Global null controllability of nonlinear delay equations with controls in a compact set
The question of controlling some nonlinear retarded functional differential equations from an initial function to the zero function is considered. The control sets M(\(\Omega)\) are square integrable functions with values in the unit closed sphere \(L_ 2([t_ 0,\infty),E^ m)\) with center the origin. Assuming that the linear approximation of the nonlinear equation is null controllable with some integrable controls on some interval \([t_ 0,t_ 1-2r]\), where \(t_ 0\) is sufficiently large and where \(r>0\) is the delay, and assuming that the nonlinear system, with \(u=0\), is uniformly globally asymptotically stable, we show that the nonlinear control process is globally null controllable with controls \(u\in M(\Omega)\). The paper gives conditions which guarantee the stability assumptions, and also indicates conditions which yield the null controllability assumptions of the linear approximation. Our research extends known results on ordinary differential processes.
nonlinear retarded functional differential equations
scientific article; zbMATH DE number 3956897
scientific article