Optimum stabilization of control systems under constraints on the output variable
type: Item
instance of: scholarly article
title: Optimum stabilization of control systems under constraints on the output variable
zbMATH Open document ID: 0838.49003
author: V. A. Yakubovich
author: E. D. Yakubovich
published in: Automation and Remote Control
publication date: 1995-02-20T00:00:00Z
review text: The authors consider the following linear-quadratic optimal control problem: \[ {{dx} \over {dt}}= Ax+ bu, \quad x(0)= a\quad (0\leq t<\infty), \qquad |x(\cdot)|\in L_2 (0, \infty), \quad |u(\cdot)|\in L_2 (0, \infty), \] \[ \alpha_j\leq y(t_j)\leq \beta_j, \quad j=1, \dots, k, \qquad \text{where } y(t)= c^* x(t), \tag{1} \] \[ I=\int^\infty_0 Q(x(t) u(t))dt\to \min. \] Here \(A\), \(b\), \(c\) are constant real matrices (resp. vectors) with \(c\neq 0\), and \(Q\) is a quadratic form. Using known results on the corresponding problem without the constraints (1), the authors establish a sufficient condition for the existence of optimal control to the above problem. An algorithm for calculating optimal controls is also discussed.
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 49N10
zbMATH DE Number: 710802
zbMATH Keywords: algorithm for optimal controls
zbMATH Keywords: linear-quadratic optimal control problem
zbMATH Keywords: existence
reviewed by: Winfried Schirotzek
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 710802