Multiple Model Predictive Control of Dissipative PDE Systems

Model predictive control (MPC) is a popular strategy, often applied to distributed parameter systems (DPSs). Most DPSs are approximated by nonlinear large-scale models. Using it directly for control applications is problematic because of the high associated computational cost and the nonconvexity of the underlying optimization problem. In this brief, we build on the notion of multiple MPC, combining it with equation-free model reduction techniques, to identify the (relatively low-dimensional) subspace of slow modes and obtain a local reduced-order linear model. This procedure results in an input/output framework, enabling the use of black-box deterministic and stochastic simulators. The set of linear low-dimensional models obtained off-line along the reference trajectories are used for linear MPC, either with off-line gain scheduling or with online identification of the reduced model. In the former approach, the decision to use the model in real time is taken a priori, whereas in the latter a local model is computed online as a function of a set stored in a model bank. The two approaches are discussed and validated using case studies based on a tubular reactor, a highly nonlinear dissipative partial differential equation system exhibiting instabilities and multiplicity of state.