Nonlinear control and state space adjustments

Abstract

In the literature some techniques traditionally used in the study of the existence of solutions of nonlinear differential equations have been extended to solve problems of control, state estimation and parameter identification of nonlinear systems. These techniques often require some topological adjustments of either the space of admissible input functions U (the control space) or the state space X of the system. These topological adjustments became possible with the use of matched sets introduced by the author (1983). The present work places its emphasis on how the matched sets can be used to adjust the spaces U and X for the problem of nonlinear control considered. A summary of the theory of complete matched sets is also shown. Moreover. The semigroup approach is used so that distributed parameter systems, delay systems and lumped parameter systems can be considered.