On the linear quadratic dynamic optimization problems with fixed-levels control functions. (English) Zbl 1382.49025
Summary: This paper deals with a constrained Linear Quadratic-type (LQ) Optimal Control Problem (OCP) in the presence of fixed levels input restrictions. We consider control processes governed by linear differential equations with a-priori known control switching structure. The set of admissible inputs reflects some important natural engineering applications and moreover, can also be interpreted as a result of a quantization procedure applied to the original dynamic system. We propose a novel implementable algorithm that makes it possible to calculate a (numerically consistent) approximative solution to the constrained LQ-type OCPs under consideration. Our contribution mainly discusses theoretic aspects of the proposed solution scheme and contains an illustrative numerical example.
MSC:
49N10 | Linear-quadratic optimal control problems |
49K20 | Optimality conditions for problems involving partial differential equations |
49M25 | Discrete approximations in optimal control |