A Multiple Model Approach Integrated Operating Space Partition And Optimal Control For Nonlinear System

Modelling and control of nonlinear dynamical systems is one of the most important but also the most challenging areas of system theory.Multiple Model approach has received a great deal of attention in past few decades due to its success in handling nonlinear system problems with both large set-point changes and wide operating rages,as well as in converting complex problems into simpler sub-problems.It has achieved abundant result both in theory and in practice applications.To deal with the fundamental problem of the multiple model approach,i.e.the "division" and the "combination",a new systematic method of integrated operating space partition and combining multiple model for nonlinear systems is initially proposed.The proposed method poses a close-loop structure.On the one hand,the active subspace of each linear subsystem is determined under the optimal control index given by combination problem.On the other hand,based on the known boundary condition,the multiple model is combined by hybrid model and the multiple model controller of hybrid model-MPC is proposed,then the Simulantenous method is introduced into sovling hybrid model-MPC to accelerate the solution efficiency.The main contributions of this dissertation are as follows:(1)When the linear model bank of the nonlinear system and the boundary condition are known,the muliptle model bank system is combined into hybrid model,then a multiple model controller of hybrid model-MPC for nonlinear system is designed under a unified and integrated performance index.Then,Simultaneous method is employed to overcome the difficulties in solving the optimal control of hybrid model,such as the many discrete variables,long running time,etc.The hybrid model-MPC controller based on simultaneous method can effectively coordinate the linear sub-models in the framework of a unified hybrid model,avoid the chatter caused by the model switching,and enhance the robust stability of the system,and short computing time of optimal problem lay the foundation for application of hybrid model-MPC.(2)A method of partitioning state space based on closed-loop performance is proposed for the nonlinear system that the state variables are measurable.Firstly,the multiple model bank of the nonlinear system at its operating points are constructed.And the multiple model bank is combined with hybrid model structure.Then,with the boundary condition taken as one of the decision variables,an optimal control problem for infinite time domain is introduced based the hybrid model and performance index given by combination problem.At the same time,the optimization of the infinite time domain optimal control condition is deduced,and the optimal boundary conditions in the state space are obtained.(3)A method of partitioning output space based on closed-loop performance is proposed for the nonlinear system with unmeasurable state variables.The input-output model bank of the nonlinear system at operating points is firstly obtained through the identification technique,and the output variable is defined as the scheduling variable.By defining the new state variables,the input-output model bank is transformed into the state space form and the state space model is combine with hybrid model structure.Then,the optimal boundary of the state space is obtained by optimal condition of optimal control problem based on state space model.Using the projection algorithm to obtain the decomposition result of the output space with the result of state space.