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.