Showing papers by "Wpmh Maurice Heemels published in 2017"

Output-Based and Decentralized Dynamic Event-Triggered Control With Guaranteed $\mathcal{L}_{p}$- Gain Performance and Zeno-Freeness

Abstract: Networked control systems are often subject to limited communication resources. By only communicating output measurements when needed, event-triggered control is an adequate method to reduce the usage of communication resources while retaining desired closed-loop performance. In this work, a novel event-triggered control (ETC) strategy for a class of nonlinear feedback systems is proposed that can simultaneously guarantee a finite $\mathcal{L}_{p}$ - gain and a strictly positive lower bound on the inter-event times. The new ETC scheme can be synthesized in an output-based and/or decentralized form, takes the specific medium access protocols into account, and is robust to (variable) transmission delays by design. Interestingly, in contrast with the majority of existing event-generators that only use static conditions, the newly proposed event-triggering conditions are based on dynamic elements, which has several advantages including larger average inter-event times. The developed theory leads to families of event-triggered controllers that correspond to different tradeoffs between (minimum and average) inter-event times, maximum allowable delays and $\mathcal{L}_{p}$ - gains. A linear and a nonlinear numerical example will illustrate all the benefits of this new dynamic ETC scheme.

Event-Triggered Control Systems Under Denial-of-Service Attacks

Abstract: In this paper, we propose a systematic design framework for output-based dynamic event-triggered control (ETC) systems under denial-of-service (DoS) attacks. These malicious DoS attacks are intended to interfere with the communication channel causing periods in time at which transmission of measurement data is impossible. We show that the proposed ETC scheme, if well designed, can tolerate a class of DoS signals characterized by frequency and duration properties without jeopardizing the stability, performance and Zeno-freeness of the ETC system. In fact, the design procedure of the ETC condition allows tradeoffs between performance, robustness to DoS attacks, and utilization of communication resources. The main results will be illustrated by means of a numerical example.

Robust Event-Triggered MPC With Guaranteed Asymptotic Bound and Average Sampling Rate

Abstract: We propose a robust event-triggered model predictive control (MPC) scheme for linear time-invariant discrete-time systems subject to bounded additive stochastic disturbances and hard constraints on the input and state. For given probability distributions of the disturbances acting on the system, we design event conditions such that the average frequency of communication between the controller and the actuator in the closed-loop system attains a given value. We employ Tube MPC methods to guarantee robust constraint satisfaction and a robust asymptotic bound on the system state. Moreover, we show that instead of a given periodically updated Tube MPC scheme, an appropriate event-triggered MPC scheme can be applied, with the same guarantees on constraints and region of attraction, but with a reduced number of average communications.

Output-Based Event-Triggered Control with Performance Guarantees

Abstract: We propose an output-based event-triggered control solution for linear discrete-time systems with a performance guarantee relative to periodic time-triggered control, while reducing the communication load. The performance is expressed as an average quadratic cost and the plant is disturbed by Gaussian process and measurement noises. We establish several connections with previous works in the literature discussing, in particular, the relation to absolute and relative threshold policies. The usefulness of the results is illustrated through a numerical example.

Hybrid integrator design for enhanced tracking in motion control

Abstract: This paper discusses a novel hybrid integrator design that (a) gives improved low-frequency disturbance rejection properties under double-integrator control, but (b) avoids the unwanted occurrence of overshoot and settling effects otherwise resulting from adding an extra linear integrator. The main principle behind this new design is that the resulting hybrid element generates a continuous control output signal based on integrator action when possible, while overall satisfying a sector condition that restricts the input-output behavior to a [0, k h ]-sector, where k h is a positive gain derived from a closed-loop stability argument. In fact, closed-loop stability can be guaranteed on the basis of a circle-criterion-like argument and checked through (measured) frequency response data, thereby avoiding the need for parametric models. The strengths of this new hybrid integrator will be demonstrated experimentally on a wafer stage system of an industrial wafer scanner.

On Lyapunov-Metzler Inequalities and S-Procedure Characterizations for the Stabilization of Switched Linear Systems

Abstract: In this note we present connections between two celebrated tools for the design of stabilising switching laws for continuous-time and discrete-time switched linear systems, namely Lyapunov-Metzler inequalities and S-procedure.

