Summary: The purpose of this paper is to solve the problem of controlling a fixed nonlinear plant in order to have its output track (or reject) a family of reference (or disturbance) signals produced by some external generator. It is shown that, under standard assumptions, this problem is solvable if and only if a certain nonlinear partial differential equation is solvable. Once a solution of this equation is available, a feedback law which solves the problem can easily be constructed. The theory developed in the paper incorporates earlier results established for linear systems [see, e.g., B. A. Francis, SIAM J. Control Optimization 15, 486-505 (1977); M. Hautus, “Linear matrix equations with applications to the regulator problem”, in: I. D. Landau (ed.), Outils et modèles mathematique pour l’automatique, pp. 399-412, C.N.R.S. (Paris 1982)].
|93C10||Nonlinear control systems|
|93C15||Control systems governed by ODE|
|93C35||Multivariable systems, multidimensional control systems|