Constrained control and set invariance

Invariant sets play an important and fundamental role in the design of control systems. An invariant set is a region of a dynamic system’s state space that has the following property: if the state of the system is within the set at some time, then it is guaranteed to remain within the set for all future times. Therefore, being able to characterize and compute these sets is of prime importance when designing control systems that offer guarantees of safety and constraint satisfaction.

The project will research the theory and computation of invariant sets, and their application to new control problems. The ultimate goal is to develop theory and methods for the construction of low-complexity invariant sets, using computationally tractable algorithms.