Solutions to Constrained Optimal Control Problems with Linear Systems
- 210 Downloads
This paper is devoted to present solutions to constrained finite-horizon optimal control problems with linear systems, and the cost functional of the problem is in a general form. According to the Pontryagin’s maximum principle, the extremal control of such problem is a function of the costate trajectory, but an implicit function. We here develop the canonical backward differential flows method and then give the extremal control explicitly with the costate trajectory by canonical backward differential flows. Moreover, there exists an optimal control if and only if there exists a unique extremal control. We give the proof of the existence of the optimal solution for this optimal control problem with Green functions.
KeywordsOptimal control problems The Pontryagin’s maximum principle Canonical backward differential flows Linear systems
Mathematics Subject Classification49J15
- 2.Hirsch, M.J., Commander, C.W., Pardalos, P.M., Murphey, R. (ed.): Optimization and Cooperative Control Strategies: Proceedings of the 8th International Conference on Cooperative Control and Optimization. Springer, New York (2009)Google Scholar
- 11.Ge, W., Li, C., Wang, H.: Ordinary Differential Equations and Boundary Valued Problems. Science Press, Beijing (2008)Google Scholar
- 12.Pontryagin, L.S.: Mathematical Theory of Optimal Processes. CRC Press, Boca Raton (1987)Google Scholar