Sampling Time Instants Research Articles

Distributed Consensus Filtering Over Sensor Networks With Asynchronous Measurements

ABSTRACTIn practical sensor networks, sensor nodes may operate with different sampling periods and initial sampling time instants, and their observations may also be nonuniform. Unfortunately, the research on distributed state estimation problems over such asynchronous sensor networks is very limited. Thus, this article focuses on the distributed consensus filtering problem over sensor networks with asynchronous measurements. First, the asynchronous measurement from each sensor is synchronized by the continuous‐time state evolution equation to a unified filtering fusion time instant within a given filtering period. After measurement synchronization, the statistical characteristics of measurement noise change. The cross‐correlations between the converted measurement noises are analyzed, as well as one‐step correlations between the converted measurement noises and the process noise. Second, an optimal asynchronous distributed consensus filter is designed based on synchronization measurements under the criterion of minimum mean‐square error with the above correlations between various types of noises taken into account. Meanwhile, a suboptimal distributed consensus filtering algorithm is further proposed to reduce computational complexity. Finally, based on the Lyapunov function method, the stability of the estimation error is theoretically demonstrated with an appropriate selection of consensus filtering gain and validated through simulations.

Event-triggered design for optimal output consensus of high-order multi-agent systems

In this paper, we study the optimal output consensus problem for networked linear multi-agent systems. Existing distributed algorithms usually rely on continuous communication among neighbouring agents or continuous update of each agent's local controller. To save communication and computation resources, we apply event-triggered technique to this optimal output consensus problem. We first constructively develop an event-triggered algorithm with a set of applicable parameters relying on event-triggered communication and control and show its effectiveness in solving the problem by rigorous proofs. Then we extend it to the case where the triggering conditions only have to be checked in some sampling time instants. Two simulation examples are given to illustrate the efficacy of our designs.

Sampled-data static output feedback robust MPC for LPV systems with bounded disturbances

This paper investigates a sampled-data static output feedback robust model predictive control (MPC) approach for continuous-time linear parameter varying (LPV) systems with unknown system states and bounded disturbances. Between two successive sampling time instants, it is assumed that the controlled LPV systems evolve in continuous-time, and the control inputs are piecewise constant. The robust stability conditions and control input constraints on the closed-loop system are considered in the formulated robust MPC optimization. The constraints in the formulated robust MPC optimizations are formulated as linear matrix inequalities (LMIs) and solved as convex optimization. The designed sampled-data static output feedback robust MPC optimization has a simple structure and directly optimizes output feedback controller. Furthermore, the system state constraint sets are on-line updated over the sampling interval. The designed sampled-data static output feedback robust MPC approach has the property of recursive feasibility, and can guarantee robust stability of the controlled continuous-time LPV systems. A simulation example is given to illustrate the effectiveness of the approach.

Asynchronous sampled-data control for connected vehicles with heterogeneous delays

This study investigates an asynchronous sampled-data control problem of vehicular platoons, with heterogeneous sampling, subjected to actuator delays. Without a synchronized clock, a completely asynchronous sampled-data controller is designed for each follower, where the state of the ith follower itself and its neighboring vehicles are sampled at their own sampling time instants. The caused closed-loop tracking error dynamics for the entire platoon considering the effect of the nonuniform sampling time intervals, heterogeneous vehicle dynamics, inter-vehicle topology and heterogeneous time delays. To simplify the stability analysis and controller design, the tracking-error dynamics of the entire platoon are decomposed into individual subsystems with reduced-order dynamics. Based on Lyapunov stability theory, the optimal conditions are explored to design an asynchronous sampled-data controller to guarantee the desired stability performance. Moreover, the exact values for the maximum allowable sampling interval and time delay are calculated for each follower using the designed feedback controller gain. The proposed asynchronous sampled-data control method is extended to a vehicular platoon using an event-based sampling scheme. Numerical examples are used to verify the effectiveness of the proposed sampled-data control method.

Sampled-Data-Based Distributed Output Feedback Leader–Following Consensus for Time-Delay Multiagent Systems

This paper addresses the distributed output feedback leader-following consensus problem for high-order nonlinear multiagent systems (MASs) with time delays and disturbances under the directed network. Using sampled relative outputs to neighbors and the discrete control input, the continuous-discrete time compensator is constructed in each agent to compensate for the consensus errors, where the sampling time instants can be asynchronous and aperiodic without exceeding an explicit upper bound of sampling intervals. Based on the compensator, we propose a co-design algorithm for constructing the dynamic event-triggered protocol with a corresponding event-triggering mechanism which is a combination of discrete-time control input, continuous dynamic variables of each agent's own compensator, and a given threshold. The proposed methods can not only achieve consensus tracking under the effects of time delays in states and communications but also implement the discrete-time execution of measurement, communication, and control. Based on the novel lemmas, it is proved that the resulting closed-loop consensus error system is globally stable. Finally, a simulation is given to illustrate the effectiveness of proposed methods.

