Maximum Allowable Sampling Period Research Articles

Stability Analysis of Sampled-Data Systems Based on Sawtooth-Characteristic-Based Hierarchical Integral Inequality.

The aim of this article is to investigate the stability of sampled-data systems (SDSs) by introducing a sawtooth-characteristic-based hierarchical integral inequality (SCBHII) and to obtain the maximum allowable sampling period that maintains the stability of the system. First, by associating the sawtooth characteristics of the input delay in SDSs with free matrices, an SCBHII is proposed; its accuracy improves as the hierarchy increases. Subsequently, a high-order two-sided looped-functional, which considers both the sampling multi-integral states and the sawtooth pattern, is introduced to cater to the aforementioned inequality. In addition, the system variables are augmented by sawtooth pattern-related terms, which eliminates the need for additional secondary processing when determining the negative-definiteness of derivatives with high-order terms. By combining the high-order two-sided looped-functional with the proposed SCBHII, a stability criterion for SDSs with reduced conservatism is achieved, presented in the form of linear matrix inequalities. The proposed inequality technique and the stability criterion are shown to be effective and superior through three numerical examples and a real-world simplified power market model.

Sampled-data observer design for Linear Kuramoto–Sivashinsky systems with non-local output

The aim of this paper is to provide a novel systematic methodology for the design of sampled-data observers for Linear Kuramoto–Sivashinsky systems (LKS) with non-local outputs. More precisely, we extend the systematic sampled-data observer design approach which is based on the use of an Inter-Sample output predictor to the class of LKS systems. By using a small-gain methodology we provide sufficient conditions ensuring the Input-to-Output Stability property of the estimation errors in the presence of measurement noise. Our Inter-Sample output predictor contains a tuning term which can enlarge significantly the Maximum Allowable Sampling Period.

Predictor-Based Global Sampled-Data Output Feedback Stabilization for Nonlinear Uncertain Systems Subject to Delayed Output

In this article, we address the problem of global sampled-data output feedback stabilization for a class of nonlinear uncertain systems with delayed output using the continuous-discrete method. Thanks to the prediction technique and feedback domination method, a novel coupled design method of predictor-based continuous-discrete observer and linear controller is proposed when only delayed sampled-data output is accessible. The proposed predictor-based observer can effectively estimate the unknown state by compensating the influences of sampling and output delay. The main advantage of the proposed control method is that the full state information and accurate model nonlinearities do not need to be known any more. The global exponential stability of the overall hybrid control system can be ensured when there hold some sufficient conditions with respect to the maximum allowable sampling period and output delay.

Periodic Event-Triggered Networked Control Systems Subject to Large Transmission Delays

This article studies periodic event-triggered networked control for nonlinear systems, where the plants and controllers are connected by multiple independent communication channels. Several network-induced imperfections are considered simultaneously, including time-varying intersampling times, sensor node scheduling, and especially, large time-varying transmission delays, where the transmitted signal may arrive at the destination node after the next transmission occurs. A new hybrid system approach is provided to model the closed-loop system that contains all communication related behavior. Then, by constructing new storage functions on the system state and updating errors, the relationship between the maximum allowable sampling period and maximum allowable delay number in sampling is analyzed, where the latter denotes how many inter-sampling periods can be included in one transmission delay. Moreover, to efficiently reduce unnecessary transmissions, a new dynamic event-triggered control scheme is proposed, where the event-triggering conditions are detected only at aperiodic and asynchronous sampling instants. From emulation-based method, where the controllers are initially designed by ignoring all the network-induced imperfections, sufficient conditions on the dynamic event-triggered control are given to ensure closed-loop input-to-state stability with respect to external disturbances. Finally, two nonlinear examples are simulated to illustrate the feasibility and efficiency of the theoretical results.

