Sufficient optimality condition for linear control of plants described by differential equations with a measure
type: Item
instance of: scholarly article
title: Sufficient optimality condition for linear control of plants described by differential equations with a measure
zbMATH Open document ID: 0564.49009
author: J. Blot
published in: Automation and Remote Control
publication date: 1984-01-01T00:00:00Z
review text: This paper considers sampled-data control of plants whose dynamics can be described by differential equations with a measure as follows: \[ dx(t)=A(t)x(t)dt+B(t)du(t),\quad x(0-)=x_ 0, \] where \(x(t)\in R^ n\), \(A(.)\in L^ 2(0,T;R^ n\times R^ n),\) \(B(.)\in C([0,T];R^ n\times R^ m)\) and \(u(t)\in R^ m\) satisfies \(v(t)=_{[0,T]}u(s)<+\infty\) and \(u(t+)=u(t)\). The set of allowed controls \[ \Omega =\{u:_{[0,T]}u(s)<+\infty,\quad u(t)-u(s-)\in K,\quad t\geq s\}, \] where K is a convex cone in \(R^ n\) and the cost functional is \(J[x(.),u(.)]=\phi_ 0(x(T),x(0-),v(T))\) where \(\phi_ 0\) is convex in all the variables. In addition, there are boundary conditions \(S_ k(x(T),x(0-),v(T))\leq 0,\) \((k=1,...,l)\), where the \(S_ k's\) are also convex in all the variables. A necessary optimality condition of maximum principle type is obtained, and under moderate constraints it is also a sufficient condition. Results can be applied to the problem of control of discrete observations that arises when dynamic systems must be controlled that operate under disturbances and with incomplete information about the system state.
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93C57
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 49K45
zbMATH DE Number: 3899633
zbMATH Keywords: sampled-data control
zbMATH Keywords: differential equations with a measure
zbMATH Keywords: maximum principle
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3899633