Control And Filtering For Nonlinear Switched Systems

In this paper,the fuzzy set theory is used to study the control/filtering problems for nonlinear systems.In addition,system environments and communication networks,including component nonlinearities,quantizers,communication protocols,attacks,etc.,are fully considered in this paper,and switching rules are employed to describe changes in system parameters,denial-of-service attacks(Do S attacks),and the selection of communication channels.Based on type-1 and interval type-2 fuzzy set theory,persistent dwell-time(PDT)switching rule and Lyapunov stability theory,the stability criterion and controller/filter design schemes for nonlinear switched systems under various communication networks are proposed in this paper.Specific research contents are as follows:1.Based on PDT switching rule and the T-S fuzzy model,non-fragile control under communication protocol and finite-time filtering with unreliable links are investigated for nonlinear switched systems.On the one hand,considering the limited bandwidth of the communication network and in order to optimize the usage of communication resources,weighted try-once-discard protocol is adopted,that is,only one node is premitted to transmit data at a certain instant via the weighted-maximum-error policy.Then,the augmented multiple Lyapunov-like functions(AMLFs)are adopted to obtain the stability criterion and analyze system performance.Finally,the effectiveness of the non-fragile controller is proved by a truck-trailer model.On the other hand,considering unreliable links between the system and the filter,random sensor nonlinearity and interference are studied.Based on the finite time stability theory,suitable multiple Lyapunov-Krasovskii functionals(MLKFs)are established.And then,a satisfied filter can be obtained.Finally,a single link robot arm model is used to demonstrate the correctness of the proposed method.2.Interval type-2 Takagi-Sugeno(IT2 T-S)fuzzy model is used to describe the nonlinearity and uncertainty features of systems.In addition,the multi-time-scale phenomenon is also studied based on the singular perturbation decomposition method.It should be noted that IT2 fuzzy set employed by the system and the controller/filter can be different,which makes the design of the controller/filter more flexible.Based on the resulting systems,an appropriate MLFs,singularly-perturbed-parameter-dependent MLFs are constructed.Sufficient conditions in the form of parameterized matrix inequalities(PMIs)are obtained to guarantee the stability of the closed-loop system/filter error system and make systems satisfy the given performance.Then,through dividing the footprint of uncertainty(FOU),advanced matrix transformation technologies and some appropriate relaxation matrices,PMIs is transformed into linear matrix inequalities(LMIs)to get the gains of the quantization controller and the passive filter that meet present requirements.Finally,a numerical example is given to illustrate the feasibility of the proposed control strategy,and a tunnel diode example is provided to illustrate the effectiveness of the filter.3.Further attempting to describe DoS attacks by a continuous-time PDT switched system,the new model is different from average-dwell-time-based Do S attacks which only have two modes(the unstable mode under successful attack and the normal mode without attacks).PDT-based Do S attacks have multiple modes,which can be further used to study multi-channel or distributed systems under Do S attacks.Then,by adopting appropriate WMLFs(weak MLFs),an observer-based controller is established to ensure the global uniformly asymptotic exponential stability of the closed-loop system.Finally,the algorithm of generating this special kind of attacks is given,and a numerical example is used to verify the correctness of the result.4.An IT2 T-S fuzzy model about load-frequency control(LFC)for uncertain nonlinear power systems is established,and the communication network with multiple channels is adopted.For the first time,a double-layer switching rule is used to select channel.The meaning of double-layer switching rule is the special Markov chains with PDT-switched transition probabilities.Afterwards,stability conditions are given.Finally,simulation results verify the effectiveness of the new LFC scheme.