Utilizing Problem Structure in Optimization Algorithms for Model Predictive Control

In this work we perform control design and demonstrate the effectiveness of model predictive control (MPC), an optimization based control approach that is capable of satisfying state and input constraints and using forecasts of disturbance inputs, for the application of energy efficient control of heating, ventilation, and air conditioning systems in buildings. We derive simplified control oriented models and express the relevant constraints and disturbance predictions, and show that online solution of the resulting optimization problems is able to reduce energy consumption while satisfying occupant thermal comfort constraints and limits on control actuator inputs.;We investigate the implementation challenges of applying model predictive control to large systems, focusing on online solution of an optimization problem at every time step. We show that it is critical to take advantage of problem structure in system modeling and the formulation of the constraints and objective function. Applying an interior point algorithm making use of parallel sparse linear algebra solvers performs well, solving nonlinear MPC problems with tens of thousands of variables and constraints in less than a minute on modern multicore processors. We design an optimization modeling tool that allows simple expression of a MPC problem and efficient interfaces to compiled optimization solvers, calculating sparse derivatives and constraint Jacobians automatically. Finally we examine specialized optimization algorithms for linear systems with polyhedral constraints, reusing repeated model data for time invariant systems to solve block banded linear systems of equations.