Computing Regions of Stability for Limit Cycles of Piecewise Affine Systems

Abstract

This paper proposes an improved algorithm to compute the regions of stability for limit cycles of piecewise affine systems. Instead of using convex optimization algorithms, such as solving linear matrix inequalities and sum-of-square programming, genetic algorithm (GA) is used to obtain the final results. With the help of GA, both the constraints and objectives can be nonconvex, leading to larger guaranteed regions of stability. Based on impact map and Lyapunov stability theory, the conditions of stability are analyzed. Algorithm-friendly criteria, both convex and nonconvex, are developed. Since randomly generated solutions are usually infeasible, initial population of GA is generated by convex optimization. To improve the diversity of the initial population, multiple convex objectives are used to generate different initial solutions. Other application-specific parts of GA, such as computing the fitness of solutions, are also introduced in detail. An example system is analyzed to illustrate the effectiveness of the proposed method.

DOI: http://dx.doi.org/10.5755/j01.itc.46.4.16072