Genetic adaptive scheme design for high initial gain problems in a L2-gain state feedback controller

This paper is a study of a genetic adaptive scheme design for L₂-gain state feedback controllers. It is known that the design of the initial gain producer of the L₂-gain state feedback controller (LC) is a difficult problem. The derivative-free optimization, the genetic algorithm, is utilized to resolve the high initial gain problem of LC for a class of nonlinear systems. It is a novel approach for robust control and can be considered as a special application of genetic algorithms. A real-value genetic algorithm with on-line characteristics is designed to search a suitable control gain of LC under auxiliary searching conditions and a specific cost function. The specific cost function is designed under Lyapunov stable theory. Since the system has the L₂-gain control properties, then the system states are bounded in an assignable region so that the stability of the initial system is guaranteed. Thus, the system stability of any searched results is guaranteed. Besides, due to the assignable L₂-gain attenuation level, the search space of the genetic algorithm is definable. The search target of the genetic algorithm is to find a suitable set of the initial gain so that the system can have required initial control performance. The simulation results indeed demonstrate the effectiveness of the proposed approach.