Sampled-Data Dynamic Output Feedback Consensus Control of Multi-Agent Systems

This paper investigates the consensus problem of multi-agent systems (MAS) with sampled-data dynamic output feedback (DOF) control. A distributed DOF control law is designed by utilizing sampled relative output information between neighboring agents, and the sampling period can be asynchronous. For the purpose of consensus analysis and appropriately choosing sampling period, a closed-loop system model with hybrid dynamics is constructed, which incorporates flow/jump dynamics and the sampling period. Based on this model, Lyapunov-based analysis is presented and stability conditions are formally developed. Compared with the existing works, observer design is not required and only sampled relative output information is used, and moreover, the maximum allowable sampling period (MASP) can be explicitly computed. Finally, illustrative examples are provided to demonstrate effectiveness of the proposed DOF control method.

Event-Triggered Control for Switched Systems With Denial-of-Service Attack

This article studies the stabilization problem for switched systems in the presence of denial-of-service (DoS) attack using the event-triggered scheme. Unlike the traditional switching signal design with DoS attack, some challenges arise in the joint influence on the constraints of DoS duration/frequency, and the asynchronous behavior caused by the controller and the subsystem mode. To this end, a novel multiple Lyapunov function involving the joint effects of DoS attack and controller mode is constructed. This allows that there are no events between two consecutive switching instants. By incorporating the dwell-time switching signal with the event-triggered scheme, the considered system can be globally exponentially stabilizable when the frequency and duration of DoS attack meet certain requirements. It also shows that apart from the codesign associated with the event-triggered parameters with controller gain, the maximum allowable sampling period can be offline calculated. Moreover, the Zeno behavior is eliminated by calculating a lower bound of the event-triggered interval, over which the DoS attack is inactive. Finally, simulations are carried out to verify the effectiveness of the theoretical results.

Periodic Event-Triggered Control for a Class of Nonminimum-Phase Nonlinear Systems Using Dynamic Triggering Mechanism

In this paper, the output feedback based periodic event-triggered control problem is considered for a class of nonminimum-phase nonlinear systems via dynamic event-triggering mechanism. When only the sampled-data output is known, a new periodic event-triggered control method is proposed via output feedback and the control input updates based on a discrete-time dynamic event-triggering condition. Despite the unstable zero dynamics, the proposed control method can asymptotically stabilize the hybrid control systems by closing the loop only when it is necessary. In contrast to the continuous-time static one, the proposed dynamic triggering condition has several advantages including the easier digital implementation and the larger average inter-event time interval. The delicate analysis gives the explicit expression of the maximum allowable sampling period, and the global asymptotic stability can be achieved for the hybrid control systems. Finally, the effectiveness of the proposed periodic event-triggered control method is verified by a numerical simulation.

Predictor-based periodic event-triggered control for nonlinear uncertain systems with input delay

In this paper we investigate the problem of predictor-based periodic event-triggered control for a class of nonlinear uncertain systems subject to input delay. When only sampled-data output is available, a novel predictor-based continuous-discrete observer is first designed to estimate system state, and an event-triggered controller is second proposed to globally exponentially stabilize the nonlinear uncertain system. Under the proposed control method, the effects of input delay and sampling of output can be considerably compensated thanks to prediction technique. As a byproduct, the Zeno behavior is avoided in nature since the proposed event-triggering mechanism is detected in the form of discrete-time. Some sufficient stability conditions on maximum allowable sampling period and input delay are presented by using feedback domination technique and small-gain argument.

