Multi-objective Lyapunov-based controller design for nonlinear systems via genetic programming

In system control, stability is considered the most important factor as unstable system is impractical or dangerous to use. Lyapunov direct method, one of the most useful tools in the stability analysis of nonlinear systems, enables the design of a controller by determining the region of attraction (ROA). However, the two main challenges posed are—(1) it is hard to determine the scalar function referred to as Lyapunov function, and (2) the optimality of the designed controller is generally questionable. In this paper, multi-objective genetic programming (MOGP)-based framework is proposed to obtain both optimal Lyapunov and control functions at the same time. In other words, MOGP framework is employed to minimize several time-domain performances as well as the ROA radius to find the optimal Lyapunov and control functions. The proposed framework is tested in several nonlinear benchmark systems, and the control performance is compared with state-of-the-art algorithms.