Metaheuristics-based Multi-objective Design of Global Robust Optimal Sliding Mode Control of Discrete Uncertain Systems

The paper introduces a new design control strategy for finite time stabilization of uncertain discrete systems. The proposed control method uses the First Order Sliding Mode Control (FOSMC), the Linear Quadratic Regulator (LQR) and Genetic Algorithms (GA). The key idea of combining two control strategies lies in the fact that a robust controller tackles the uncertainties when the optimal controller performances are unaffected. Firstly, as the performances of the Sliding Mode Control (SMC) greatly depends on the choice of the sliding surface, a novel method based on the resolution of a Sylvester equation is proposed. Secondly, to ensure the robustness in the whole space, the Integral Sliding Mode Control (ISMC) is combined with the above LQR method. Rigorous stability analysis for the closed-loop system is given and proves that the system states are always bounded even the unknown disturbances. In order to handle the problem accompanying the LQR synthesis as well as the gain of the robust compensator, a multi-objective optimization problem considering a set of competing objectives is solved using GA. For that, a novel dynamically aggregated objective function is proposed. A set of non-dominated optimal solutions are provided to the control engineer and then may select the most adequate solution among the resulting optimal Pareto set. The novel method has successfully solved the robust stabilization of two known benchmarks and the different results asserts not merely the efficiency as well as the quality of the designed controller but also its supremacy compared to some existing ones.