Accelerated model-reference adaptation via Lyapunov and steepest descent design techniques

A method for accelerating the convergence in model-reference adaptive control systems is presented. The novel feature is to feed back an appropriate function of the parameter misalignment signal to each adjusting mechanism channel. The adaptive loops incorporating feedback can be synthesized either directly from a Lyapunov function or indirectly from the minimization of a Lyapunov function along the steepest descent path. In both cases the derivative of the Lyapunov function is negative definite in error and parameter misalignment, whereas it is only semidefinite in previous work. The advantages are easy implementation and rapid convergence to zero of both the system-response error and the errors of the adjustable parameters. Simulation studies on a second-order system confirm the theoretical predictions.