Set-theoretic Approaches to the Aperiodic Control of Linear Systems

In this thesis, we employ set-theoretic properties of additively disturbed linear discrete-time systems to develop stabilizing aperiodically updated control laws for plants controlled over communication networks. In particular, we design event-triggered and self-triggered controllers with a priori guarantees on closed-loop characteristics such as stability, asymptotic bound, and average communication rate. Different models for the disturbances are taken into account, namely arbitrary disturbances of which only a bound in the form of a compact set is known and stochastic disturbances with known probability distribution. For setups with hard constraints on the states and inputs, we propose aperiodic schemes based on robust model predictive control methods. Both the full information (state-feedback) case, as well as the limited information (output-feedback) case are investigated. It is demonstrated that the proposed controllers achieve a considerable reduction in the required network usage with only moderate or non-existing deterioration of the closed-loop properties guaranteed by comparable controllers that transmit information at every point in time.