Filtering Design Of Networked Fuzzy Affine System

With the rapid development of modern technology,the controlled objects are usually subject to nonlinearities,external disturbances,and other uncertainties.Due to the influence of above factors,it is difficult to establish a linear control model that meets the requirements.In such a case,the T-S fuzzy system with nonlinear characteristics can describe the controlled object very well,which makes the Lyapunov stability theory applying in nonlinear system control.However,when the system is more complex,using the common T-S fuzzy model will increase the amount of calculation,and the designed controller is more conservative.To solve this problem,in 1999,Professor Johansson proposed a class of T-S fuzzy affine systems.It has been proved that T-S fuzzy affine systems have stronger function approximation than common T-S fuzzy systems.Therefore,it has attracted the attention of many scholars.On the other hand,the communication resources of the networked control system are limited and the network security problems has received extensive attention.In this article,we will carry out related research based on the networked fuzzy affine system.The main contents are as follows:(1)The issue of nonstationary filtering for uncertain fuzzy Markov switching affine systems(FMSASs)with quantization effects and deception attacks(DAs)is investigated.The resulting FMSASs are comprised of Markov switching piecewise-affine systems over a set of operating regions.To characterize the multinetwork-induced constraints,the measurement output is quantized before being transmitted,and a compensation scheme is applied to tackle the quantized measurement output loss intermittently.Meanwhile,the randomly occurring DAs are involved,in which the attack behaviors are identified by the bounded stochastic signals.Differently,to deal with the multinetwork-induced constraints,a novel nonstationary region-dependent affine filter strategy is developed.By resorting to a mode-dependent and region-dependent Lyapunov functional and S-procedure theory,sufficient conditions are elicited such that the filtering error system is mean-square exponentially stable.Finally,the practicability of the derived results is verified by a practical tunnel diode circuit model.(2)The reduced-order filter design method for fuzzy Markov jump affine systems with dynamic event-triggered protocol and uncertain packet dropouts is studied.Aiming at ap-proximating the nonlinearities with high accuracy and broadening practical application,the fuzzy Markov jump affine systems associated with mode-dependent operating regions are developed.A novel nonhomogeneous Markov process is proposed to describe the general-ized stochastic jumping among subsystems,whose time-varying transition probabilities are orchestrated by a higher-level deterministic switching signal.Compared with the conven-tional Markov process with arbitrary switchings,the average dwell-time strategy is adopted in the novel nonhomogeneous Markov process to improve the dynamic performance.A dy-namic event-triggered protocol is provided to alleviate the network transmission burden by elongating the interval between any two consecutive events.Based on the variation of state-space partitions,nonsynchronous reduced-order generalized filters are considered.Under this framework,sufficient criteria are attained to ensure the stochastic stability and prescribed7)₂-7)_?performance for the filtering error systems.Eventually,the theoretical findings are verified by two simulation examples.(3)A novel dynamic event-triggered protocol is constructed to deal with the filtering problem for affine systems presented by T-S fuzzy model.For achieving desirable perfor-mance while saving communication resources,the memory-based dynamic event-triggered protocol is constructed by flexibly exploiting a series of the historical triggered packets.The fading channel is time-varying and described as a novel nonhomogeneous Markov process,in which a higher-level deterministic switching signal regulates the variation of transition probabilities.By adopting the region-dependent Lyapunov theory,the mean-square expo-nentially stable,and expected_?performance for resulting systems is guaranteed.In the end,an inverted pendulum model is applied to verify the results of the theoretical analysis.