Optimization of Linear Differential Systems by Lyapunov's Direct Method - Demchenko, H. (Vysoké učení technické v Brně, Fakulta elektrotechniky a komunikačních technologií, 2015)
Two approaches to solving optimization problems of dynamic systems are well-known. The first approach needs to find a fixed control (program control) for which the system described by differential equations reaches a predetermined value and minimizes an integral quality criterion. Proposed by L.S. Pontryagin, this method was in essence a further development of general optimization methods for dynamical systems. The second method consists in finding a control function (in the form of a feedback) guaranteeing that, simultaneously, the zero solution is asymptotically stable and an integral quality criterion attains a minimum value. This method is based on what is called the second Lyapunov method and its founder is N.N. Krasovskii. In the paper, the latter method is applied to linear differential equations and systems with integral quality criteria.
Keywords: Lyapunov function; optimization problem; integral quality criterion; control function