Nonlinear \(H_\infty\) control via measurement feedback using neural network
In this paper, we solve the nonlinear \(H_\infty\) optimal control with output feedback via the neural network (NN)–least squares method for the affine nonlinear system. The approach is based on successive approximate solution of two Hamilton–Jacobi–Isaacs (HJI) equations, which appear in the \(H_\infty\) optimal output feedback control. Successive approximation (SA) approach combined with neural network (NN) for updating control and disturbance inputs in the case of state-feedback control is first proposed to solve an HJI equation with two players. The obtained solution is then used to solve, with the SA-NN approach for updating disturbance input, an HJI equation with one player in the output feedback control problem. Simulations on the Translational oscillator with rotational actuator mechanical system are presented to illustrate the effectiveness of the proposed method.
KeywordsNonlinear \(H_\infty\) control Output feedback Hamilton–Jacobi–Isaacs equation Successive approximation Neural-network approximation
The authors would like to thank the referees and the editor for the detailed comments that have helped significantly improve the quality of presentation.
- 9.Finlayson BA, Scriven LE (1966) The method of weighted residuals—a review. Appl Mech Rev 19(9):735–748Google Scholar
- 12.Mehraeen S, Dierks T, Jnagannathan S (2012) Zero-sum two player game theoretic formulation of affine nonlinear discrete-time systems using neural network. IEEE Trans CybernGoogle Scholar
- 14.Park J, Chung W, Youngil Y (1998a) Analytic nonlinear \(H_\infty\) optimal control for robotic manipulators. Proc IEEE Int Conf Robot Autom, pp 2709–2715Google Scholar
- 16.Saridis GN, Lee CSG (1979) An pproximation theory of optimal control for trainable manipulators. IEEE Trans Syst Man Cybern 9(3):152–159Google Scholar
- 20.Urs C, Cirillo R (1997) Nonlinear \(H_\infty\) control, derivation and implementation. IMRT, Report 31Google Scholar
- 22.Lin W, Byrnes CI (1996) \(H_\infty\) control od discret-time nonlinear systems. IEEE Trans Autom Control 41(4):494–510Google Scholar
- 24.Huang Y, Liu D, Wei Q (2012) Generalized Hamilton–Jacobi–Isaacs formulation-based neural network \(H_\infty\) control for constrained input nonlinear systems. 19th international conference, ICONIP 2012, Doha, Qatar, November 12-15, 2012, proceedings, Part I. Springer, Berlin, Heidelberg, pp 218–225Google Scholar