Adaptive H∞ control of polynomial Hamiltonian systems via symbolic computation: controller parameterisation

This paper deals with controller parameterisation method of adaptive H-infinity control for polynomial Hamiltonian systems (PHSs) with disturbances and unknown parameters. We design a simplified controller with a set of tuning parameters which can guarantee that the systems are adaptive H-infinity stable by using Hamiltonian function method. Then, a method for solving the set of tuning parameters of the controller with symbolic computation is presented. The proposed parameterisation method avoids solving Hamilton-Jacobi-Issacs (HJI) equations and the obtained controller is easier as compared to some existing ones. Simulation example shows that the controller is effective as it can optimise adaptive H-infinity control by adjusting tuning parameters. All these results are expected to be of use in the study of adaptive H-infinity control for nonlinear systems with disturbances and unknown parameters.