Optimal Recursive Backstepping for Nonlinear Systems in a Strict-Feedback Form with Continuous and Intermittent Updates

This paper develops a novel optimal recursive backstepping design for the optimal regulation of a class of nonlinear systems in a strict-feedback form. In contrast to classical backstepping design, the presented recursive design takes the optimality of the solution into account. It is shown that the optimal recursive design results in the asymptotic stability of the equilibrium point for the isolated systems and ultimate boundedness for the cascade systems. In addition to the optimal recursive backstepping control design with continuous feedback, the optimal intermittent feedback design is also considered.