Efficient stability analysis approaches for nonlinear weakly-hard real-time control systems

This article considers the stability analysis of nonlinear control systems with failures in the feedback loop that satisfy weakly-hard real-time (WHRT) constraints. Such WHRT constraints are window-based guarantees like for example, that the feedback loop is at least closed for n times in each window of m sampling times. WHRT constraints can, e.g., describe the packet loss properties of a communication network. We consider two different actuation strategies to deal with failures in the feedback loop: holding the last received input or setting the input to zero if no new input arrives. We present stability analysis procedures for both strategies. The procedures are based on the emulation of a sampled-data controller from continuous-time feedback. For the hold strategy, we use a graph description for the WHRT constraints and a modified version of the Viterbi algorithm to bound a Lyapunov function candidate. For the zero strategy, we employ a bound on the evolution of the Lyapunov function candidate for zero input. For both strategies, efficient stability analysis procedures based on non-monotonic Lyapunov functions are derived. In addition, we demonstrate how switched controllers, that switch depending on the past dropout sequence, can be used for the hold strategy. Such switched controllers can significantly increase the maximum allowable sampling period for the hold strategy. The proposed approaches are illustrated with a numerical example.

Leader-following consensus for multi-agent systems with nonlinear dynamics subject to additive bounded disturbances and asynchronously sampled outputs

This paper is concerned with the leader-following consensus problem for a class of Lipschitz nonlinear multi-agent systems with uncertain dynamics, where each agent only transmits its noisy output, at discrete instants and independently from its neighbors. The proposed consensus protocol is based on a continuous-discrete time observer, which provides a continuous time estimation of the state of the neighbors from their discrete-time output measurements, together with a continuous control law. The stability of the multi-agent system is analyzed with a Lyapunov approach and the exponential practical convergence is ensured provided that the tuning parameters and the maximum allowable sampling period satisfy some inequalities. The proposed protocol is simulated on a multi-agent system whose dynamics are ruled by a Chua’s oscillator.

Observer design for linear models of multi-rate asynchronous aerospace systems

This paper proposes an optimization-based computational approach to design multi-rate observers for linear models of aerospace systems with asynchronous measurements. A case study on the estimation of the state of an autonomous quadrotor UAV around its hovering operating point will be used as an example of the applicability of the proposed method. There are two theoretical contributions of the proposed method. The first is the derivation of a set of Linear Matrix Inequalities (LMIs) for the design of linear observers yielding convergence of the state estimation error given the maximum allowable sampling period (MASP) for each sensor. The second contribution is to propose an optimization problem subject to LMIs for finding the MASPs that guarantee exponential stability of the estimation error. The two contributions enable the analysis and design of multi-rate observers for systems with linear models, including quadrotor UAVs around a hovering operating point. The examples show a very intuitive result: as the sampling frequency of one sensor decreases, another sensor must sample faster to guarantee convergence of the estimated state to the real state. Simulations of a quadrotor with 12 states and 9 measurements show the effectiveness of the approach.

Consensus for hybrid multi-agent systems with pulse-modulated protocols

We consider consensus in this paper for hybrid multi-agent systems (HMASs) consisting of continuous-time dynamic agents and discrete-time dynamic agents via designing pulse-modulated protocols. By assuming all the agents communicate with its neighbors only at some sampling instants, and the input of each continuous-time agent is determined by a pulse function, the consensus for first-order HMASs and second-order HMASs are addressed, respectively. According to the model transformation, stochastic matrix theory and the mathematical analysis technique, some sufficient criteria for consensus of these two types of HMASs are derived where it shows that the consensus in the considered HMASs can be achieved when the network structure, pulse function and sampling period respectively satisfy some suitable conditions. And, an algorithm is presented to evaluate the maximum allowable sampling period for achieving consensus. Finally, three numerical simulation examples are performed to validate the main theoretical results.

