Inverse optimal adaptive control for non-linear uncertain systems with exogenous disturbances

A Lyapunov-based inverse optimal adaptive control-system design problem for non-linear uncertain systems with exogenous L-2 disturbances is considered . Specifically, an inverse optimal adaptive nonlinear control framework is developed to explicitly characterize globally stabilizing disturbance rejec tion adaptive controllers that minimize a nonlinear-nonquadratic performanc e functional for nonlinear cascade and block cascade systems with parametri c uncertainty. It is shown that the adaptive 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 s tability. Additionally, the adaptive Lyapunov function is dissipative with respect to a weighted input-output energy supply rate guaranteeing closed-l oop disturbance rejection. For special integrand structures of the performa nce functionals considered, the proposed adaptive controllers additionally guarantee robustness to multiplicative input uncertainty. In the case of li near-quadratic control it is shown that the operations of parameter estimat ion and controller design are coupled illustrating the breakdown of the cer tainty equivalence principle for the optimal adaptive control problem. Fina lly, the proposed framework is used to design adaptive controllers for jet engine compression systems with uncertain system dynamics. Copyright (C) 20 00 John Wiley & Sons, Ltd.