Time-varying Sampling Period Research Articles

On robustification of digital event-based controllers for control-affine nonlinear systems

In this paper, the robust digital stabilization problem of nonlinear systems is investigated. In particular, a methodology for the design of robust quantized sampled-data stabilizers updated via an event-triggered mechanism is provided for time-varying control-affine nonlinear systems affected by actuation disturbances and measurement noises. The notion of time-varying steepest descent feedback (TSDF), continuous or not, and the Input-to-State Stability (ISS) redesign methodology are used for the development of the proposed robust event-based digital controller. Under the assumption that the actuation disturbances and measurement noises are bounded with a-priori known bounds and that the amplitude of the measurement noises satisfies a certain condition related to the new added robustification term, the following result is proved: there exist a suitably fast sampling and an accurate quantization of the input/output channels such that the digital implementation of robustified TSDF controllers, updated through a proposed event-triggered mechanism, ensures semi-global practical stability of the related closed-loop system regardless of the above uncertainties. In the methodology here proposed, time-varying sampling periods and the non-uniform quantization of the input/output channels are allowed. Moreover, the theory here developed includes the analysis of the intersampling system behaviour. Possible discontinuities in the function describing the TSDF at hand are also managed. The provided results are validated through a numerical example.

Data-Driven Practical Cooperative Output Regulation Under Actuator Faults and DoS Attacks.

This article addresses the resilient practical cooperative output regulation problem (RPCORP) for multiagent systems subjected to both denial-of-service (DoS) attacks and actuator faults. Fundamentally different from the existing solutions to RPCORPs, the system parameters considered in this article are unknown to each agent, and a novel data-driven control approach is introduced to handle such an issue. The solution starts with developing resilient distributed observers for each follower in the presence of DoS attacks. Then, a resilient communication mechanism and a time-varying sampling period are introduced to, respectively, ensure the neighbor state is available as soon as attacks disappear and to avoid targeted attacks launched by intelligent attackers. Furthermore, a model-based fault-tolerant and resilient controller is designed based on the Lyapunov approach and the output regulation theory. In order to remove the reliance on system parameters, we leverage a new data-driven algorithm to learn controller parameters via the collected data. Rigorous analysis shows that the closed-loop system can resiliently achieve practical cooperative output regulation. Finally, a simulation example is given to illustrate the effectiveness of the achieved results.

Distributed Resilient Secondary Control for DC Microgrids Against Heterogeneous Communication Delays and DoS Attacks

In this article, a cooperative resilient control method for dc microgrid (MG) is proposed to dispel the adverse influences of both communication delays and denial-of-service (DoS) attacks. To avoid that the sampling period is captured by intelligent attackers, a new time-varying sampling period, and an improved communication mechanism are first introduced under the sampling control framework. Based on the designed sampling period and communication mechanism, a resilient secondary controller is designed. It is theoretically shown that the developed method can achieve the goals of bus voltage restoration and current sharing even in the presence of both DoS attacks and heterogeneous communication delays. Finally, a dc MG test system is built in a controller-hardware-in-the-loop testing platform to illustrate and verify the effectiveness of our developed method against both communication delays and DoS attacks.

MAS-Based Distributed Resilient Control for a Class of Cyber-Physical Systems With Communication Delays Under DoS Attacks.

In this article, we investigate the distributed resilient control problem for a class of cyber-physical systems with communication delays under denial-of-service (DoS) attacks. In contrast to the previous DoS attacks results based on multiagent systems (MASs), a new distributed resilient control approach is proposed for more general heterogeneous linear MASs with nonuniform communication delays. Two types of sampled-based observers are, respectively, proposed. Namely, adaptive distributed observers are designed by introducing a buffer mechanism to eliminate the heterogeneous behavior caused by communication delays while adaptive distributed resilient observers are designed by introducing resilient mechanisms to resist the DoS attacks. Furthermore, a time-varying sampling period sequence is provided to prevent the attacker from identifying the sampling period of the system. Based on the developed resilient observers, a controller is developed. It is proved that the considered problem can be solved by the developed method. Finally, a numerical example is given to illustrate the effectiveness of the obtained result.

