Novel Robust Adaptive Algorithms for Estimation and Control: Theory and Practical Examples

This chapter introduces a new robust adaptive parameter estimation algorithm with the aim to further address convergence and robustness issues encountered in classical gradient descent and least-squares methods. We first review these classical methods for parameter estimation and discuss our motivations. Then the principle of our new algorithm is presented, which is designed on the basis of the parameter estimation error. This can be derived and extracted by application of stable filter operations to the available system dynamics and the subsequent introduction of several auxiliary variables. With this estimation error, several adaptive laws are investigated and their convergence properties are proven. An online verification of the persistent excitation condition is also developed. This algorithm can be easily incorporated into an adaptive controller or observer to provide superior results in terms of parameter estimation and control performance. In the second part of this chapter, we present the application of this estimation algorithm for vehicle parameter estimation (incorporated into an adaptive observer scheme), adaptive control for a robotic arm, and adaptive optimal control (incorporated into an adaptive control scheme). Simulations and practical experiments are also included to exemplify the theoretical claims.