Robust Model Predictive Control with Aperiodic Actuation

Abstract

In this thesis, a control design problem, in which communication between different elements of the control system takes place through a shared (possibly wireless) channel, is considered. With the implementation of the proposed approach, the use of limited resources such as network bandwidth and battery life may be reduced.

The proposal consists of a robust model predictive control (MPC) approach, that is only executed at instants at which a decentralized triggering mechanism triggers. As long as no triggering occurs, inputs that have been computed at the previous MPC update are used. The triggering mechanism uses the trajectories from the MPC to calculate bounds on the error between each actual state and predicted state, for all instants up to the horizon. When all individual errors are inside their respective bounds at some instant, violation at the next instant still results in an MPC problem that is (1) guaranteed to have a feasible solution and (2) for which an upper bound for the objective function value is given that is lower than the value at the previous instant. These two properties result in stability of the closed loop system.

Simulation results are given to demonstrate the effectiveness of the proposed approach. Compared to approaches that solve similar problems that can be found in literature, the proposed approach differs in the need for weaker assumptions and/or in the maximization of the bounds on the error signal. This is made possible by letting the triggering mechanism depend on the sequences that are generated by the MPC at the last update instant, as well as the measured state.