Approximate discrete nonlinear H/sub /spl infin// control for inverted pendulum system

Designing a discrete nonlinear H/sup /spl infin// control law requires solving the discrete Hamilton-Jacobi-Issac (DHJI) equations, which are a set of mixed nonlinear partial and algebraic differential equations. An algorithm for obtaining the Taylor series solution of DHJI equations was given in which showed that the coefficients of the Taylor series solution were governed by an algebraic Ricatti equation, and a sequence of linear algebraic equations. in this paper, we will further apply the algorithm to design a third order H/sub /spl infin// controller for the well known inverted pendulum system. Simulation is given to show the performance of the third order controller in stabilization and disturbance attenuation.