A simple nonlinear H∞ control design method: Polynomial nonlinear control

The question of how to construct a noniterative analytical solution for nonlinear H-infinity control is still an open challenge. This paper focuses on this challenge and proposes a novel simple approach, namely, polynomial nonlinear control, to design a nonlinear H-infinity control law without any iteration. Moreover, the solution of PNC is transformed into solvable LMIs. The design of PNC can be carried out in three steps: firstly, expand nonlinear system matrices via Taylor series expansions; secondly, choose and compute design parameters according to the proposed explicit formulas; and thirdly, obtain an analytical control law of PNC by solving an LMI optimization problem. Thus, the algorithm and the computation of PNC are quite simple and straightforward in engineering. In addition, stability and L-2 gain for the nonlinear closed-loop system are also guaranteed by PNC. The numerical simulations show that PNC can improve the control performances including transient responses, disturbance rejection, control effort, and the domain of attraction.