- Main
Utilizing Problem Structure in Optimization Algorithms for Model Predictive Control
- Kelman, Anthony David
- Advisor(s): Borrelli, Francesco
Abstract
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.
Main Content
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