Control designs for the nonlinear benchmark problem via the state-dependent Riccati equation method

Abstract

A nonlinear control problem has been posed by Bupp et al. to provide a benchmark for evaluating various nonlinear control design techniques. In this paper, the capabilities of the state-dependent Riccati equation (SDRE) technique are illustrated in producing two control designs for the benchmark problem. The SDRE technique represents a systematic 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 state-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)BT(x)P(x)x, where P(x) is the solution of the SDRE. Analysis of the first design shows that in the absence of disturbances and uncertainties, the SDRE nonlinear feedback solution compares very favorably to the optimal open-loop solution of the posed nonlinear regulator problem, the latter being obtained via numerical optimization. It is also shown via simulation that the closed-loop system has stability robustness against parametric variations and attenuates sinusoidal disturbances. In the second design it is demonstrated how a hard bound can be imposed on the control magnitude to avoid actuator saturation. © 1998 John Wiley & Sons, Ltd.