Explicit construction of [formula omitted] control law for a class of nonminimum phase nonlinear systems

Abstract

This paper addresses a nonlinear H ∞ control problem for a class of nonminimum phase nonlinear systems. The given system is first transformed into a special coordinate basis, in which the system zero dynamics is divided into a stable part and an unstable part. A sufficient solvability condition is then established for solving the nonlinear H ∞ control problem. Moreover, based on the sufficient solvability condition, an upper bound of the best achievable L 2 gain from the system disturbance to the system controlled output is estimated for the nonlinear H ∞ control problem. The proofs of our results yield explicit algorithms for constructing required control laws for solving the nonlinear H ∞ control problem. In particular, the solution to the nonlinear H ∞ control problem does not require solving any Hamilton–Jacobi equations. Finally, the obtained results are utilized to solve a benchmark problem on a rotational/translational actuator (RTAC) system.