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Robust finite-time \(H _{\infty}\) control for nonlinear jump systems via neural networks. (English) Zbl 1191.93028

Summary: This paper presents a neural network-based robust finite-time \(H _{\infty }\) control design approach for a class of nonlinear Markov jump systems (MJSs). The system under consideration is subject to norm bounded parameter uncertainties and external disturbance. In the proposed framework, the nonlinearities are initially approximated by multilayer feedback neural networks. Subsequently, the neural networks undergo piecewise interpolation to generate a linear differential inclusion model. Then, based on the model, a robust finite-time state-feedback controller is designed such that the nonlinear MJS is finite-time bounded and finite-time stabilizable. The \(H _{\infty }\) control is specified to ensure the elimination of the approximation errors and external disturbances with a desired level. The controller gains can be derived by solving a set of linear matrix inequalities. Finally, simulation results are given to illustrate the effectiveness of the developed theoretic results.

MSC:

93B36 \(H^\infty\)-control
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