A Control-Performance-Based Partitioning Operating Space Approach in a Heterogeneous Multiple Model

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.Processes 2020, 8, 215 2 of 13 the heterogeneous multiple model have the capacity to fit the system complexity in each operating space with different dimensions of sub-models. Hence, this kind of multiple model has much more flexibility and generality than a homogeneous multiple model, having more extensive prospect. The heterogeneous model was initially proposed by Filev [23], and different heterogenous model structures, such as the local model network [24][25][26][27] and decoupled multiple model [28,29], have been applied to nonlinear system modeling, control, optimization, etc. [30,31].There are two problems in the multiple model approach-operating/state space decomposition and sub-model combination. In decomposition, a nonlinear system decomposes into several sub-models and the operating/state space of the nonlinear system is partitioned into corresponding operating zones. In the usual multiple model approach, researchers used to consider the decomposition and the combination as two independent procedures [32]. The decomposition is first accomplished, and then the combination of sub-models is carried out [33]. Du et al. used the gap metric to decompose the nonlinear system into model bank determination [34]. Song et al. developed a closed loop decomposition method based on an optimal control problem for nonlinear systems [35,36].However, the above-mentioned decomposition/combination method is mostly applied to homogeneous multiple model structures. 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. Initially, the heterogeneous multiple model is obtained at given equilibrium points of a nonlinear system, then auxiliary variables are selected to transform a heterogeneous multiple model into a homogeneous multiple model. An optimal problem where decision variables are composed of control input and the boundary condition of sub-m...