Tracking control with aperiodic sampling over networks with delay and dropout

This paper introduces a discrete-time technique for output feedback tracking control with aperiodic sampling over networks suffering delay and dropout. Introducing the concept of pseudo sampling, NCS is modelled as a linear parameter varying (LPV) system. Two methods are explained to obtain a convex approximation of the uncertainty region. It is clarified how to perform the approximation to have the uncertainty space as small as possible. Using this uncertainty space, a polytopic approximation is obtained for the LPV model. The approximated model is used to synthesise a controller for set-point tracking and disturbance rejection. An observer is also synthesised based on this model. The simplicity of the model together with a small uncertainty space, results in less conservative LMI conditions. Compared to the existing results, an improved tracking performance is obtained. The final value theorem for discrete-time LTI systems with constant sampling period is extended to time varying sampling periods. This theorem is used to design a feedforward gain for zero steady-state tracking of staircase reference signals.

Guaranteed Cost Control Research for Networked Control System with Time-Varying Sampling Period

In practical industrial applications, the networked control system is often affected by external factors and internal components in operation, which leads to the fluctuation of some data transmitted by the system and reduces the system performance. Therefore, to ensure the normal operation of the system is the key, on this basis, we also need to make the system satisfy certain performance indicators. In this paper, guaranteed cost control for networked control systems with time delay and time-varying sampling period is studied. By constructing a more general system model, we give a design method of guaranteed performance controller to make the closed-loop system asymptotically stable within the allowable range and and satisfies certain performance indicators. Firstly, we construct the reasonable Lyapunov function and performance index function. According to the relevant lemma, the sufficient conditions for the stability of the system are obtained by equivalent transformation of LMI. Then, we design a guaranteed performance controller to minimize the upper bound of the system performance index. In the design process, more free variables are introduced, and the convexity of the function is used for equivalent transformation as far as possible to make the results less conservative. Finally, we use MATLAB to simulate and prove that the method is feasible.

Sampled-data scaled group consensus for second-order multi-agent systems with switching topologies and random link failures

This article studies the sampled-data scaled group consensus problem for second-order multi-agent systems with switching topologies and random link failures. It is assumed that each agent only interacts with its neighbors at discrete sampling instants rather than the complete continuous process. It is further assumed that the phenomenon of random link failures on the communication links is characterized by a Bernoulli stochastic variable. By supposing that each agent has a unique scale, a distributed control protocol that uses the sampled position information of the neighbors is designed. With the assistance of hybrid tools including graph theory and matrix theory, a sufficient condition based on the structures of topologies, the time-varying sampling periods, and the gain parameter, is established to ensure the asymptotic convergence of the agents under the action of sampled distributed protocol. Finally, some simulation instances are provided to verify our theoretical finding.

Fractional-order flight control of quadrotor UAS on vision-based precision hovering with larger sampling period

Fractional-order flight control has a history of nearly 10 years. Fractional-order controllers (FOCs) have been proved to be better in rising time, overshoot and robustness against plant variation. However, there are still not many real applications of FOC in industry. More case studies need to be carried out to accelerate the maturation of FOC. Quadrotor vision-based control often has a large and time-varying sampling period due to drone’s resource limitation. Therefore, our research has been focused on a specific case for drone vision-based control to investigate the benefits of FOC. In this paper, FOC has been first discovered to be able to tolerate larger sampling period than integer-order controllers. This fact has been proved both theoretically and numerically. First of all, the speed model was identified from real flight tests. Then an integral-order proportional, integral and derivative (IOPID) controller and a fractional-order proportional–derivative (FOPD) controller were designed. After that, a stability criteria, optimization method, graphic method and parallel computing techniques were employed to theoretically prove that the largest sampling period of the designed FOC (0.933 s) is much larger than that of the designed integral-order controller (0.546 s). Later, Simulink simulation with identified linear model proved that the FOC can tolerate larger sampling period. Finally, flight tests showed that the designed FOC has a nearly 20% better precision on drone vision-based hovering than the IOC.

