Global asymptotic stabilization of second-order nonlinear systems by inverse optimal control

This paper presents a procedure for the control Lyapunov function (CLF) based determination of inverse optimal control (IOC) feedback. Firstly, the dynamic system equations are represented in state-dependent coefficient (SDC) form, commonly used in extended linearization approaches like state-dependent Riccati equation (SDRE). Based on this SDC matrix representation, the necessary and then the sufficient conditions for closed-loop stability are proposed. Finally, IOC feedback is so designed such as to satisfy these conditions and accordingly ensure global asymptotic stability (g.a.s). The proposed conditions for g.a.s has the merit of having high flexibility of design in addition to its applicability to a broad category of systems. Numerical examples validate the applicability, simplicity, and performance of the methodology.