Cost-preserving Control Of Neutral Neural Networks With Mixed Delays Dependent On Markov Processes

The neutral-type neural network with time delay is a kind of important neural network.Its characteristic is,in addition to occurring in the system states,time delays also appear in the derivatives of system states.In other words,the evolution of the system state depends not only on the current state,but also on the rate of change in the past state.Therefore,compared with the general time-delay neural network,neutral delay neural network is a more general dynamical system,so the control problem of neutral-type neural network has attracted more and more attention in recent years.In addition,in the actual production,the structure of control system may cause change due to some sudden factors such as the external environment,sudden change of parameters and connection interruption,and so on.However,these emergencies cause the system structural changes,or cause random switching between subsystems.The changes of the system structure or the switching between subsystems can often be described by a Markov process.When designing the controller of system,not only the stability of the system is discussed,but also to ensure that closed-loop system can meet certain performance index,so we introduce the cost function and the guaranteed cost control,the study of the optimal control problem of quadratic form performance index has a practical significance.In this article,we mainly study the guaranteed cost control for a class of the neutral-type neural network with Markovian jumping and mixed time delays.The time delays involved consist of the mode-dependent discrete delay and the mode-dependent bounded distributed delay.The paper is divided into four chapters:In the first chapter,we introduce the development and application of the artificial neural network,the research background and the present situation of the network control system,the optimal control and the guaranteed cost control.Finally,we formulate the main problems of this article.In the second chapter,we firstly give Markov chain taking values in a finite state space,and describe the neutral-type Markovian jumping system with mixed time delays.The concepts of cost function,asymptotically stability in mean square,guaranteed cost and guaranteed cost controller are defined.In the third chapter,by constructing novel Lyapunov-Krasovskii functionals,and using some stability theory and combining with linear matrix inequality method,the sufficient conditions are obtained for the existence of guaranteed cost controller in closed-loop system under the given cost function.In the fourth chapter,based on the above sufficient conditions,employing a convex optimization approach,we design the optimal guaranteed cost controller of closed-loop system.Finally,numerical simulations are presented to further demonstrate the effectiveness of the proposed approach.