Energy saving optimal multifunctional regulator (Q2780444)

One considers the control system NEWLINE\[NEWLINE\dot{x}=Ax(t)+Bu(t),\;t \in [t_{0}, t_{K}],\qquad \forall t \in [t_{0}, t_{K}]:u(t) \in [u_{H}, u_{B}],NEWLINE\]NEWLINE where \(x : \mathbb{R} \rightarrow \mathbb{R}^{n}\) is the state vector of the system, \(x(t_{0})=x^{0}, x(t_{K})=x^{K}\) are the starting state and target state respectively, and \(J=\int_{t_{0}}^{t_{K}}u^{2}(t) dt\) is a quality functional. The aim of this paper is to create the controller that minimizes the quality functional \(J\). An optimal control problem is considered that is solved using the maximum principle. The work may be understood as a small supplement to classical monographs on optimal control, such as those by \textit{M. Athans} and \textit{P. L. Falb} [Optimal control (McGraw-Hill, Berkshire) (1966; Zbl 0196.46303)] or \textit{G. Leitman} [An introduction of optimal control (Russian) (Nauka, Moskva) (1968; Zbl 0167.39003)].