POD-based State-Constrained Economic Model Predictive Control of Convection-Diffusion Phenomena

Abstract

Motivated by an application to energy efficient building, in this thesis optimal control of a linear time-dependent convection-diffusion equation is considered together with bilateral control and state constraints. To obtain regular Lagrange multipliers, two different approaches are investigated. The first one is called virtual control approach and it consists in introducing an artificial control, which allows replacing the pointwise state constraints with mixed constraints. The regularized problem is then solved with the Primal Dual Active Set Strategy (PDASS). The second applied technique is the augmented Lagrangian method: penalization terms dependent on the state constraints are added to the cost functional and many only control constrained problems are iteratively solved applying projected gradient or projected BFGS methods. To speed-up the computational time proper orthogonal decomposition (POD) is considered together with an a-posteriori error analysis, which ensures the quality of the POD approximation. Furthermore, model predictive control (MPC) helps to handle the long-time horizon and the problem parameter changes in an efficient way. At last, numerical simulations show the advantages and disadvantages of these techniques.