Design and performance analysis of optimal reduced order H-infinity controller: L1 norm based genetic algorithm technique

The H-infinity methods are widely used in control system to synthesize controller, achieving stabilization with assured performance. Usually, the order of designed H- infinity controller is as high as the order of the considered system. The design and implementation of full-order H- infinity controller often require advanced hardware and high computational cost. However, if a restriction on the maximum order of the controller is imposed, that is lower than the order of the system, the problem becomes non-convex and non- smooth (non-differentiable), and it is relatively difficult to solve. In this paper, an optimal reduced order H-infinity controller, based on Hankel singular values (HSV), has been proposed using genetic algorithm (GA) on the basis of minimization of Li norm of the error function. The algebraic Riccati equation (ARE) has been used to design H-infinity controller for a boiler system. The obtained results have been compared with well know hybrid algorithm for non-smooth and non-convex optimization based on quasi-Newton updating and gradient sampling method.