| As a natural extension of Boolean network,multi-valued logic network can better describe the dynamic behavior between genes in the cell,and it is also widely used in the field of computer science,artificial intelligence,game theory and complex neural network.Therefore,many researchers paid more attention to multi-valued logic dynamic network.In this paper,optimal control problems of multi-valued logic dynamic network system are studied.By using the semi-tensor product method,the multi-valued logic dynamic system and cost function are expressed in algebraic form,and then the dynamic programming method for solving the optimal control problem is given.When the decision of one party is fixed and known,the game problem can be transformed into the optimal control problem.This paper addressed man-machine game problems under the strategy of the machine is fixed and known.Optimal control problems is how the person chooses the strategy to maximize its benefits.Using the tool of matrix semi-tensor product,we reduce algebra expressions for the one-to-one and many-many games with the same strategy type,and the game with different strategy types for each opponent.Furthermore,the corresponding methods of solving the optimal control problem is given.Through introducing the value function and prove the optimality principle,dynamic programming algorithm for multivalued network is established.Finally,for optimal control problems of one-person-one-machine,multiperson-multi-machine and mixed value dynamic logic,several examples are calculated with the proposed algorithm.The innovation of this thesis lies in: The evolution process of multi-valued logic networks is characterized by the nodes in the network according to their update rules.It is generally difficult to describe them with logical expressions.Meanwhile,in the process of evolutionary game,the benefits of both sides of the game are also It is also difficult to describe by the expression of the multi-valued logical variable,but after introducing the semi-tensor expression of the logical variable,we can easily introduce the algebraic expression of the semi-tensor of the evolution equation and the income function.It can be solved by the traditional solution method of discrete optimal control problem. |