Data-driven predictive point-to-point iterative learning control

Integrating the idea of predictive control and point-to-point iterative learning control, this paper presents a data-driven predictive point-to-point iterative learning control scheme for a class of unknown repetitive non-affine nonlinear SISO systems. The tracking task is driven by the optimal control input sequence generated by the proposed algorithm, and the tracking errors at the specified sampling time instants are minimized. The advantages of this scheme are that the structure of the controller and its stability analysis both are based on an equivalent dynamic linearization data model of the nonlinear system, and the proposed scheme does not involve the operation of matrix inversion. Numerical simulations verify the effectiveness of this method.

Event-Triggered Stabilizing Bit Rate Conditions for an n-Dimensional Linear System With i.i.d. Feedback Dropouts.

This article aims to stabilize an n -dimensional linear time-invariant (LTI) system, whose feedback packets are transmitted through a digital communication network. The digital network suffers from network delay and independent and identically distributed (i.i.d.) feedback dropouts, which may destabilize the system. The coupling among multiple state variables may further harm the stability of the system. In order to deal with these issues and save the occupied bandwidth of the feedback network, we propose a periodic event-triggering strategy. In our strategy, the state is measured periodically, but only quantized and transmitted when a certain condition is triggered. By well balancing the state coupling and making full use of both the information inside transmitted feedback packets and the one carried by sampling time instants, our strategy can maintain the desired mean square stability at a lower bit rate than conventional periodic sampling policies. The obtained stabilizing bit rate conditions are determined by the processing and network delays, the dropout rate, and the unstable eigenvalues of the system matrix, but independent of the process noise. Moreover, the lack of the direct state access does not incur any additional stabilizing bit rate. Simulations are done to confirm the effectiveness of the obtained stabilizing bit rate conditions.

On the Properties of a Class of Impulsive Competition Beverton–Holt Equations

This paper is devoted to a type of combined impulsive discrete Beverton–Holt equations in ecology when eventual discontinuities at sampling time instants are considered. Such discontinuities could be interpreted as impulses in the corresponding continuous-time logistic equations. The set of equations involve competition-type coupled dynamics among a finite set of species. It is assumed that, in general, the intrinsic growth rates and the carrying capacities are eventually distinct for the various species. The impulsive parts of the equations are parameterized by harvesting quotas and independent consumptions which are also eventually distinct for the various species and which control the populations’ evolution. The performed study includes the existence of extinction and non-extinction equilibrium points, the conditions of non-negativity and boundedness of the solutions for given finite non-negative initial conditions and the conditions of asymptotic stability without or with extinction of the solutions.

Discrete‐time sliding mode output tracking control for a class of nonlinear perturbed systems

SummaryThe output tracking problem for a class of sampled‐data nonlinear systems exposed in nonlinear block controllable form is faced. This article considers both matched and unmatched perturbations. To formulate a desired sliding manifold on which the impact of unmatched perturbation is attenuated, the block control technique combined with the perturbation estimation, is implemented. A discrete‐time sliding mode nonswitching controller is synthesized such that the closed‐loop system state is driven toward a vicinity of the designed sliding manifold and stays there for all sampled time instants, avoiding chattering, and reducing the matched perturbation effect. The effectiveness of the proposed technique is confirmed by simulation.

On the convergence of event-triggered distributed algorithm for economic dispatch problem

The economic dispatch problem (EDP) is a basic problem of energy management in the actual smart grids operation. This paper studies a general EDP of minimizing a sum of local convex cost functions subjected to both local interval constraints and coupling linear constraint over an undirected network. To reduce the amount of computation and interaction, we bring out a fresh event-triggered distributed accelerated primal-dual algorithm, named as ET-DAPDA, with uncoordinated step-sizes for solving the EDP. ET-DAPDA (with respect to the dual updates) incorporates two types of momentum terms into gradient tracking scheme and assumes that each node independently interacts with neighbors only at the event-triggered sampling time instants. Presuming the smoothness and strong convexity cost functions, the linear convergence of ET-DAPDA is analyzed by using the generalized small gain theorem. Moreover, ET-DAPDA strictly excludes the behavior of Zeno-like, thus heavily reducing the interaction cost. ET-DAPDA is studied on 14 bus and 118 bus systems to evaluate its applicabilities. The simulation results of the convergence rate are further compared with the prior art, which proves the superiority of ET-DAPDA.

