|H∞ Suboptimal Tracking Controller Design for a Class of Nonlinear Systems
International Journal of Control, Automation, and Systems, vol. 15, no. 5, pp.2080-2087, 2017
Abstract : "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."
"H∞ tracking controller, nonlinear two-player zero-sum differential (NTPZSD) game, time-varying desired trajectory, state-dependent Riccati equation (SDRE)."