Hierarchical model predictive control for Local Model Networks

Nonlinear model structures based on multiple linear models, which are overblended by validity functions (Local Model Networks) have proven to be successful for many examples in nonlinear system identification. Here a novel method for computing a suboptimal solution of the model predictive control (MPC) problem for local model networks with a hierarchical structure is developed. Therefore a representation of the local model networks as a binary directed tree is introduced. The novel method does not try to solve the nonlinear program of the model predictive control algorithm directly for the local model network, but provides a suboptimal solution by a hierarchical scheme. In the first step the optimal control problem is solved for a global linear model and in the next step the trajectory of this model is used to compute the linearization of a local model network with two local models. For this linearized model the predictive control problem is solved. Afterwards the number of used models is increased again and the procedure is iterated until the maximum number of local models is reached. Thus the method subsequently improves the quality and accuracy of the suboptimal predictive control solution. The feasibility of the approach is demonstrated for a highly nonlinear pH process.