Output Feedback Control for Active Suspension Electro-Hydraulic Actuator Systems With a Novel Sampled-Data Nonlinear Extended State Observer

In this paper, an output feedback controller based on a novel sampled-data nonlinear extended state observer (SDNLESO) is proposed for an active suspension electro-hydraulic actuator (ASEHA) system to address the heavy nonlinearities, model uncertainties and sampled-data behavior. The designed controller only requires little prior knowledge about the controlled system for the purpose of position tracking. The SDNLESO, integrating a novel nonlinear extended state observer and an output predictor, is developed to simultaneously and continuously estimate the unmeasurable states and total disturbance for an error dynamic system rather than the original ASEHA system, where the actual discrete displacement tracking error between measurement output and the reference signal serves as the observer input. Then, a compensated controller is synthesized based on the obtained estimates, which is robust against the matched and mismatched disturbances of the system while being able to ensure an expected transient tracking performance and final tracking accuracy. By constructing weighted error system and using the geometric homogeneity theory, the SDNLESO convergence is proven, while the maximum allowable sampling period is derived theoretically for guiding the selection of the actual sampling interval. Moreover, the closed-loop system stability and the tracking error exponential convergence are guaranteed within the Lyapunov framework. Finally, a number of practical experiments are carried out on the ASEHA system test platform. The results show that the proposed control method is applicable and valid for nonlinear and uncertain ASEHA system despite the existence of a large actuator area ratio.

Observer based leader-following consensus of second-order multi-agent systems with nonuniform sampled position data

This paper deals with the leader-following consensus problem of multi-agent systems with the consideration that each agent can only transmit its position state to the neighbors at irregular discrete sampling times. In the proposed algorithm, a continuous-discrete time observer is designed for the continuous estimation of both position and velocity from the discrete position information of the neighbors. These estimated states are then used for designing a continuous control law which solves the leader-following consensus problem. Moreover, the dynamics of the leader is not fixed and can be controlled through an external input. The stability analysis has been carried out by employing the Lyapunov approach which provides sufficient conditions to tune the parameters according to the maximum allowable sampling period. The developed algorithm has been simulated and then tested on an actual multi-robot system consisting of three differential drive wheeled robots. Both simulation and hardware results validate the effectiveness of the control algorithm.

Explicit Computation of Sampling Period in Periodic Event-Triggered Multiagent Control Under Limited Data Rate

This paper investigates the coordination of nonlinear sampled-data multiagent systems subject to a data rate constraint. The purpose is to design resource-efficient communication and control strategies that guarantee exponential synchronization. Two implementation scenarios are considered: the period time-triggered control and the period event-triggered control. One of the main difficulties of the problem is to obtain an explicit formula for the maximum-allowable sampling period (MASP). To this end, an approach on finding the MASP for period time-triggered control is proposed first. Then, an asynchronous period event-triggered control strategy is formulated, and a communication function and a control function are designed for each agent to determine, respectively, whether the sampled state and control input should be transmitted at each sampling instant. Finally, the constraint of the limited data rate is considered. An observer-based encoder–decoder and a finite-level quantizer are designed, respectively, for the sensor-controller communication and the controller-actuator communication such that a certain constraint on the data rate is satisfied. It is shown that exponential synchronization can still be achieved in the presence of the data-rate constraint. A simulation example is given to illustrate the effectiveness of the theoretical results.

Polynomial LPV approach to robust H ∞ control of nonlinear sampled-data systems

This paper addresses -gain analysis and robust control of nonlinear sampled-data systems described by a polynomial linear parameter varying (PLPV) model. First, conditions for -gain analysis of sampled-data PLPV systems are derived using a modified Krasovskii functional in which the distance between the real and measured parameters are considered as uncertainties. The resulting conditions are formulated in terms of parameterised linear matrix inequalities (PLMI). Second, a solution approach for satisfying PLMI conditions over the set of whole parameters and uncertainties is proposed using the sum-of-squares decomposition method. Third, conditions for robust sampled-data controller synthesis for nonlinear systems described by PLPV models are derived in terms of parameterised bilinear matrix inequalities (PBMI) with the maximum allowable sampling period as the parameter. To make the resulting bilinear matrix inequality (BMI) problems tractable, an iterative algorithm is developed and utilised to solve the problem. Finally, the effectiveness of the proposed approach is verified using several real-world examples.

H∞ Synchronization of Networked Master-Slave Oscillators With Delayed Position Data: The Positive Effects of Network-Induced Delays.

