A new observer-based controller for continuous-time nonlinear systems with applications on electrical energy systems

Abstract

In this paper a new observer-based controller is developed for continuous-time input constrained nonlinear systems. Firstly, a new developed continuous time Regularized Least Square (CRLS) estimator is presented. The estimated states are then used to generate the desired constrained state feedback control strategies to regulate the performance of a perturbed system to the desired steady state. Unlike the well-known continuous-time nonlinear state estimators, such as the high gain observer and others, the developed observer does not show large overshoots at the start of the estimation process, the estimation errors reach zero steady state very shortly, has no pre-specified limitations on the class of nonlinear systems to be estimated, …etc. As a result, when used as an element in observer-based controlled systems, then the desired behaviors of the state trajectories of the controlled system are reached very shortly. The asymptotic stability of the proposed constrained observer-based controlled nonlinear system is rigorously analyzed. Simulation results are presented to justify the applicability and the efficiency of the proposed approach. Firstly, to show the superiority of the developed CRLS estimator, the states of illustrative practical problems are firstly estimated using the proposed approach. The achieved results are then compared with those achieved from applying the most famous and widely used observers in the literature. Then, two nonlinear practical control problems are used to demonstrate the effectiveness of the developed observer- based control approach.