Pareto design of decoupled fuzzy sliding mode controller for nonlinear and underactuated systems using a hybrid optimization algorithm

This paper introduces Pareto design of the decoupled fuzzy sliding mode controller (DFSMC) based on a hybrid optimization algorithm for a number of fourth-order coupled nonlinear systems. In order to achieve an optimal controller, at first, a decoupled fuzzy sliding mode controller is utilized to stabilize the fourth-order coupled nonlinear systems around the equilibrium point. Then, a robust hybrid optimization algorithm is employed to enhance the capabilities of the control system. The mentioned algorithm is an optimal combination of artificial bee colony (ABC) and bacterial foraging (BF) algorithms enjoying the advantages of both. To evaluate this algorithm and to challenge its capabilities, firstly, the required test functions and evaluation criteria have been defined, and then, the results have been compared to those of the well-known algorithms including NSGAII, SPEA2 and Sigma MOPSO. The comparison illustrates the superiority and more accurate performance of this novel hybrid algorithm. Moreover, juxtaposition of Pareto solutions offered by the proposed method and the true optimal Pareto front demonstrate that the proposed algorithm is able to accurately overlap the true solutions. Eventually, by simulating three nonlinear systems, i.e. the inverted pendulum, ball and beam, and seesaw via MATLAB software and choosing proper objective functions, the coefficients of control law for both decoupled sliding mode and decoupled fuzzy sliding mode controllers are optimized so as to reach the most optimal performance for these dynamic systems. Simulations indicate that the decoupled fuzzy sliding mode controller surpasses the non-fuzzy counterpart in terms of accurately controlling the aforementioned systems. This technique can optimally stabilize the system states at their equilibrium points in a relatively short time. Besides, in order to validate the solutions obtained in this paper, they are compared with previous works.