This paper is concerned with H∞ synchronization of coupled oscillators in a master-slave framework, in which the oscillators cannot be stabilized by nondelayed sampled position data, but can be stabilized by sampled position data with delays restricted by nonzero lower bounds and upper bounds. A configuration of networked master-slave oscillators with a remote controller is first constructed. Then the positive effects of delays on master-slave synchronization are investigated. Some delay-dependent H∞ synchronization criteria are derived by constructing augmented discretized Lyapunov-Krasovskii functionals for determinate sampling and stochastic sampling, respectively. The controller can be designed by solving a set of linear matrix inequalities. Finally, two numerical examples are given to verify the theoretical results. It is shown that the maximum allowable sampling period in the case of stochastic sampling is larger than the one in the case of determinate sampling. Stochastic sampling can also provide a tradeoff between network-induced delays and the sampling periods, enhancing the master-slave synchronization performance.

Stability analysis and design of nonlinear sampled‐data systems under aperiodic samplings

SummaryIn this paper, the problem of exponential stability analysis and the design of sampled‐data nonlinear systems have been studied using a polytopic linear parameter‐varying approach. By means of modeling a new double‐layer polytopic formulation for nonlinear sampled‐data systems, a modified form of piecewise continuous Lyapunov‐Krasovskii functional is proposed. This approach provides less conservative robust exponential stability conditions by using Wirtinger's inequality in terms of linear matrix inequalities. The distances between the real continuous parameters of the plant and the measured parameters of the controller are modeled by convex sets, and the analysis/design conditions are given at the vertices of some hyper‐rectangles. In order to get tractable linear matrix inequality conditions for the stabilization problem, we performed relaxation by introducing a slack variable matrix. Under the new stability criteria, an approach is introduced to synthesize a sampled‐data polytopic linear parameter‐varying controller considering some constraints on the location of the closed‐loop poles in the presence of uncertainties on the varying parameters. It is shown that the proposed controller guarantees the exponential stability of the closed‐loop system for aperiodic sampling periods smaller than a known value, ie, maximum allowable sampling period. Finally, the effectiveness of the proposed approach is verified and compared with some state‐of‐the‐art existing approaches through numerical simulations.

Optimal Sensor and Actuator Scheduling in Sampled-Data Control of Spatially Distributed Processes

This work presents an optimization-based methodology for the placement and scheduling of measurement sensors and control actuators in spatially-distributed processes with low-order dynamics and discretely-sampled output measurements. Initially, a sampled-data observer-based controller, with an inter-sample model predictor, is designed based on an approximate finite-dimensional system that captures the infinite-dimensional system’s dominant dynamics. An explicit characterization of the interdependence between the stabilizing locations of the sensors and actuators and the maximum allowable sampling period is obtained. Based on this characterization, a constrained finite-horizon optimization problem is formulated to obtain the sensor and actuator locations, together the corresponding sampling period, that optimally balance the tradeoff between the control performance requirements on the one hand, and the demand for reduced sampling, on the other. The objective function penalizes both the control performance cost, expressed in terms of the response speed and the control effort, and the sampling cost, expressed in terms of the sampling frequency. The optimization problem is solved in a receding horizon fashion, leading to a dynamic policy that varies the sensor and actuator spatial placement, together with the sampling period, over time. The developed methodology is illustrated through an application to a simulated diffusion-reaction process example.

Estimation of Sampling Period for Stochastic Nonlinear Sampled-Data Systems With Emulated Controllers

This note focuses on determining the value of the maximum allowable sampling period (MASP) that guarantees the stability of stochastic nonlinear sampled-data systems with emulated controllers. Two methods are proposed to compute MASP, one based on sufficient Lyapunov-like conditions on stabilization of stochastic nonlinear systems in mean square and the other from applying Barbalat's Lemma. Comparison studies are made and illustrated for the two methods by a numerical example.