Romain Postoyan

Mahmoud Abdelrahim, Romain Postoyan, Jamal Daafouz et al.

The objective is to design output feedback event-triggered controllers to stabilize a class of nonlinear systems. One of the main difficulties of the problem is to ensure the existence of a minimum amount of time between two consecutive transmissions, which is essential in practice. We solve this issue by combining techniques from event-triggered and time-triggered control. The idea is to turn on the event-triggering mechanism only after a fixed amount of time has elapsed since the last transmission. This time is computed based on results on the stabilization of time-driven sampled-data systems. The overall strategy ensures an asymptotic stability property for the closed-loop system. The results are proved to be applicable to linear time-invariant (LTI) systems as a particular case.

Romain Postoyan, Paulo Tabuada, Dragan Nesic et al.

Event-triggered and self-triggered control have recently been proposed as implementation strategies that considerably reduce the resources required for control. Although most of the work so far has focused on closing a single control loop, some researchers have started to investigate how these new implementation strategies can be applied when closing multiple-feedback loops in the presence of physically distributed sensors and actuators. In this paper, we consider a scenario where the distributed sensors, actuators, and controllers communicate via a shared wired channel. We use our recent prescriptive framework for the event-triggered control of nonlinear systems to develop novel policies suitable for the considered distributed scenario. Afterwards, we explain how self-triggering rules can be deduced from the developed event-triggered strategies.

Mahmoud Abdelrahim, Romain Postoyan, Jamal Daafouz et al.

We present a procedure to simultaneously design the output feedback law and the event-triggering condition to stabilize linear systems. The closed-loop system is shown to satisfy a global asymptotic stability property and the existence of a strictly positive minimum amount of time between two transmissions is guaranteed. The event-triggered controller is obtained by solving linear matrix inequalities (LMIs). We then exploit the flexibility of the method to maximize the guaranteed minimum amount of time between two transmissions. Finally, we provide a (heuristic) method to reduce the amount of transmissions, which is supported by numerical simulations.

Mahmoud Abdelrahim, Romain Postoyan, Jamal Daafouz

Controllers are often designed based on a reduced or simplified model of the plant dynamics. In this context, we investigate whether it is possible to synthesize a stabilizing event-triggered feedback law for networked control systems (NCS) which have two time-scales, based only on an approximate model of the slow dynamics. We follow an emulation-like approach as we assume that we know how to solve the problem in the absence of sampling and then we study how to design the event-triggering rule under communication constraints. The NCS is modeled as a hybrid singularly perturbed system which exhibits the feature to generate jumps for both the fast variable and the error variable induced by the sampling. The first conclusion is that a triggering law which guarantees the stability and the existence of a uniform minimum amount of time between two transmissions for the slow model may not ensure the existence of such a time for the overall system, which makes the controller not implementable in practice. The objective of this contribution is twofold. We first show that existing event-triggering conditions can be adapted to singularly perturbed systems and semiglobal practical stability can be ensured in this case. Second, we propose another technique that combines event-triggered and time-triggered results in the sense that transmissions are only allowed after a predefined amount of time has elapsed since the last transmission. This technique has the advantage, under an additional assumption, to ensure a global asymptotic stability property and to allow the user to directly tune the minimum inter-transmission interval. We believe that this technique is of its own interest independently of the two-time scale nature of the addressed problem. The results are shown to be applicable to a class of globally Lipschitz systems.

Claudio de Persis, Romain Postoyan

The objective is to design distributed coordination strategies for a network of agents in a cyber-physical environment. In particular, we concentrate on the rendez-vous of agents having double-integrator dynamics with the addition of a damping term in the velocity dynamics. We start with distributed controllers that solve the problem in continuous-time, and we then explain how to implement these using event-based sampling. The idea is to define a triggering rule per edge using a clock variable which only depends on the local variables. The triggering laws are designed to compensate for the perturbative term introduced by the sampling, a technique that reminds of Lyapunov-based control redesign. We first present an event-triggered solution which requires continuous measurement of the relative position and we then explain how to convert it to a self-triggered policy. The latter only requires the measurements of the relative position and velocity at the last transmission instants, which is useful to reduce both the communication and the computation costs. The strategies guarantee the existence of a uniform minimum amount of times between any two edge events. The analysis is carried out using an invariance principle for hybrid systems.

Robert H. Moldenhauer, Karl Worthmann, Romain Postoyan et al.

We study closed-loop stability and suboptimality for MPC and infinite-horizon optimal control solved using a surrogate model that differs from the real plant. We employ a unified framework based on quadratic costs to analyze both finite- and infinite-horizon problems, encompassing discounted and undiscounted scenarios alike. Plant-model mismatch bounds proportional to states and controls are assumed, under which the origin remains an equilibrium. Under continuity of the model and cost-controllability, exponential stability of the closed loop can be guaranteed. Furthermore, we give a suboptimality bound for the closed-loop cost recovering the optimal cost of the surrogate. The results reveal a tradeoff between horizon length, discounting and plant-model mismatch. The robustness guarantees are uniform over the horizon length, meaning that larger horizons do not require successively smaller plant-model mismatch.