Sufficient stabilizing bit rate conditions for an [formula omitted]-dimensional nonlinear system based on event triggering

This paper investigates the problem of stabilizing an n-dimensional nonlinear system whose feedback packets are transmitted via the digital network. In the presence of the bounded processing delay and network delay, the sampling time instant of a feedback packet is not the same as its receiving time instant. The larger difference between these time instants, the higher bit rate is required to stabilize the concerned system. Moreover, not only these delays, but also feedback dropouts and process noise will deteriorate the system performance. Thus we propose a model-based event-triggered control method to stabilize the system and save the occupied network bandwidth. Besides the transmission bits inside the feedback packets, their sampling time instants also convey the state information. The proposed event-triggered method can make full use of the feedback packets, especially their receiving time instant information. Compared with the periodic sampling method, our method performs better and requires lower stabilizing bit rates while the desired input-to-state stability can still be ensured. The obtained bit rate conditions only depend on the Lipschitz constant, the upper bounds of the delays and the dropout rate, and are independent of the bounded process noise.

Event-Triggering Interaction Scheme for Discrete-Time Decentralized Optimization With Nonuniform Step Sizes.

In this article, we study the discrete-time decentralized optimization problems of multiagent systems by an event-triggering interaction scheme, in which each agent privately knows its local convex cost function, and collectively minimizes the total cost functions. The underlying interaction and the corresponding weight matrix are required to be undirected connected and doubly stochastic, respectively. To resolve this optimization problem collaboratively, we propose a decentralized event-triggering algorithm (DETA) that is based on the consensus theory and inexact gradient tracking technique. DETA involves each agent interacting with its neighboring agents only at some independent event-triggering sampling time instants. Under the assumptions that the global convex cost function is coercive and has Lipschitz continuous gradient, we prove that DETA steers all agents' states to an optimal solution even with nonuniform constant step sizes. Moreover, our analysis also shows that DETA converges at a rate of O(1/√t) if the step sizes are uniform and do not exceed some upper bounds. We illustrate the effectiveness of DETA on a canonical simple decentralized parameter estimation problem.

Sliding Mode Tracking Control for Nonlinear Sampled-Data Systems with Unmatched Perturbation

The output tracking problem for a class of sampled-data nonlinear systems exposed in Nonlinear Block Controllable (NBC) form is faced. This paper considers both matched and unmatched perturbations. To formulate a desired sliding manifold on which the impact of unmatched perturbation is attenuated, the Block Control technique combined with the perturbation estimation, is implemented. A discrete-time sliding mode non-switching controller is synthesized such that the system state is driven toward a vicinity of the designed sliding manifold and stays there for all sampled time instants, avoiding chattering and reducing the matched perturbation effect. The effectiveness of the proposed technique is confirmed by simulation.

Distributed Event-Triggered Communication Scheme for Economic Dispatch Problem in Power System With Uncoordinated Step-Sizes

Inspired by the distributed economic dispatch problem (EDP) in power system, this paper considers a problem of optimizing a sum of m local convex cost functions on an undirected network of m agents. Each agent in the network privately knows its own local convex objective function and is subjected to both coupling linear constraint and individual box constraints. To be able to reduce the requirements for information exchange among agents, we propose a novel fully event-triggered based distributed primal-dual algorithm for the convex optimization problem. Our algorithm allows the use of uncoordinated step-sizes and assumes that each agent communicates with its neighboring agents (the corresponding variables are updated) only at some independent event-triggered sampling time instants. Under some relatively standard assumptions (strong convexity and smoothness) on the objective functions, our theoretical analysis proves that the proposed algorithm can linearly seek the exact optimal solution when the upper bound of the uncoordinated step-sizes is smaller than a certain constant. We also conduct a clear estimate of the rate. Finally, a simple numerical example on distributed economic dispatch problem in power system is provided to illustrate the effectiveness of our event-triggered based optimization algorithm and validate the correctness of the analysis process.

Model-Based Periodic Event-Triggered Control Strategy to Stabilize a Scalar Nonlinear System

This article focuses on the problem of stabilizing a scalar continuous-time nonlinear system under bounded network delay and process noise. In order to save the feedback network's bandwidth, a model-based periodic event-triggered control policy is utilized to maintain longer intersampling intervals, which are at least as long as the sampling period of periodic policies. Furthermore, the event-triggering condition is only checked intermittently at fixed time instants, i.e., the sampling time instants. Without acknowledgment (ACK), the updating of nominal models at the sensor and at the controller are asynchronous. The two cases, where the network delay is either less than the sampling period or larger than the sampling period, are investigated. In comparison with periodic sampling methods, our scheme can make full use of the received data packets, particularly their sampling time instant information, which yields a lower occupied bit rate while guaranteeing the desired input-to-state stability. Note that the obtained bit rate conditions are only related to the Lipschitz parameter, the bound of network delay, the number of quantization bits, and the sampling period. The bounded process noise will not incur any increase of the stabilizing bit rate under the proposed strategy.

