Utilizing Problem Structure in Optimization Algorithms for Model Predictive Control

In this work we perform control design and demonstrate the effectivenessof model predictive control (MPC), an optimization based control approachthat is capable of satisfying state and input constraints and using forecastsof disturbance inputs, for the application of energy efficient control ofheating, ventilation, and air conditioning systems in buildings. We derivesimplified control oriented models and express the relevant constraintsand disturbance predictions, and show that online solution of the resultingoptimization problems is able to reduce energy consumption while satisfyingoccupant thermal comfort constraints and limits on control actuator inputs.We investigate the implementation challenges of applying model predictivecontrol to large systems, focusing on online solution of an optimizationproblem at every time step. We show that it is critical to take advantage ofproblem structure in system modeling and the formulation of the constraintsand objective function. Applying an interior point algorithm making use ofparallel sparse linear algebra solvers performs well, solving nonlinear MPCproblems with tens of thousands of variables and constraints in less than aminute on modern multicore processors. We design an optimization modelingtool that allows simple expression of a MPC problem and efficient interfacesto compiled optimization solvers, calculating sparse derivatives andconstraint Jacobians automatically. Finally we examine specializedoptimization algorithms for linear systems with polyhedral constraints,reusing repeated model data for time invariant systems to solve blockbanded linear systems of equations