A class of nonlinear time-delay systems and related optimal problems

The method of synthesis for a class of time-delay nonlinear systems affine in control is considered. The proposed approach is based on the solution of a special optimal control problem. The integrand of the optimized functional is chosen in such a way that the Bellman equation has a desired solution. The nonlinear system design is reduced to the examination of the integrand of the optimized functional. To extend the domain of asymptotic stability of the nonlinear system, a sequence of the Lyapunov-Krasovskii functionals is used. The whole system becomes the system with variable structure. The proposed approach gives a systematic framework for an “almost sliding mode control”.