A new optimal robust adaptive fuzzy controller for a class of non-linear under-actuated systems

In this paper, a new optimal robust adaptive fuzzy controller is proposed for stabilization of the inverted pendulum (IP) system as a non-linear under-actuated quadratic dynamic model. To reach this goal, a fuzzy controller (FC) is utilized to generate a proper control effort to stabilize the system via a product inference engine, a singleton fuzzifier and a centre average defuzzifier. Since the IP is an under-actuated system, the decoupled sliding mode structure is utilized to find a general sliding surface and produce the adaptive laws based on the gradient descent method. The existing constant coefficients in the suggested control system are optimized by the multi-objective particle swarm optimization algorithm with regard to conflicting objective functions. The performance of the proposed strategy is compared with those of other controllers introduced in literature. The results demonstrate that the time integral of the absolute value of errors for the designed optimal robust adaptive fuzzy controller is much lower in comparison with those obtained by the other methods.