Showing papers by "Wpmh Maurice Heemels published in 2013"

Periodic event-triggered control for nonlinear systems

Abstract: Event-triggered control (ETC) is a control strategy that is especially suited for applications where communication resources are scarce. By updating and communicating sensor and actuator data only when needed for stability or performance purposes, ETC is capable of reducing the amount of communications, while still retaining a satisfactory closed-loop performance. In this paper, an ETC strategy is proposed by striking a balance between conventional periodic sampled-data control and ETC, leading to so-called periodic event-triggered control (PETC). In PETC, the event-triggering condition is verified periodically and at every sampling time it is decided whether or not to compute and to transmit new measurements and new control signals. The periodic character of the triggering conditions leads to various implementation benefits, including a minimum inter-event time of (at least) the sampling interval of the event-triggering condition. The PETC strategies developed in this paper apply to both static state-feedback and dynamical output-based controllers, as well as to both centralized and decentralized (periodic) event-triggering conditions. To analyze the stability and the L2-gain properties of the resulting PETC systems, three different approaches will be presented based on 1) impulsive systems, 2) piecewise linear systems, and 3) perturbed linear systems. Moreover, the advantages and disadvantages of each of the three approaches will be discussed and the developed theory will be illustrated using a numerical example.

Tracking Control for Hybrid Systems With State-Triggered Jumps

Abstract: This paper addresses the tracking problem in which the controller should stabilize time-varying reference trajectories of hybrid systems. Despite the fact that discrete events (or jumps) in hybrid systems can often not be controlled directly, as, e.g., is the case in impacting mechanical systems, the controller should still stabilize the desired trajectory. A major complication in the analysis of this hybrid tracking problem is that, in general, the jump times of the plant do not coincide with those of the reference trajectory. Consequently, the conventional Euclidean tracking error does not converge to zero, even if trajectories converge to the reference trajectory in between jumps, and the jump times converge to those of the reference trajectory. Hence, standard control approaches can not be applied. We propose a novel definition of the tracking error that overcomes this problem and formulate Lyapunov-based conditions for the global asymptotic stability of the hybrid reference trajectory. Using these conditions, we design hysteresis-based controllers that solve the hybrid tracking problem for two exemplary systems, including the well-known bouncing ball problem.

Stability analysis of nonlinear networked control systems with asynchronous communication: A small-gain approach

Abstract: In this paper, we study the stability of decentralized networked control systems (NCSs) in which the sensors, controllers and actuators communicate through a finite number of local networks. These local networks accommodate the communication between local (decentralized) controllers at uncertain transmission times and operate asynchronously and independently of each other. In addition, each of the local networks exhibits communication constraints that require the presence of a protocol that decides which of the (local) network nodes is allowed to transmit its corresponding information at which transmission time. Due to the asynchronous nature of the networks, most existing works on the stability analysis of NCSs are not applicable as their stability characterizations assume that there is only one global communication network, or at least one global coordinator (or clock). Therefore, we present a novel approach that leads to maximal allowable transmission intervals for each of the individual local networks that guarantee the global asymptotic stability of the overall closed-loop system. The approach combines ideas from emulation-based stability analysis for NCSs and techniques from the stability of large-scale systems.

Compensation-based control for lossy communication networks

Abstract: In this paper, we are concerned with the stability analysis and the design of stabilising compensation-based control algorithms for networked control systems (NCSs) that exhibit packet dropouts. In order to increase the robustness against packet dropouts for such NCSs, we propose a new type of model-based dropout compensator, which depends on the local dropout history. Moreover, we provide linear matrix inequality based synthesis conditions for such compensators guaranteeing robust stability. The analysis and design framework includes both worst-case-bound and stochastic models to describe the packet-dropout behaviour in both the sensor-to-controller and the controller-to-actuator channels. Numerical examples demonstrate the significantly improved robustness with respect to packet dropouts using the proposed dropout compensator, compared to using the existing zero strategy and the hold strategy.

On minimum inter-event times in event-triggered control

Abstract: In this paper we study fundamental properties of minimum inter-event times in event-triggered control systems, both in the absence and presence of external disturbances. This analysis reveals, amongst others, that for several popular event-triggering mechanisms no positive minimum inter-event time can be guaranteed in the presence of arbitrary small external disturbances. This clearly shows that it is essential to include the effects of external disturbances in the analysis of the computation/communication properties of event-triggered control systems. In fact, this paper also identifies event-triggering mechanisms that do exhibit these important event-separation properties.

Controllability of a class of bimodal discrete-time piecewise linear systems

Abstract: In this paper we will provide algebraic necessary and sufficient conditions for the controllability/reachability/null controllability of a class of bimodal discrete-time piecewise linear systems including several instances of interest that are not covered by existing works which focus primarily on the planar case. In particular, the class is characterized by a continuous right-hand side, a scalar input and a transfer function from the control input to the switching variable with at most two zeroes whereas the state can be of any dimension. To arrive at the main result, we will make use of geometric control theory for linear systems and a novel result on controllability for input-constrained linear systems with non-convex constraint sets.

Stability analysis of nonlinear networked control systems with asynchronous communication : a small-gain approach

Abstract: In this paper, we study the stability of decentralized networked control systems (NCSs) in which the sensors, controllers and actuators communicate through a finite number of local networks. These local networks accommodate the communication between local (decentralized) controllers at uncertain transmission times and operate asynchronously and independently of each other. In addition, each of the local networks exhibits communication constraints that require the presence of a protocol that decides which of the (local) network nodes is allowed to transmit its corresponding information at which transmission time. Due to the asynchronous nature of the networks, most existing works on the stability analysis of NCSs are not applicable as their stability characterizations assume that there is only one global communication network, or at least one global coordinator (or clock). Therefore, we present a novel approach that leads to maximal allowable transmission intervals for each of the individual local networks that guarantee the global asymptotic stability of the overall closed-loop system. The approach combines ideas from emulation-based stability analysis for NCSs and techniques from the stability of largescale systems.

Extension and evaluation of model-based periodic event-triggered control

Abstract: 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 and performance properties, PETC is capable of reducing the number of transmissions significantly, while still retaining a satisfactory closed-loop behavior. In this paper, we provide an extension of an existing model-based PETC strategy for linear systems by including an (approximate) disturbance model. This extension can further enhance communication savings in the presence of disturbances. In addition, we evaluate the extended model-based PETC strategy by comparing this strategy to the standard model-based PETC and to a model-based periodic time-triggered control (PTTC) strategy. In this PTTC strategy, data is transmitted at fixed sampling times. For the evaluation, we present techniques for stability and l2-gain performance analysis for both the PETC strategy and the PTTC strategy. Finally, the advantage of the (extended) PETC strategy over the PTTC strategy will be demonstrated by providing numerical examples.