Performance improvement and Lyapunov stability analysis of nonlinear systems using hybrid optimization techniques

Abstract

Using Hybrid optimization algorithms for nonlinear systems analysis is a novel approach. It is a powerful technique that uses the exploitation ability of one algorithm and the exploration ability of another algorithm, to find the best solution. Literature survey reveals that hybrid algorithms not only show quality response but also give faster convergence of error for nonlinear systems. In this paper, hybrid optimization techniques based proportional integral derivative (PID) controller is used for benchmark problems: Continuous stirred tank reactor (CSTR), Inverted pendulum and blood glucose system. Two recent hybrid algorithms: Particle swarm optimization-Gravitational search algorithm (PSO-GSA) and Particle swarm optimization-Grey wolf algorithm (PSO-GWO) are implemented to control the temperature and concentration of CSTR, pendulum angle of inverted pendulum, glucose concentration and insulin level of blood glucose system. In PID and PSOGWO algorithms, the exploration abilities of GSA and GWO combined with the exploitation ability of PSO have been used. The performance of these algorithms is then compared with individual PSO, GSA, and GWO algorithms proving their superiority. Stability is ensured using the Lyapunov approach while the robustness of the systems is checked using the parameter perturbation technique. Simulation results show substantial improvement in the performance of these systems by using these meta-heuristic hybrid optimization techniques. A comparative analysis of these algorithms has also been done.