Study Of Complex Systems

Large-scale systems and multi-model adaptive control systems are twocomparatively typical problems in complex systems. As to large-scale systems,the control and optimization problems can be solved using the conventionalhierarchical optimization theory if the objective functions are separable. Besides, inorder to solve the problems of long optimization duration caused by the iteration in theconventional hierarchical optimization algorithms, some researchers presented theintelligent steady-state algorithms of separable large-scale systems based onthe Hopfield network, which greatly reduced the optimization time. However, if theobjective functions of systems are nonseparable, the above algorithms cannot solvethose problems. Therefore, some researchers presented the multi-objectiveoptimization technique that first converts the nonseparable problems intoseparable ones and then solves them. But it has the same disadvantage of theiteration algorithms, i.e., the optimization duration is too long. Tomulti-model adaptive control systems, the existing multi-model adaptivecontrol based on weighted probability often spends long time finding out thecorresponding control strategy when the system parameters change so that theintegral performance of the system is badly influenced. Therefore,improvement has to be made to meet the practical demands. For this purpose,the two classes of complex systems are studied carefully in this paper.In order to solve the above nonseparable large-scale system problems,this paper first describes the nonseparable large-scale system problems, thenbriefly summarizes its two hierarchical algorithms, i.e., IBM and IPM andmeantime analyses the intelligent steady-state optimization algorithms oflarge-scale systems based on the Hopfield networks. Subsequently the paperintroduces the multi-objective optimization technique to convert thenonseparable problems into separable ones using primal-dual algorithm.Based on this, Hopfield networks are studied carefully in this paper. Bymeans of a series of conversion of the hierarchical optimization problems innonseparable large-scale systems, the constraint functions are merged into theobjective functions and the Hopfield networks hierarchical optimizationcontrol models of large-scale systems based on IBM and IPM are establishedrespectively. At the same time the paper theoretically proves that the networksare steady and optimized and thus solve the iteration problems of large-scalesystems in conventional hierarchical optimization methods. The network,which actually has three layers, i.e., decomposition layer, coordination layerand local decision layer, has the advantages of non-iteration and rapidity andeven the optimal solution can be approached. It is a new way to solve thehierarchical optimization problems in nonseparable large-scale systems and ofhigh research value.After soIving the problems of the large-scale systems, this paper alsoattempts to realize the analog optimization circuit of the Hopfield networkhierarchical optimization control over nonseparable large-scale systems tomake the methods more practical. Therefore, first the analog optimizationnetwork of the general quadratic optimization problems is studied andcombined with examples, the analog hierarchical optimization network of thenonseparable large-scale systems based on the penalty function and Lagrangefunction is constructed according to the thoughts of analog optimizer.Hopfield network analog optimization circuit of the nonseparable large-scalesystems is realized through the research on the information feedback problemof the circuit. The anaIog realization circuit is capab1e of eliminating theconstraint errors of equations and in equations and further increasing theoptimization accuracy. What is more important, the optimization duration ofthis analog optimizer is so short that it can meet the needs of some special'occasions, which is worthy...