A novel multi-objective optimization algorithm for Pareto design of a fuzzy full state feedback linearization controller applied on a ball and wheel system

Abstract

The control and stabilization of a ball and wheel system around the equilibrium point are challenging tasks because it is an underactuated, nonlinear, and open-loop unstable plant. In this paper, Pareto design of a Fuzzy Full State Feedback Linearization Controller (FFSFLC) for the ball and wheel system based upon a novel multi-objective optimization algorithm is introduced. To this end, at first, a full state feedback linearization approach is employed to stabilize the dynamics of the system. Next, appropriate fuzzy systems are determined to tune the control gains. Then, a new multi-objective optimization algorithm is utilized to promote the proposed control scheme. This optimization algorithm is a combination of Simulated Annealing (SA) and Artificial Bee Colony (ABC) approaches benefiting advantages of the non-dominated Pareto solutions. To evaluate the capabilities of the suggested algorithm, its optimal solutions of several standard test functions are compared with those of five renowned multi-objective optimization algorithms. The results confirm that the proposed hybrid algorithm yields closer non-dominated Pareto solutions to the true optimal Pareto front with shorter runtimes than other algorithms. After selecting proper objective functions, multi-objective optimization of FFSFLC for the ball and wheel system is performed, and the results are compared with previous works. Simulations illustrate that the proposed strategies can accurately converge the system states to the desired conditions and yield superior robustness against disturbance signals in comparison with former studies.