Modelling Of Micro-Extended Analog Computer With Array And Network Extensions

Compared with the blossom of digital computer in the second half of the 21 th century,the research of analog computation is relatively limited,but in the past few decades,more and more researchers have turned to the research of a variety of analog computation models,and this stems partly from the appearance and rapid development of these novel computation models.This thesis focuses on a kind of unconventional analog computation model named micro Extended Analog Computer(uEAC),we start by studying some properties of uEAC hardware construction and its mathematical model,and particularly,some extended models including feedback uEAC model and uEAC cell are discussed.On these bases,a uEAC array topology is proposed,the impact of uEAC unit number is analyzed and a comprehensive optimization strategy based on Particle Swarm Optimizer(PSO)is proposed to optimize the array structure and parameters simultaneously.Moreover,a uEAC network considering the analog field dynamic properties is studied,which brings a delay item in the differential equation,then its stability and computability are studied.The main contents of this thesis can be summarized as follows:(1)Based on the resistance property of uEAC analog field conductive material,its input/output relationship is constructed and the uEAC unit mathematical model is studied.An example of uEAC unit model with a particular Lukasiewicz function is given to illustrate the limitation of such a uEAC unit,while a more complicated uEAC cell are proposed to extend its computation capability.Two adaptive controllers based on uEAC unit and uEAC cell are designed respectively to control a cam-spring mechanism with load disturbance,the parameters of these two controllers are updated by gradient descent and the simulation results verify their capability and efficiency.(2)A uEAC array topology is proposed,in which a particular uEAC unit is connected to all the other units by some weights.The inner structure of the uEAC array can be described by two matrices,i.e.connection matrix and weight matrix.Considering the correspondence of these two matrices,a comprehensive optimization strategy based on PSO is designed to optimize them simultaneously.Two simulation experiments,including data classification and data prediction,are designed to test the proposed uEAC array and optimization strategy,and promising results are achieved.Moreover,the impact of uEAC unit number on array computational capability are compared and analyzed in detail,which offers theoretical basis for the design of uEAC array.(3)Resistance property of the of uEAC analog field conductive material can not reflect its dynamic properties,thus the capacitance and inductance properties are considered,which makes the computation of uEAC unit not instantaneous.To extend the basic uEAC unit,a uEAC network is constructed and a constant delay item is added in the differential equation.The Lipschitz continuity of a class of Lukasiewicz basic functions is discussed and for the uEAC network with Lipschitz-Lukasiewicz functions,its global asymptotic stability is analyzed with the nonsingular M matrix and Lyapunov functional.Different Lyapunov functional candidates are discussed and several stability criteria are obtained,some specific numerical examples are given to test the criteria.(4)For the uEAC network with constant delay,its computability is studied.A specific definition of uEAC-computable functions is psoposed,and it is pointed out that exponential function,trigonometric function and their combinations are all uEAC-computable as basic elementary functions.Then by this uEAC-computable function definition,the main theorem is proved by showing that all the functions employed in a simulation of Turing machine are uEAC-computable,which is theoretical foundation of the comparison of uEAC network and other analog computation models.In conjunction with the aforementioned several respects,a more detailed and complete understanding of the uEAC is provided in this thesis,on the one hand,by constructing uEAC cell structure,its nonlinear mapping capability is enhanced.On the other hand,an uEAC array optimization method is designed,and its capabilities in pattern classification and data prediction are verified,with which the applicability of uEAC is also improved.Moreover,the build of uEAC network and the corresponding stability and computability results provide a theoretical basis for the future research of uEAC.