Networked Fusion Estimation With Bounded Noises

Most of time-varying systems in fusion estimation are generally modeled without bounded noises. In this paper, we study the distributed fusion estimation problem for networked time-varying systems with bounded noises, where the resource constraints (i.e., bandwidth or energy) and quantization effect are described by a unified model. A new local estimator with time-varying gain is designed by solving a class of convex optimization problems such that the square error of the estimator is bounded. When each local estimate is transmitted to the fusion center over communication networks, the selection probability criterion is derived such that the mean square error of the each compensating state estimate is bounded. Then, a convex optimization problem on the design of an optimal weighting fusion criterion is established in terms of linear matrix inequalities, which can be solved by standard software packages. Target tracking system with time-varying sampling period is given to show the effectiveness of the proposed method.

Digital control and sampling period assignment of multiple plants in networked control systems

This study investigates the problem of sampling period assignment and design of digital state feedback controllers for systems subject to time-varying sampling periods and uncertain delays. The system is controlled through a communication network, where the sampling period and the network-induced delay are bounded in a known interval. The sampled system is described by a linear parameter-varying discrete-time model obtained by means of the Cayley–Hamilton theorem. The proposed discretisation procedure improves the current approaches in the literature and allows the design of controllers that are robust to the delay and depending on the sampling period defined by a scheduling policy in a scenario with concurrent access to the communication network by multiple plants. The gain-scheduled linear quadratic controller is designed by means of linear matrix inequalities. The policy to access the network is dynamic and formulated as an optimisation problem. Numerical experiments illustrate the efficiency and the validity of the proposed approach.

Leader–follower H∞ consensus of linear multi-agent systems with aperiodic sampling and switching connected topologies

This paper is concerned with the distributed H∞ consensus of leader–follower multi-agent systems with aperiodic sampling interval and switching topologies. Under the assumption that the sampling period takes values from a given set, a new discrete-time model is proposed for the tracking error system. For the multi-agent systems with time-varying sampling period, switching topologies and external disturbance, the considered tracking problem is converted to a robust H∞ control problem. With help of the Lyapunov stability theory, a sufficient condition for the existence of mode-dependent controller is established and it guarantees the exponential stability of tracking error system and a prescribed H∞ disturbance attenuation level. The influence of sampling period on the overall control performance is also discussed. Two simulation examples are given to show the effectiveness of the proposed control algorithm.

Chattering analysis for discrete sliding mode control of distributed control systems

The chattering characteristic of sliding mode control is analyzed when it is applied in distributed control systems (DCSs). For a DCS with random time delay and packet dropout, a discrete switching system model with time varying sampling period is constructed based on the time delay system method. The reaching law based sliding mode controller is applied in the proposed system. The exponential stability condition in the form of linear matrix inequality is figured out based on the multi-Lyaponov function method. Then, the chattering characteristic is analyzed for the switching system, and a chattering region related with time varying sampling period and external disturbance is proposed. Finally, numerical examples are given to illustrate the validity of the analysis result.

Stability analysis and stabilization of aperiodic sampled-data systems based on a switched system approach

This paper investigates the stability analysis and controller design problems for aperiodic sampled-data control systems. The time-varying sampling period is assumed to take only a finite number of values, and the considered system is modeled as a discrete-time switched system with both stable and unstable subsystems. A sufficient condition is derived for the system to be exponentially stable, and a state feedback stabilizing controller is designed such that the system is exponentially stable and achieves an optimal guaranteed cost performance. The obtained exponential decay rate and guaranteed cost performance level critically depend on both the lengths and activation frequencies of the varying sampling periods, and it is revealed that nonuniformly sampled control systems can remain to be stable even in the appearance of a very large sampling period, provided that the activation frequency of the large sampling period is small enough. Finally, an illustrative example is given to show the effectiveness of the proposed approach.

Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays

This study examines the exponential synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Additionally, sampled-data controller with time-varying sampling period is considered and is assumed to switch between m different values in a random way with given probability. Then, a novel Lyapunov–Krasovskii functional (LKF) with triple integral terms is constructed and by using Jensen’s inequality and reciprocally convex approach, sufficient conditions under which the dynamical network is exponentially mean-square stable are derived. When applying Jensen’s inequality to partition double integral terms in the derivation of linear matrix inequality (LMI) conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters appears. In order to handle such a combination, an effective method is introduced by extending the lower bound lemma. To design the sampled-data controller, the synchronization error system is represented as a switched system. Based on the derived LMI conditions and average dwell-time method, sufficient conditions for the synchronization of switched error system are derived in terms of LMIs. Finally, numerical example is employed to show the effectiveness of the proposed methods.

