Event-Triggered Robust Model Predictive Control
Creators: Deng, Li
Publisher: name: University of Alberta Library
Year: 2023

<p>Model predictive control (MPC) is one of the most popular control strategies in modern control systems and has been used in a variety of applications due to its ability to handle hard constraints. As a significant branch of MPC, robust MPC is an effective strategy to deal with external disturbances or system uncertainties, and guarantee robust stability of uncertain systems. However, with the increase of system complexity and various demands, robust MPC optimization problems become more and more complicated, leading to high computational loads. By contrast, event-triggered control, which executes control actions only when some events occur, has shown advantages over traditional periodic control in dealing with resource constraints in energy, computation, and communication. Hence, this thesis is concerned with the combination of robust MPC and event-triggered control to address the challenges in traditional MPC. </p>

<p>Three research topics are considered. Firstly, from a deterministic point of view, a two-step triggering scheme involving a tentative verification of a deterministic triggering condition and a delayed triggering with a waiting horizon is proposed to ensure necessary events and  reduce the number of times of solving the MPC optimization problem. Secondly, the stochasticity is considered into the design of event-triggered schemes, which is investigated in two aspects: i) Based on the probability density function of disturbances, an event-triggered scheme related to a designed minimal robust positively invariant set of tube-based MPC is constructed to generate dynamic triggering sets, leading to a prescribed expectation of inter-execution times and a reduction of computational burden, while not sacrificing the quadratic performance significantly.  ii) With an updating law for the transition probabilities of a Markov chain, a stochastic triggering scheme involving a prescribed triggering function  and a checking function is proposed to achieve aperiodic and non-persistent event verification and enlarge the inter-execution time. Both tube-based MPC and linear matrix inequality-based (LMI-based) MPC are presented  with such a stochastic triggering scheme. Thirdly, for unknown systems with initially measured input-output data, a robust data-driven MPC with a terminal inequality constraint is developed to complete the analysis of recursive feasibility and stability, and an event-triggered scheme  is designed based on a mismatch between the data-driven model and the original plant to reduce computational burden. Finally,  an event-triggered stochastic MPC approach is applied to constrained queueing networks with a dynamic topology for the scheduling problem.</p>

<p>Different from most existing results which focus on only triggering action, the proposed approaches also incorporate event checking into the event-triggered scheme design and make use of optimal control sequences of MPC, resulting in more flexible triggering schemes with longer inter-execution times. The effectiveness of the proposed approaches is verified by numerical examples and comparative studies with existing work. Recursive feasibility of MPC and robust stability of linear discrete-time systems are theoretically analyzed. These results provide some new insights  for the design of event-triggered robust MPC.</p>