Multi-Parametric Optimization & Control

Abstract

Model based multi-parametric optimization provides a complete map of solutions of an optimization problem as a function of, unknown but bounded, parameters in the model, in a computationally efficient manner, without exhaustively enumerating the entire parameter space. In a Model-based Predictive Control (MPC) framework, multi-parametric optimization can be used to obtain the governing control laws – the optimal control variables as an explicit function of the state variables. The main advantage of this approach is that it reduces repetitive on-line control and optimization to simple function evaluations, which can be implemented on simple computational hardware, such as a microchip, thereby opening avenues for many applications in chemical, energy, automotive, and biomedical equipment, devices and systems. In this half-day workshop, we will first provide a historical progress report of the key developments in multi-parametric optimization and control. We will then describe PAROC, a systematic framework and prototype software system which allows for the representation, modelling and solution of integrated design, operation and advanced control problems. Its main features include: (i) a high-fidelity dynamic model representation, also involving global sensitivity analysis, parameter estimation and mixed integer dynamic optimization capabilities; (ii) a suite/toolbox of model approximation methods; (iii) a host of multi-parametric programming solvers (POP – parametric Optimization] for mixed continuous/integer problems; (iv) a state-space modelling representation capability for scheduling and control problems; and (v) an advanced control toolkit for multi-parametric/explicit MPC and receding horizon estimation/schedulingproblems. Algorithms that enable the integration capabilities for design, scheduling and control are presented along with applications in sustainable energy systems, smart manufacturing and process intensification.