CONTROL DESIGNS FOR THE NONLINEAR BENCHMARK PROBLEM VIA THE STATE-DEPENDENT RICCATI EQUATION METHOD

A nonlinear control problem has been posed by Bupp et al.(1) to provid e a benchmark for evaluating various nonlinear control design techniqu es. In this paper, the capabilities of the state-dependent Riccati equ ation (SDRE) technique are illustrated in producing two control design s for the benchmark problem. The SDRE technique represents a systemati c way of designing nonlinear regulators. The design procedure consists of first using direct parameterization to bring the nonlinear system to a linear structure having state-dependent coefficients (SDC). A sta te-dependent Riccati equation is then solved at each point x along the trajectory to obtain a nonlinear feedback controller of the form u = -R-1(x)B-T(x)P(x)x, where P(x) is the solution of the SDRE. Analysis o f the first design shows that in the absence of disturbances and uncer tainties, the SDRE nonlinear feedback solution compares very favorably to the optimal open-loop solution of the posed nonlinear regulator pr oblem, the latter being obtained via numerical optimization. It is als o shown via simulation that the closed-loop system has stability robus tness against parametric variations and attenuates sinusoidal disturba nces. In the second design it is demonstrated how a hard bound can be imposed on the control magnitude to avoid actuator saturation. (C) 199 8 John Wiley & Sons, Ltd.