Stability and Performance Analysis of Spatially Invariant Systems with Networked Communication

Abstract: In this paper, tractable stability and performance conditions are presented for systems consisting of an infinite number of spatially invariant, i.e., identical subsystems that are described by (non)linear differential equations and interconnected (partly) through packet-based communication networks. These networks transmit packets asynchronously and independently of each other and are equipped with scheduling protocols that determine which actuator, sensor, or controller node is allowed access to the network. The overall system is modeled as an infinite interconnection of spatially invariant hybrid subsystems. To underline the relevance of this framework, it is shown how two well-known and natural system configurations can be captured in this hybrid modeling framework. Moreover, for the resulting overall infinite-dimensional hybrid system, a proper solution concept is introduced, which is necessary as many standard concepts do not apply as Zeno behavior is inevitable for the systems under study. Based on the proposed hybrid modeling framework, conditions leading to a maximally allowable transmission interval (MATI) for all of the individual communication networks are derived such that uniform global asymptotic stability (UGAS) or $\mathcal {L}_{p}$ -stability of the overall system is guaranteed. Interestingly, by exploiting the interconnection structure, the conditions guaranteeing UGAS or $\mathcal {L}_{p}$ -stability can be stated locally in the sense that they only involve the (local) dynamics of one subsystem in the interconnection and local conditions on the scheduling protocol. Finally, it is shown that in the linear case the derived conditions can even be stated in terms of “local” LMIs, making them amenable for computational verification.

Computing minimal and maximal allowable transmission intervals for networked control systems using the hybrid systems approach

Abstract: A popular design framework for networked control systems (NCSs) is the emulation-based approach combined with hybrid systems analysis techniques. In the rich literature regarding this framework, bounds on the maximally allowable transmission interval (MATI) are provided to guarantee stability properties of the NCS, while the minimal allowable transmission interval (MIATI) is always taken to be (essentially) zero. In this letter, we show for the first time how knowledge of the MIATI can also be exploited in the hybrid systems/emulation-based framework leading to (guaranteed) higher values for the MATI, while still obtaining stability of the NCS.

MAX-consensus in open multi-agent systems with gossip interactions

Abstract: We study the problem of distributed maximum computation in an open multi-agent system, where agents can leave and arrive during the execution of the algorithm. The main challenge comes from the possibility that the agent holding the largest value leaves the system, which changes the value to be computed. The algorithms must as a result be endowed with mechanisms allowing to forget outdated information. The focus is on systems in which interactions are pairwise gossips between randomly selected agents. We consider situations where leaving agents can send a last message, and situations where they cannot. For both cases, we provide algorithms able to eventually compute the maximum of the values held by agents.

MAX-consensus in open multi-agent systems with gossip interactions

Abstract: We study the problem of distributed maximum computation in an open multi-agent system, where agents can leave and arrive during the execution of the algorithm. The main challenge comes from the possibility that the agent holding the largest value leaves the system, which changes the value to be computed. The algorithms must as a result be endowed with mechanisms allowing to forget outdated information. The focus is on systems in which interactions are pairwise gossips between randomly selected agents. We consider situations where leaving agents can send a last message, and situations where they cannot. For both cases, we provide algorithms able to eventually compute the maximum of the values held by agents.

Self-triggered and event-driven control for linear systems with stochastic delays

Abstract: Delays are often present in embedded and networked control loops and represent one of the main sources of performance limitations. In this paper, we propose two aperiodic control strategies to optimize closed-loop performance in the presence of stochastic delays: (i) a self-triggered strategy, in which the deadline to drop data is decided on-line based on the current state; (ii) an event-driven strategy, whereby the control input is updated immediately after the delayed data becomes available, leading in general to faster but time-varying control loops. These schemes are designed and analyzed using a standard LQG framework, which allows for assessing and comparing closed-loop performance. We establish that our self-triggered strategy always achieves a better closed-loop performance than periodic control with an optimal sampling period. Moreover, we provide examples where the event-driven strategy outperforms the self-triggered strategy and examples where the opposite is observed.

Optimal control of a wave energy converter

Abstract: The optimal control strategy for a wave energy converter (WEC) with constraints on the control torque is investigated. The goal is to optimize the total energy delivered to the electricity grid. Using Pontryagin's maximum principle, the solution is found to be singular-bang. Using higher order conditions, the optimal control on the singular arc is found as a function of the state and costate trajectories. Furthermore, it is shown that the transitions between bang and singular subarcs are discontinuous. Based on these findings the results of a numerical direct method are validated. Finally, the optimal control is used to benchmark an existing MPC strategy. It is found that for active control torque constraints the MPC strategy does not result in the discontinuous singular-bang transitions. However, the difference in harvested power is small.

