Sampled-data Control Systems Research Articles

Stabilization of T–S fuzzy membership-function dependent H$$_\infty $$-based sampled-data control systems using an improved exponential two-sided looped-functional approach

Stabilization of T–S fuzzy membership-function dependent H$$_\infty $$-based sampled-data control systems using an improved exponential two-sided looped-functional approach

Quantized Zero Dynamics Attacks Against Sampled-Data Control Systems

Quantized Zero Dynamics Attacks Against Sampled-Data Control Systems

Sampled-data controller synthesis using dissipative linear periodic jump-flow systems with design applications

In this paper, we will propose linear-matrix-inequality-based techniques for the design of sampled-data controllers that render the closed-loop system dissipative with respect to quadratic supply functions, which includes passivity and an upper-bound on the system’s H∞-norm as a special case. To arrive at these results, we model the sampled-data control system as a linear periodic jump-flow system, study dissipativity in terms of differential linear matrix inequalities (DLMIs) and then convert these DLMIs into a single linear matrix inequality. We will present three applications of these synthesis techniques: (1) passivity-based controller synthesis, as found in teleoperations, (2) input–output-response matching of a continuous-time filter with a discrete-time filter (by minimizing the H∞-norm of a generalized plant) and (3) a sampled-data controller redesign problem, where the objective is to find the best sampled-data controller, in the H∞-norm sense, for a given continuous-time controller. We will show that synthesizing sampled-data controllers leads to better closed-loop system behaviour than using a Tustin discretization of a continuous-time controller.

Improved stability and stabilization criteria for multi-rate sampled-data control systems via novel delay-dependent states

This paper aims to obtain less conservative stability and stabilization conditions for sampled-data linear systems with multiple sampling rates. To this end, three novel delay-dependent states resulting from sampling are introduced in the augmented state, enabling the exploitation of the sawtooth-type characteristics of the sampling-induced delay in both stability and stabilization processes. Additionally, a novel discontinuous function is included in Lyapunov–Krasovskii-based functional to enhance the capacity to extract more information from specific sampling pattern for each state. Especially, to strengthen the interdependence among the components of the augmented state, supplementary zero equalities are incorporated into the stability analysis conditions. Furthermore, by including a novel weighted state derivative in the augmented state, this paper proposes an effective method that can transform the parameter-dependent stability conditions into stabilization conditions formulated in terms of linear matrix inequalities. Finally, the validity and practicality of the proposed method are demonstrated through two illustrative examples.

Integrated Stabilizing Control for Sampled-Data NCSs With Intermittent Observation and Multiple Random Transmission Delays

In this paper, we study sampled-data networked control systems (NCSs) that operate over communication networks with multi-path channels. Due to limited bandwidth power, the delivery of observed state signals from the sensor to the controller may suffer packet loss possibility, which leads to intermittent observation. An unreliable multi-path routing network is responsible for the transmission of control signals from the controller to the actuator, subject to random transmission delays. These communication problems lead to degradation in system performance, which may even cause instability. By utilizing an idle-time-based scheduling policy with a pre-defined deadline constraint on the actuator side, we transform the affiliated integrated system into a stochastic model with constant input delay. For such implementation, we propose a set of Riccati-type stabilization conditions, which are necessary and sufficient. It is remarkable that the stabilizing control policy is designed based on the feedback of the optimal estimate with minimum mean square error. Moreover, for the scalar system, we study the uniqueness and existence property of the maximum sampling period, and derive its close form representation in terms of system parameters, service capability and packet dropout rate.