Optimal tracking control for networked control systems with random time delays and packet dropouts

This paper studies the problem of optimal output tracking control for networked control system with uncertain time delays and packet dropouts. Active time-varying sampling period strategy is proposed to ensure the random variable time delays always shorter than one sampling period. Hybrid driven modes are adopted by sensor to solve the issues of long time delay and packet dropout. By using augmentation approach, the tracking problem of this formulated within-one-step delayed discrete-time system is transformed into a general problem of non-delayed state linear quadratic regulator. A “gridding” approach is introduced to guarantee the realization of optimal output feedback control law by the solution of a series of Riccati matrix equations from an offline database that is constructed by different combination of time delays and packet dropouts. Simulation results demonstrate the effectiveness of the optimal tracking control law.

Nonfragile Reliable Guaranteed Cost Controller Design for Networked Control System with Variable Sampling Period Sensors

In this paper, the problem of nonfragile reliable guaranteed cost control for networked control systems with time-varying sampling period sensors and actuator failures is concerned for a given quadratic cost function. For linear time-invariant controlled plant, under the assumption that the sampling period is time-varying within a certain known bound, the time delay is constant and shorter than the sampling period of the sensors, the system is transformed into a time-varying discrete time system, where the time-varying sampling period parts are transformed into norm bounded un- certainties of the structure parameter. A new linear matrix inequality (LMI)-based approach is proposed to derive a suffi- cient condition for the existence of nonfragile reliable guaranteed cost controller. Furthermore, the design method of the optimal nonfragile reliable guaranteed cost controller is formulated to minimize the upper bound of the closed-loop sys- tem cost. A numerical example is given to show the usefulness and effectiveness of the proposed method.

Consensus of Discrete Multiagent System with Various Time Delays and Environmental Disturbances

In this paper, the consensus problem of discrete multiagent systems with time varying sampling periods is studied. Firstly, with thorough analysis of various delays among agents, the control input of each agent is designed with consideration of sending delay and receiving delay. With construction of discrete dynamics of state error vector, it is proved by applying Halanay inequality that consensus of the system can be reached. Further, the definition of bounded consensus is proposed in the situation where environmental disturbances exist. In order to handle this problem, the Halanay inequality is extended into a more general one with boundedness property. Based on the new Halanay inequality obtained, the boundedness of consensus error is guaranteed. At last, simulation examples are presented to demonstrate the theoretical conclusions.

Design of Robust Repetitive Control With Time-Varying Sampling Periods

This paper proposes the design of robust repetitive control with time-varying sampling periods. First, it develops a new frequency domain method to design a low-order, stable, robust, and causal IIR repetitive compensator using an optimization method to achieve fast convergence and high tracking accuracy. As such, a new stable and causal repetitive controller can be implemented independently to reduce the design complexity. The comprehensive analysis and comparison study are presented. Then, this paper extends the method to design a robust repetitive controller, which compensates time-varying periodic signals in a known range. A complete series of experiments is successfully carried out to demonstrate the effectiveness of the proposed algorithms.

H∞ Control of Networked Control Systems with TimeVarying Sampling Periods and Partially Known Packet Dropout Information

H∞ Control of Networked Control Systems with TimeVarying Sampling Periods and Partially Known Packet Dropout Information

Mixed H_/H<SUB align="right">∞ fault detection observer design for networked control system with variable sampling period

For networked control system (NCS) with time-varying sampling period and time-delay, a discrete-time model with parameter uncertainties lying inside a polytopic framework is proposed. Based on the finite frequency parameter dependent quadratic H∞ index performance for minimising the disturbance and the corresponding H– index performance for maximising the worst-case fault sensitivity, a fault detection observer is designed for residual generation. By the aid of the generalised Kalman-Yakubovich-Popov (GKYP) lemma, the existence conditions of such an observer are given in terms of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed approach.