# American Institute of Mathematical Sciences

April  1995, 1(2): 223-236. doi: 10.3934/dcds.1995.1.223

## Suboptimal feedback control for a class of nonlinear systems using spline interpolation

 1 Department of Mathematics, University of Western Australia, Nedlands, WA, 6009, Australia, Australia, Australia

Received  September 1994 Published  February 1995

We consider a class of nonlinear quadratic regulator problems where the system dynamics are affine in the control. It has been shown recently that an optimal feedback control law for this class of problems can be given in terms of the solution of a state dependent algebraic Ricatti equation (ARE) at each instance of time. However, in most practical problems it is not possible to find an analytic solution to the ARE and hence numerical schemes to calculate suboptimal controls are required. In this paper, we consider one such scheme based on cubic basis spline interpolation. It is shown that if the chosen partitioning of the state space is sufficiently small, the resulting suboptimal controller leads to a stable closed loop system.
Citation: V. Rehbock, K.L. Teo, L.S. Jennings. Suboptimal feedback control for a class of nonlinear systems using spline interpolation. Discrete & Continuous Dynamical Systems, 1995, 1 (2) : 223-236. doi: 10.3934/dcds.1995.1.223
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