Data-driven model reduction-based nonlinear MPC for large-scale distributed parameter systems

Model predictive control (MPC) has been effectively applied in process industries since the 1990s. Models in the form of closed equation sets are normally needed for MPC, but it is often difficult to obtain such formulations for large nonlinear systems. To extend nonlinear MPC (NMPC) application to nonlinear distributed parameter systems (DPS) with unknown dynamics, a data-driven model reduction-based approach is followed. The proper orthogonal decomposition (POD) method is first applied off-line to compute a set of basis functions. Then a series of artificial neural networks (ANNs) are trained to effectively compute POD time coefficients. NMPC, using sequential quadratic programming is then applied. The novelty of our methodology lies in the application of POD's highly efficient linear decomposition for the consequent conversion of any distributed multi-dimensional space-state model to a reduced 1-dimensional model, dependent only on time, which can be handled effectively as a black-box through ANNs. Hence we construct a paradigm, which allows the application of NMPC to complex nonlinear high-dimensional systems, even input/output systems, handled by black-box solvers, with significant computational efficiency. This paradigm combines elements of gain scheduling, NMPC, model reduction and ANN for effective control of nonlinear DPS. The stabilization/destabilization of a tubular reactor with recycle is used as an illustrative example to demonstrate the efficiency of our methodology. Case studies with inequality constraints are also presented.