Controllable Stability and Equivalent Nonlinear Programming Problem

Abstract

Publisher Summary This chapter presents controllable stability and equivalent nonlinear programming problem for a system, where the ui are control variables that should be adjusted within specified limits The quantities ui are adjusted as functions of time to achieve the desired controlled response. The assumptions concerning the fi stated are sufficient to insure that there is a unique continuous solution x(t) to this control problem. The mathematical programming problem pertinent to controllable stability is, therefore, a max min problem. The chapter extends the concept of a ϕ-stable system to the control problem by defining a controllable ϕ-stable system in different ways. One can answer the question as to whether a particular system is p-stable by solving a single nonlinear mathematical programming problem