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.