I&I Adaptive Control for Systems with Varying Parameters

This paper combines the so-called congelation of variables method with adaptive immersion and invariance (I&I) to adaptively control systems with varying parameters. A dynamic scaling estimator without overparameterization is proposed. This does not require solving partial differential equations and removes other restrictive assumptions in the classical I&I estimator design. A controller that guarantees input-to-state stability of the closed-loop system is then used. The joint estimator-controller design guarantees global stability of the adaptive closed-loop system, convergence of the plant state and global boundedness of the estimator state. A design example for the position/force control of a series elastic actuator is discussed. This exploits the idea that bounded nonlinearities in the system dynamics can be viewed as time-varying parameters. Simulation results show a well-damped transient response and illustrate the theoretical results.