Benders Decomposition Algorithm For Hybrid Control System

There are both continuous and discrete variables in the hybrid system, and contain continuous dynamics and discrete dynamics. It is an object of study between control theory and compute science. Because of wide use of computers in control system, lots of complex systems have hierarchy structure which is composed by computer at high level and controller at low level, and hybrid system has been widely used in industry. Traditional modeling and control method can not accurately describe the system and give satisfied control effect.The thesis focuses on modeling and optimal control of hybrid system. For the optimal control of motorbike velocity regulating system based on a typical hybrid system as discrete hybrid automaton model, a transformation to mix-integer linear programming is given. And Benders decomposition algorithm is proposed to solve the problem of optimal control of hybrid system. For the inventory control problem in hot-rolling process, control theory is used to develop mathematical model to reflect the dynamics of inventory. The Model is solved by Benders decomposition algorithm and order strategy to minimize the cost of inventory is given.Major work in this thesis is as following:(1) To address the difficulty in solving optimal control problem of hybrid system that has both continuous and discrete variables, the corresponding transformation method is proposed, and the model is transformed into regular mix-integer linear programming problem. As an example, formulate the MILP model for the motorbike velocity regulating system.(2) Benders decomposition algorithm is proposed to solve optimal control problem of hybrid system. And the algorithm is used to solve the motorbike velocity regulation system model. Some valid inequalities are added to improve the algorithm in the problem of motorbike velocity regulation system. It is verified the feasibility and efficiency of Benders decomposition algorithm for solving the optimal control problem of hybrid system.(3) Based on control theory, the problem of solving the order strategy for multiple products in multiple periods with minimizing inventory cost as objective is formulated. For grouping constraints of products in hot-rolling process, discrete variables are imported to reflect this constraint. Based on control theory, a mathematical model which reflects the dynamics of inventory is developed. The model is a typical MILP model, and is solved by Benders decomposition algorithm.