Extension and experimental evaluation of an event-based state-feedback approach

Event-based control aims at reducing the traffic load of the communication network used to implement feedback control. The communication is invoked only if an event indicates that the control error exceeds a certain threshold. This paper extends a state-feedback approach to event-based control published recently and proves that the extended control loop asymptotically reaches the set-point for arbitrary constant disturbances. This control method is applied to a thermofluid process to illustrate the main characteristics of event-based control and to evaluate the closed-loop performance. Experiments with a pilot plant show that the event-based control scheme is robust against severe model uncertainties.     

A timed discrete-event abstraction of continuous-variable systems

The paper concerns continuous-variable systems whose state can only be observed through a quantizer, which indicates the time instant and the direction of the change of the quantized state value. These changes are considered as events. The problem is to find a concise representation of the quantized system, which allows to determine for a given initial event all timed event sequences that the quantized system can generate. Since the quantized system does not possess the Markov property, the modelling aim is to find a semi-Markov process which describes a superset of the event sequences of the quantized system. The paper shows how such a semi-Markov process can be obtained for a given quantized system. The model provides information about the occurrence time of the events and about the probability of the occurrence. The modelling problem and its solution are illustrated by considering a quantized oscillator.     

Discrete reachability of hybrid systems

This paper concerns hybrid systems subject to discrete-event supervisory control. It investigates the discrete reachability, where the hybrid system should be moved from a discrete initial state z init into a given discrete goal state z goal by a sequence of discrete inputs. The reachability analysis is carried out in three steps. First, a discrete-event model of the hybrid system is set up. Stochastic automata are used to describe all state sequences which may be generated by the hybrid system. Such a model is called complete. Second, methods for the reachability analysis of stochastic automata are elaborated which concern a weak and a strong condition for reachability. Third, these methods are applied to the hybrid system. It is shown that the reachability of the automaton implies the discrete reachability of the hybrid system, because the model is complete. Therefore, the weak and the strong condition for reachability of the stochastic automaton yield a necessary and a sufficient condition for discrete reachability of the hybrid system.     

Complete synchronisation of linear oscillator networks

Oscillators with individual natural frequencies are not synchronisable by diffusive couplings, which are usually used for solving consensus and synchronisation problems. This article proves that, however, such oscillators can be synchronised by dynamical couplings if and only if the interconnection network includes local dynamical units with integrator dynamics. A necessary and sufficient synchronisation condition shows that oscillators with arbitrary positive parameters are synchronised by any coupling network that possesses a spanning tree and has sufficiently large coupling strength. Simulation results illustrate the results of this article.     

Qualitative model based fault diagnosis using a threshold level

This paper deals with the effect of using a threshold level in qualitative model based fault diagnosis algorithm. By introducing the concept of α-consistency, a fault diagnosis algorithm is presented in this paper. In this method for each measured input and output signal, a measure of consistency is computed for each fault. If this measure is less than a threshold level α, then the observed input and output are not consistent with the fault. Therefore the fault is excluded from the set of the possible faults. In order to illustrate the proposed method, this algorithm is applied on a 2-tank system. The obtained results show that the faults can be isolated faster. Furthermore to illustrate the diagnosis reliability, a confidence interval is defined. This interval determines the probability of correct fault diagnosis.     

Small-world architecture of networked control systems

The paper proposes a method to generate communication structures for networked controllers that have the small-world property. This property, which is known from complex networks, means that in a large ring of agents, a small number of shortcut links substantially improve the performance of the overall system. To investigate the consequences of this property for control systems, the paper considers multi-agent systems with leader–follower structure where additional communication links among the local control stations are selected by the agents in a random way. The performance of the overall system is evaluated in terms of the delay with which the agents react on leader commands. The main result provides a relation between the probability p of the existence of additional edges in the communication graph and the performance of the overall system. It is proved that for any probability p > 0 there exists an upper bound of the performance index and that this bound is independent of the number of agents. Furthermore, a quantitative analysis shows that it is sufficient to connect the agents with a very low probability p ≈ 10% in order to get a satisfactory performance. These results are illustrated by a robot formation example.     

Integral-based event-triggered control for multi-agent systems with general linear dynamics

ABSTRACT

This paper proposes an integral-based event-triggered control strategy to solve the consensus problem of multi-agent systems with general linear dynamics. We first consider the leader-following consensus problem where the communication topology has a directed spanning tree with the leader as the root. It is proved that under the proposed strategy leader-following consensus is guaranteed and the inter-event intervals are lower bounded by positive constants. Then, the leaderless consensus problem of multi-agent systems is investigated under directed topology. We show that consensus is achieved and no Zeno behaviour occurs. Simulation results verify the effectiveness of the obtained results.