Stochastic sampled-data stabilization of neural-network-based control systems.

*(English)*Zbl 1348.90524Summary: This paper addresses the problem of stochastic sampled-data stabilization for neural-network-based control systems (NNBCSs) with an optimal guaranteed cost. In order to stabilize the closed-loop system, continuous-time nonlinear plant and three-layer fully connected feed-forward neural networks based on stochastic sampling are connected to the closed loop. By introducing new Lyapunov-Krasovskii functional with triple integral terms and by using second-order reciprocal convex technique, new stability and stabilization criteria for NNBCSs are derived in terms of linear matrix inequalities (LMIs). The desired stochastic sampled-data controllers can be calculated by solving these LMIs. Finally, physical example is given to verify the effectiveness and usefulness of the obtained results.

##### MSC:

90C25 | Convex programming |

93C10 | Nonlinear systems in control theory |

93D99 | Stability of control systems |

##### Keywords:

stabilization; nonlinear systems; neural networks; linear matrix inequalities; stochastic sampled-data control
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\textit{R. Rakkiyappan} et al., Nonlinear Dyn. 81, No. 4, 1823--1839 (2015; Zbl 1348.90524)

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