Constrained Control and Estimation of Homogeneous Reaction Systems using Extent-Based LPV Models

In this paper, a Model Predictive Control (MPC) strategy for nonlinear homogeneous reaction systems is proposed. The nonlinear system is first transformed to a Linear Parameter Varying (LPV) system by means of a linear transformation known as extents decomposition. The resulting LPV system is further converted to a Linear Time Invariant (LTI) system by means of a parametric state feedback and feedforward control laws. The use of this description results in linear MPC with a quadratic performance index and nonlinear state parameter constraints. However, based on the polytopic nature of the parameter of the LPV systems, the constraints are transformed into a set of intersected polyhedrons. The final result is a linear MPC problem with linear constraints that can be easily converted and solved as a quadratic programming problem. Finally, the performance of the control strategy is illustrated in simulation and compared with a controller based on a constant-parameter LTI model.