Lyapunov Redesign of Model Reference Adaptive Control Systems (Part I)

Abstract

A new approach for geaeraticn of Lyapunov function, due to Nagaraja aid Chalam (1974) has been applied to the redesign of first-order and second-order model-reference adaptive control systems considered earlier by Parks (1966) and Phillipson (1967). They chose the V function rather arbitrarily, whereas a systematic method is presented here for choosing an appropriate V function. In the present work, V includes all state variables, whereas in the previous work of Parks (1966), V included only error e for first-order system and e for second-order system. Inclusion of all state variables in V ensures that if the gain-parameter misalignment tends to zero, the error will also tend to zero. The same approach was applied to modified first-order and second-order systems (Phillipson 1967).