Candidate: Liam Shawn Pritchard Lawrence
Title: The Optimal Steady-State Control Problem
Date: March 4, 2019
Time: 9:00 am
Place: EIT 3151/3
Supervisor(s): Simpson-Porco, John W.
Abstract:
Many engineering systems – including electrical power networks, chemical processing plants, and communication networks – have a well-defined notion of an “optimal” steady-state operating point. This optimal operating point is often defined mathematically as the solution of a constrained optimization problem that seeks to minimize the monetary cost of distributing electricity, maximize the profit of chemical production, or minimize the communication latency between agents in a network. Optimal steady-state regulation is obviously of crucial importance in engineering systems.
At present, this regulation is performed in a manner that involves time-scale separation: the optimization problem determining the optimal steady-state is solved first, and then feedback controllers force the system to track this predefined operating point. Since the optimal steady-state often depends on external influences to the system such as disturbances, this process must be repeated at regular intervals. However, the two-step approach is inefficient if the optimal operating point changes at a rapid rate.
A better strategy is to employ a controller that continuously and automatically regulates the dynamical system to an optimal operating point, even as this operating point changes over time. Designing such a controller is the optimal steady-state control problem. An optimal steady-state controller must simultaneously solve the optimization problem and force the plant to track its solution.
In this talk, I will detail an important special case of the optimal steady-state control problem, in which the plant to be controlled is an uncertain linear time-invariant system and the optimization problem is convex. My controller architecture is centred on the notion of an “optimality model,” a system which produces a proxy for the error between the current output and the optimal output; an optimality model reduces the optimal steady-state control problem to a standard tracking problem. I will elaborate on the idea of an optimality model, and examine when one may be constructed despite parametric uncertainty in the plant. Finally, I will give several simulation examples to demonstrate the main concepts of the talk.