Explicit construction of H∞H∞ control law for a class of nonminimum phase nonlinear systems

This paper addresses a nonlinear H∞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∞H∞ control problem. Moreover, based on the sufficient solvability condition, an upper bound of the best achievable L2L2 gain from the system disturbance to the system controlled output is estimated for the nonlinear H∞H∞ control problem. The proofs of our results yield explicit algorithms for constructing required control laws for solving the nonlinear H∞H∞ control problem. In particular, the solution to the nonlinear H∞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.