Abstract
An operating space partition method with control performance is proposed, where the heterogeneous multiple model is applied to a nonlinear system. Firstly, the heterogeneous multiple model is obtained from a nonlinear system at the given equilibrium points and transformed into a homogeneous multiple model with auxiliary variables. Secondly, an optimal problem where decision variables are composed of control input and boundary conditions of sub-models is formulated with the hybrid model developed from the homogeneous multiple model. The computational implementation of an optimal operating space partition algorithm is presented according to the Hamilton–Jacobi–Bellman equation and numerical method. Finally, a multiple model predictive controller is designed, and the computational implementation of the multiple model predictive controller is addressed with the auxiliary vectors. Furthermore, a continuous stirred tank reactor (CSTR) is used to confirm the effectiveness of the developed method as well as compare with other operating space decomposition methods.
Highlights
Modeling and control of nonlinear dynamical systems is one of the most important and most challenging areas of system theory
Following our previous work [33,34], which proposed an integrated framework of operating space partition and optimal control of the homogeneous multiple model, this paper proposes a new systematic operating space partition method of the heterogeneous multiple model where the closed loop performance is considered
The heterogeneous multiple model of nonlinear systems is obtained by an identification technique and formulated by an input–output model
Summary
Modeling and control of nonlinear dynamical systems is one of the most important and most challenging areas of system theory. According to the partition strategy, sub-model structure, sub-model transition, method of realization, and different structures of the multiple model are presented in the literature, including the Takagi–Sugeno (T–S) model [4], piecewise affine model [5], piecewise linear model [6], linear parameter varying model [7], and local model network [8,9] Most of these model structures can be classified into heterogeneous and homogeneous structures [10,11]. With the idea of closed loop decomposition and combination methods [34], a control-performance-based partitioning operating space approach in heterogeneous multiple models is proposed. An optimal problem where decision variables are composed of control input and the boundary condition of sub-models is formulated with the hybrid model developed from the homogeneous multiple model.
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