Despite the recent advances in the area of adaptive control, most of today's adaptive control schemes often exhibit poor transient and steady-state performance. Phenomena such as bursting, chaos and large transient oscillations are often observed in simulations of stable adaptive schemes. The proposed research aims to eliminate these undesirable phenomena by studying new design approaches and introducing the appropriate mathematical tools that can be used to quantify and analyze transient and steady state performance in addition to stability and robustness. The design approaches proposed are based on the augmentation of the certainty equivalence control laws that are used in almost every adaptive control scheme, by using performance considerations in addition to stability and robustness. Such augmentation includes discontinuous control laws as well as smooth ones. The research goal is to develop a procedure for designing and analyzing adaptive control schemes that can meet prespecified performance and robustness requirements.
