Abstract

A novel state dependent control approach for continuous-time nonlinear systems with general performance criteria is presented in this paper. This controller is optimally robust for model uncertainties and resilient against control feedback gain perturbations in achieving general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. For the system model, unstructured uncertainty description is assumed, which incorporates commonly used types of uncertainties, such as norm-bounded and positive real uncertainties as special cases. By solving a state dependent linear matrix inequality at each time, sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this paper unify existing results on nonlinear quadratic regulator, H ∞ and positive real control. The effectiveness of the proposed technique is demonstrated by simulations of the nonlinear control of the Furuta pendulum.

Highlights

  • Optimal control of nonlinear systems is traditionally characterized in terms of Hamilton Jacobi Equations (HJEs)

  • In the past few years, it has been shown that the problems of quadratic regulation and H∞ nonlinear control can be approached by the state-dependent Riccati equation (SDRE) and nonlinear matrix inequality (NLMI) techniques (Cloutier, 1997; Cloutier, D’Souza, & Mracek, 1996; Huang & Lu, 1996)

  • We find that the novel state-dependent LMI control has better performance compared with the traditional linear quadratic regulator (LQR) technique based on linearization

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Summary

Introduction

Optimal control of nonlinear systems is traditionally characterized in terms of Hamilton Jacobi Equations (HJEs). As for uncertain nonlinear systems, we consider a general form of L2-bounded uncertainty description, without any standard structure, incorporating commonly used types of uncertainty, such as norm-bounded and positive real uncertainties as special cases. The purpose behind this novel approach is to convert a nonlinear system control problem into a convex optimization problem which is solved by state-dependent LMI. The general performance criteria are a generalization of the NLQR, H∞, positive realness and sector-bounded constraint; the results of the paper unify existing control results and provide a more general control design framework.

System model and general performance criteria analysis
State-dependent LMI control
Application to the inverted pendulum on a cart
Conclusions
Full Text
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