A Dual-Mode Strategy for Performance-Maximisation and Resource-Efficient CPS Design

The emerging scenarios of cyber-physical systems (CPS), such as autonomous vehicles, require implementing complex functionality with limited resources, as well as high performances. This paper considers a common setup in which multiple control and non-control tasks share one processor, and proposes a dual-mode strategy. The control task switches between two sampling periods when rejecting (coping with) a disturbance. We create an optimisation framework looking for the switching sampling periods and time instants that maximise the control performance (indexed by settling time) and resource efficiency (indexed by the number of tasks that are schedulable on the processor). The latter objective is enabled with schedulability analysis tailored for the dual-mode model. Experimental results show that (i) given a set of tasks, the proposed strategy improves the control performances whilst retaining schedulability; and (ii) given requirements on the control performances, the proposed strategy is able to schedule more tasks.

A Simplified Model Predictive Control of Four-Leg Two-Level Inverter

This article proposes current control strategy for four-leg two-level voltage source inverters (VSI). This strategy is based on model predictive control (MPC) approach and presents its comparison with finite control set (FCS) model technique. Besides providing a fast dynamic response, proposed technique replaces complex modulation stage and PI controller being used in earlier classical control techniques. Moreover, the proposed methodology selects the switching sequence which reduces tracking error between output and applied reference currents using cost function optimization. This shows the improvement of system response like FCS model technique. However, FCS model technique results in calculation stress and computation burden; resulting computational delay and extra power consumption by the processor. This problem is solved with the help of proposed single predictive technique which makes the inverter more suitable for large time horizon operations and small sampling time instants. The computational delay is reduced up to 6% compared to the case of FCS-MPC controlled inverter. Performance of proposed simplified technique is analyzed and compared with FCS-MPC controlled system with the help of different types of reference signals. This work will boost the industrial application of four-leg two-level VSI by increasing dynamic response and removing complex modulation stage.

Distributed event‐triggered scheme for economic dispatch in power systems with uncoordinated step‐sizes

Considering potential applications in power systems, economic dispatch problem (EDP) in time-varying balanced communication networks is studied, aiming to minimise the total cost of generating electricity. This is equivalent to dealing with the problem of optimising the sum of local functions while a single generator possesses only its local function. The variables of generators, satisfying some local constraints, are coupled by a linear constraint. In order to resolve the EDP, the authors design a fully distributed primal-dual optimisation algorithm with time-varying uncoordinated step-sizes. In consideration of saving computation and communication resources, an event-triggered scheme is introduced into the algorithm, based on which each generator is only allowed to interact with their neighbouring generators at some independent event-triggered sampling time instants. The proposed algorithm is able to achieve a linear convergence rate under the strong convexity and smoothness of the local objective functions. The Zeno-like behaviour is rigorously excluded, which means that the interval between any two consecutive sampling time instants of each generator is not less than two. Effectiveness of the algorithm and correctness of the theoretical analysis are verified by numerical experiments.

Periodic Event-Triggered Quantization Policy Design for a Scalar LTI System With i.i.d. Feedback Dropouts

This technical note proposes an event-triggered quantization policy design method to stabilize a scalar continuous-time linear time-invariant (LTI) system, whose feedback loop is closed over an unreliable digital communication network. The feedback packets suffer from network delay and may be dropped in an independent and identically distributed (i.i.d.) way. In order to save quantization bit rate, we implement a periodic event-triggering strategy which periodically samples the state and only quantizes and transmits the sampled state when a predefined event is triggered. By making good use of both the information bits and the sampling time instants of the feedback packets, our policy can obtain the desired mean-square stability at a lower bit rate than the conventional time-triggered quantization policies which utilize only the information bits inside the feedback packets. Under our quantization policy, the stabilizing bit rate condition is up to the dropout rate, the processing and network delays and the unstable eigenvalue of the system, and is independent of the bounded process noise.

Sampling-based self-triggered coordination control for multi-agent systems with application to distributed generators

ABSTRACTThis work investigates the coordination control problem for multiple distributed generation (DG) units with a hierarchical control structure. At the secondary control level, an event-triggered power sharing strategy based on the concept of multi-agent consensus has been proposed for the DG coordination control. Unlike existing consensus-based DG control approaches, the proposed control algorithm is based on sampled data. Thus the event triggering and controller updating actions can only be executed at the sampling time instants. To further reduce the amount of communication among DGs, the proposed event-triggered algorithm is extended to a self-triggered algorithm, where the inter-agent communication transmission is no longer required to be executed at each sampling time instant. The case study results show that the self-triggered algorithm can achieve nearly the same performance on DG coordination as that of the event-triggered algorithm, while significantly reduces the amount of communication.