H∞ suboptimal tracking controller design for a class of nonlinear systems

In this paper, a new technique is proposed to solve the H∞ tracking problem for a broad class of nonlinear systems. Towards this end, based on a discounted cost function, a nonlinear two-player zero-sum differential (NTPZSD) game is defined. Then, the problem is converted to another NTPZSD game without any discount factor in its corresponding cost function. A state-dependent Riccati equation (SDRE) technique is applied to the latter NTPZSD game in order to find its approximate solution which leads to obtain a feedback-feedforward control law for the original game. It is proved that the tracking error between the system state and its desired trajectory converges asymptotically to zero under mild conditions on the discount factor. The proposed H∞ tracking controller is applied to two nonlinear systems (the Vander Pol’s oscillator and the insulin-glucose regulatory system of type I diabetic patients). Simulation results demonstrate that the proposed H∞ tracking controller is so effective to solve the problem of tracking time-varying desired trajectories in nonlinear dynamical systems.