On Analysis and Control of Monotone Systems

Thursday, May 5, 2016 - 11:00am - 12:00pm
Lind 305
Anders Rantzer (Lund University)
Monotone systems are receiving growing attention in the control community for their superior properties when it comes to analysis and synthesis of large systems. In this seminar, we will review some exciting developments in the area from the past year.

New scalable methods for control synthesis in linear monotone systems have raised a neutral question: How restrictive is the requirement that the closed loop system should be monotone? Here we will present an important class of problems for which this requirement is not restrictive at all. The problem class includes control of diffusive systems, for example the heat equation.

For linear time-invariant positive systems, it is well known that stability can be analysed using either sum-separable or max-separable Lyapunov functions. This is the main technical reason behind the powerful scalability properties of these systems. For non-linear monotone systems the situation is more complicated. Both positive and negative results, as well as open problems, will be reported.

Some systems are converging to a point which is not known in advance. Also in this case, monotonicity is a useful property. We will give examples in economic theory, as well as in optimization.