Control And Applications Of Composite Asynchronous Sequential Machines Via Algebraic Method

Finite automata are a mathematical abstraction of discrete and digital systems with finite memory.Asynchronous sequential machines(ASM),a special category of finite automata,is an important tool for analyzing and designing digital circuits and high speed CPUs.With the development of science and technology,automata theory attracts more and more attention.This dissertation investigates the model matching problem for three kinds of composite ASM(cascaded ASMs,switched ASMs and parallel interconnected ASMs)and the static correction method for ASMs.There are seven chapters in this dissertation.Chapter 1 introduces the research background and current status of finite automata and ASMs.Chapter 2 introduces some necessary preliminaries on finite automata,ASMs and semi-tensor product.Chapter 3 investigates the model matching problem of cascaded ASMs.A cascaded ASM consists of several input/state ASMs in a cascading fashion.By using the semi-tensor product method,the algebraic expression of composite ASMs is presented,based on which reachability of composite ASMs is investigated.Then,a necessary and sufficient condition for the existence of a controller for model matching is obtained and an algorithm to design the corresponding controller is established.Finally,an example is proposed to illustrate the effectiveness of the obtained resultsChapter 4 investigates the model matching problem of switched ASMs.A switched ASM is composed of several input/state ASMs and it cutovers between submachines in asynchronous mechanism.By using the semi-tensor product method,four kinds of algebraic expressions are proposed for switched ASMs.Under this framework,stable transition matrix and admissible model-input-state transition matrix are defined.Then,two important problems,reachability and optimal control input design of switched ASMs,are discussed by these two new matrices,respectively.Finally,a necessary and sufficient condition for the existence of a controller for model matching is obtained and a practical example on asynchronous error accumulators is provided to show the feasibility of the proposed method.Chapter 5 investigates fault tolerant control of parallel interconnected ASMs.This problem is challenging since each submachine can fall into an unauthorized transition caused by adversarial inputs.By using the semi-tensor product method,the dynamics of parallel interconnected ASMs are depicted as a discrete-time algebraic form.Under this framework,reachability and detectability of parallel interconnected ASMs are discussed.Then,a necessary and sufficient condition for the existence of a controller is obtained.Finally,for better presentation,a system composed by three asynchronous error accu-mulators in parallel connection is provided to illustrate the feasibility of the proposed method.Chapter 6 investigates the static control of ASMs.For an input/state ASM,the static control is to find a static state feedback controller to solve the model matching problem,which does not contain memory unit and consists of only some logic gates.First,using the semi-tensor product method,two algebraic forms are derived to describe the dynamics of an input/state ASM and the function of a static state feedback controller,respectively.Then,as two special cases,the static state feedback controllers for no mismatch and only one mismatch are given.Based on these two cases and analyzing reachability of an ASM,a static state feedback controller design for model matching is presented.Moreover,the number of working points this controller contains is least.Finally,the proposed method is applied to a simple home security system.Chapter 7 states some possible future works about finite automata and asynchronous sequential machines.