Reduced order model predictive control for parametrized parabolic partial differential equations

Model Predictive Control (MPC) is a well-established approach to solve infinite horizon optimal control problems. Since optimization over an time generally infeasible, MPC determines suboptimal feedback by repeatedly solving finite Although has been successfully used in many applications, applying large-scale systems – arising, e.g., through discretization of partial differential equations requires the solution high-dimensional problems and thus poses immense computational effort. We consider governed parametrized parabolic employ reduced basis method as low-dimensional surrogate model for problem. The order serves original system. analyze proposed RB-MPC first developing posteriori error bounds errors associated cost functional. These can be evaluated efficiently offline-online procedure allow us guarantee asymptotic stability closed-loop system using several practical scenarios. also propose adaptive strategy choose prediction Numerical results are presented illustrate theoretical properties our approach.