| Abstract: | A Lyapunov‐based inverse optimal adaptive control‐system design problem for non‐linear uncertain systems with exogenous ℒ︁2 disturbances is considered. Specifically, an inverse optimal adaptive non‐linear control framework is developed to explicitly characterize globally stabilizing disturbance rejection adaptive controllers that minimize a nonlinear‐nonquadratic performance functional for non‐linear cascade and block cascade systems with parametric 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 stability. Additionally, the adaptive Lyapunov function is dissipative with respect to a weighted input–output energy supply rate guaranteeing closed‐loop disturbance rejection. For special integrand structures of the performance functionals considered, the proposed adaptive controllers additionally guarantee robustness to multiplicative input uncertainty. In the case of linear‐quadratic control it is shown that the operations of parameter estimation and controller design are coupled illustrating the breakdown of the certainty equivalence principle for the optimal adaptive control problem. Finally, the proposed framework is used to design adaptive controllers for jet engine compression systems with uncertain system dynamics. Copyright © 2000 John Wiley & Sons, Ltd. |
