A novel functional regression based estimation and control algorithm

In this paper, a δ novel strategy for a class of system identification problems is proposed. Similar to adaptive learning methods, the new algorithm is also built on a linearly parameterized model where system output is expressed as a linear combination of signals generated from measurements and system inputs. In contrast to existing methodology, the new method employs a set of functionals of the regressors instead of the regressors themselves to estimate the unknown parameters. The new adaptive learning algorithm is also applied to the state feedback and the output feedback of a standard Model Reference Adaptive Control (MRAC) structure. Stability and convergence properties of the new algorithm are studied in the this paper. Simulation results show that the new method exhibits a fast rate of convergence and the ability to converge even when the systems are not persistently excited. In addition, it is observed qualitatively in the simulations that the chattering effect in the system response and the control signal are suppressed in comparison to simulations using other conventional adaptive methods.