. 41, no. 1–4, pp. 257–279, 1991.
View at: Google Scholar | Zentralblatt MATH | MathSciNetY. Z. Chen, “Linear quadratic problems for time-varying systems: the cases without constraints and with the control energy constraint,” Control Theory & Applications, vol. 16, no. 4, pp. 474–477, 1999.
View at: Google Scholar | Zentralblatt MATH | MathSciNetZ. Emirsajłow, “Linear-quadratic control problem with terminal state constraints,” Systems Analysis Modelling Simulation, vol. 4, no. 3, pp. 227–240, 1987.
View at: Google Scholar | Zentralblatt MATH | MathSciNetZ. Emirsajłow, “A unified approach to optimal feedback in the infinite-dimensional linear-quadratic control problem with an inequality constraint on the trajectory or terminal state,” IMA Journal of Mathematical Control and Information, vol. 8, no. 2, pp. 179–208, 1991.
View at: Google Scholar | Zentralblatt MATH | MathSciNetH. Jaddu, “Spectral method for constrained linear-quadratic optimal control,” Mathematics and Computers in Simulation, vol. 58, no. 2, pp. 159–169, 2002.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetR. Kalman, “When is a linear control law optimal?” Transactions of the ASME Journal of Basic Engineering, vol. 86D, pp. 51–60, 1964.
View at: Google ScholarY. Liu, S. Ito, H. W. J. Lee, and K. L. Teo, “Semi-infinite programming approach to continuously-constrained linear-quadratic optimal control problems,” Journal of Optimization Theory and Applications, vol. 108, no. 3, pp. 617–632, 2001.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetD. H. Martin and D. H. Jacobson, “Optimal control laws for a class of constrained linear-quadratic problems,” Automatica, vol. 15, no. 4, pp. 431–440, 1979.
View at: Publisher Site | Google ScholarA. Matveev and V. Yakubovich, “Nonconvex problems of global optimization: linear-quadratic control problems with quadratic constraints,” Dynamics and Control, vol. 7, no. 2, pp. 99–134, 1997.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetF. W. Sears, An Introduction to Thermodynamic: The Kinetic Theory of ASES, and Statistical Mechanics, Addison-Wesley, Massachusetts, 1956.
G. Stefani and P. Zezza, “Constrained regular LQ-control problems,” SIAM Journal on Control and Optimization, vol. 35, no. 3, pp. 876–900, 1997.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetD. D. Thompson and R. A. Volz, “The linear quadratic cost problem with linear state constraints and the nonsymmetric Riccati equation,” SIAM Journal on Control and Optimization, vol. 13, no. 1, pp. 110–145, 1975.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetY. Xu, “A linear quadratic control problem with constrained state feedback matrix,” submitted to Journal of Optimization Theory and Applications.
View at: Google ScholarJ. Yong and X. Y. Zhou, Stochastic Controls. Hamiltonian Systems and HJB Equations, vol. 43 of Applications of Mathematics (New York), Springer, New York, 1999.
View at: Zentralblatt MATH | MathSciNet