Indirect adaptive control of nonlinearly parameterized nonlinear dissipative systems

In this note we address the problem of indirect adaptive (regulation or tracking) control nonlinear, input affine dissipative systems. It is assumed that supply rate, storage and internal dissipation functions may be expressed as nonlinearly parameterized regression equations where mappings (depending on unknown parameters) satisfy a monotonicity condition—this encompasses large class physical systems, including passive We propose to estimate system parameters using “power-balance” equation, which differential version classical inequality, with new estimator ensures global, exponential, parameter convergence under very weak assumption interval excitation power-balance equation regressor. To design controller make standard existence an asymptotically stabilizing depends—possibly nonlinearly—on plant parameters, apply certainty-equivalent law. The benefits proposed approach, respect other existing solutions, are illustrated examples.