Model-based periodic event-triggered control for linear systems

Periodic event-triggered control (PETC) is a control strategy that combines ideas from conventional periodic sampled-data control and event-triggered control. By communicating periodically sampled sensor and controller data only when needed to guarantee stability or performance properties, PETC is capable of reducing the number of transmissions significantly, while still retaining a satisfactory closed-loop behavior. In this paper, we will study observer-based controllers for linear systems and propose advanced event-triggering mechanisms (ETMs) that will reduce communication in both the sensor-to-controller channels and the controller-to-actuator channels. By exploiting model-based computations, the new classes of ETMs will outperform existing ETMs in the literature. To model and analyze the proposed classes of ETMs, we present two frameworks based on perturbed linear and piecewise linear systems, leading to conditions for global exponential stability and ℓ2ℓ2-gain performance of the resulting closed-loop systems in terms of linear matrix inequalities. The proposed analysis frameworks can be used to make tradeoffs between the network utilization on the one hand and the performance in terms of ℓ2ℓ2-gains on the other. In addition, we will show that the closed-loop performance realized by an observer-based controller, implemented in a conventional periodic time-triggered fashion, can be recovered arbitrarily closely by a PETC implementation. This provides a justification for emulation-based design. Next to centralized model-based ETMs, we will also provide a decentralized setup suitable for large-scale systems, where sensors and actuators are physically distributed over a wide area. The improvements realized by the proposed model-based ETMs will be demonstrated using numerical examples.