Coverage control for outbreak dynamics

Abstract: In this paper we investigate the problem of containing an outbreak using multiple cooperative agents. We present a general mathematical description of outbreak dynamics, which models the behaviour of many real-world situations including outbreaks of epidemic diseases, wild fires, riots, insect spreads, etc. Based on the outbreak dynamics we provide conditions on the positions of the control agents that guarantee that an outbreak can be contained before a deadline. A coverage control law that maximizes the area in which agents are able to contain a future unknown outbreak is deduced from these conditions. Simulation results illustrate the potential of the approach.

Filtered Split-Path Nonlinear Integrator (F-SPANI) for improved transient performance

Abstract: The recently introduced Split-Path Nonlinear Integrator (SPANI) is designed to improve the transient performance of linear (motion) systems in terms of overshoot. The SPANI was shown to be an effective nonlinear controller to improve transient performance by enforcing the same sign in the integrator action and the error. However, to avoid (fast) switching in the control input in steady-state, conservatism had to be introduced in the SPANI design, thereby limiting the performance. In this paper, this conservatism is removed by introducing a new design, called the Filtered Split-Path Nonlinear Integrator (F-SPANI). This design is based on the inclusion of an additional filter in the phase path, which enables the full potential behind the main idea of the SPANI. The ease of the design and implementation and the potential of the proposed controller are illustrated both in simulation and in experiments on a motion system.

Suboptimal event-triggered control over unreliable communication links with experimental validation

Abstract: We propose an event-triggered control policy for a discrete-time linear system with unreliable actuators' and sensors' links, captured by Bernoulli packet dropout models. The proposed policy is a threshold-based policy by which transmissions occur if a weighted norm of an error state vector exceeds a threshold. The threshold and the weights of the norm depend on the underlying characteristics of the packet dropout model. Such a policy is shown to guarantee a given performance, defined in terms of a quadratic cost, while reducing transmissions. The proposed event-triggered control policy is experimentally validated in the context of remotely steering an omni-directional ground robot along a predefined trajectory over an unreliable wireless network, while keeping transmissions to a minimum.

L 2 -gain analysis of periodic event-triggered systems with varying delays using lifting techniques

Abstract: In this paper we study the stability and L 2 — gain properties of periodic event-triggered control (PETC) systems including time-varying delays. We introduce a general framework that captures these PETC systems and encompasses a class of hybrid systems that exhibit linear flow, aperiodic time-triggered jumps (possibly with different deadlines) and arbitrary nonlinear time-varying jump maps. New notions on the stability and contractivity (L 2 -gain strictly smaller than 1) from the beginning of the flow and from the end of the flow are introduced and formal relationships are deduced between these notions, revealing that some are stronger than others. Inspired by ideas from lifting, it is shown that the internal stability and contractivity in L 2 -sense of a continuous-time hybrid system in the framework is equivalent to the stability and contractivity in l 2 -sense of an appropriate time-varying discrete-time nonlinear system. These results recover existing works in the literature as special cases and indicate that analysing different discrete-time nonlinear systems (of the same level of complexity) than in existing works yield stronger conclusions on the L 2 -gain. At the end of the paper we indicate several extensions of the framework, which even include the possibility of the interjump times depending on the state, such that, for instance, self-triggered control systems can also be included allowing their stability and contractivity analysis. A numerical example is presented showing how stability and contractivity analyses are carried out for PETC systems with delays.

Resource-aware cooperative driving

Abstract: Intelligent Transport Systems (ITS) based on wireless communication have the potential to improve road safety, traffic throughput and fuel consumption. For example, Cooperative Adaptive Cruise Control (CACC) is a promising ITS technology, which exploits vehicle-to-vehicle (V2V) communication to enable the formation of vehicle platoons with small inter-vehicle distances while avoiding amplifications of disturbances (causing ghost traffic jams) along the vehicle string. The control design for such a safety-critical cyberphysical system is, however, challenging. Firstly, the introduction of wireless communication involves inevitable network imperfections, such as a limited communication bandwidth and time-varying transmission delays. Secondly, it is shown that excessive utilization of communication resources jeopardizes the reliability of the communication channel. Especially the latter might restrict the minimum time gap that can be realized safely. As such, to be able to harvest all the benefits of CACC, it is of interest to design resource-aware controller such that only the information, which is actually needed to establish a (string-)stable platoon, is transmitted over the wireless network.