Inverse optimal adaptive control for nonlinear uncertain systems with exogenous disturbances

A Lyapunov-based optimal adaptive control-system design problem for nonlinear uncertain systems with exogenous L₂ disturbances is considered. Specifically, an inverse optimal adaptive nonlinear control framework is developed to explicitly characterize globally stabilizing disturbance rejection adaptive controllers that minimize a nonlinear-nonquadratic performance functional for nonlinear systems with parametric uncertainty. It is shown that the adaptive control Lyapunov function guaranteeing closed-loop stability is a solution to the Hamilton-Jacobi-Isaacs equation for the controlled system and thus guarantees both optimality and robust stability. Additionally, the adaptive control Lyapunov function is dissipative with respect to a weighted input-output energy supply rate guaranteeing closed-loop disturbance rejection