An Investigation of Stability Criteria for Sampled-data Control System Using New Integral Inequality for Application to Electric Power Market

An Investigation of Stability Criteria for Sampled-data Control System Using New Integral Inequality for Application to Electric Power Market

Secure Nonlinear Sampled-Data Control System Against Stealthy Attack: Multirate Approach

In this paper, we provide a novel defence strategy for a nonlinear sampled-data control system under zero-dynamics attacks. In a sampled data structure, sampling zeros induced by discretization make a system vulnerable to deception attacks. we analyze the dissipativity in the zero-dynamics part of the system equipped with a multi-rate setup and find conditions on sampling rates to neutralize the attacker's target plan. We show that, under some mild conditions, using multi-rate sampling in the nonlinear sampled-data system not only preserves the dissipativity property of the intrinsic zero-dynamics but also stabilizes the extrinsic zero-dynamics induced by the sample and hold process, and as a result attenuate the effects of attacks on the system stability. Finally, a numerical example is used to illustrate the effectiveness of the proposed approach.

Peak-to-Peak Stabilization of Sampled-Data Systems Subject to Actuator Saturation and Its Practical Application to an Inverted Pendulum

This paper investigates the local stability and stabilization criteria of sampled-data control systems, taking into account actuator saturation and peak-bounded exogenous disturbances. Specifically, this study introduces two innovations to extend the maximum upper bound of the sampling interval: two novel time integrals of the weighted state derivative are introduced to formulate an improved looped-functional; second, the introduction of two supplementary zero-equalities to improve the relationship among the components of the augmented state. Building on this, a set of linear matrix inequality-based stabilization conditions is derived. These conditions ensure that a closed-loop sampled-data system can become exponentially stable and achieve a guaranteed peak-to-peak performance in the domain of attraction. Finally, the efficacy of the proposed methodology is substantiated through both simulation and experimental results, focusing on the sampled-data control of an inverted pendulum system.

Hypertracking and Hyperrejection: Control of Signals Beyond the Nyquist Frequency

This paper studies the problem of signal tracking and disturbance rejection for sampled-data control systems, where the pertinent signals can reside beyond the so-called Nyquist frequency. In light of the sampling theorem, it is generally understood that manipulating signals beyond the Nyquist frequency is either impossible or at least very difficult. On the other hand, such control objectives often arise in practice, and control of such signals is much desired. This paper examines the basic underlying assumptions in the sampling theorem and pertinent sampled-data control schemes, and shows that the limitation above can be removed by assuming a suitable analog signal generator model. Detailed analysis of multirate closed-loop systems, zeros and poles are given, which gives rise to tracking or rejection conditions. Robustness of the new scheme is fully characterized; it is shown that there is a close relationship between tracking/rejection frequencies and the delay length introduced for allowing better performance. Examples are discussed to illustrate the effectiveness of the proposed method here.

Resilient quantized control for asynchronous sampled-data networked control systems under DoS attacks

Resilient quantized control for asynchronous sampled-data networked control systems under DoS attacks

Improved stability and stabilization criteria of sampled-data control systems based on an enhanced looped-functional

This paper proposes improved stability and stabilization criteria that can increase the upper bound of sampling interval for the sampled-data systems while decreasing the computational complexity. To realize such improvement, an enhanced looped-functional is devised so that it can include 1) two time integrals of the weighted state derivative and 2) a single-integral quadratic terms with an augmented vector stacked with the state and its derivative. In addition, to aid the efficient use of the looped-functional, two zero equalities are newly established in the main derivation, which plays a key role in reinforcing the relationship between the time integrals of the weighted state derivative and other considered states. Furthermore, an improved free-matrix-based integral inequality is provided to obtain a tight upper bound on the single-integral quadratic terms in the stability analysis and control synthesis process. Finally, the validity of proposed method is verified through three numerical examples.

Stability analysis of sampled-data control systems with input saturation: A hybrid system approach

This work addresses the stability analysis of sampled-data control systems subject to variable sampling intervals and input saturation. From a hybrid system representation, stability conditions based on quadratic timer-dependent Lyapunov functions are proposed. Considering affine and generic polynomial timer-dependence, these conditions are cast in semidefinite and sum-of-squares optimization problems to provide maximized estimates of the region of attraction or to provide a lower bound for the maximum allowable intersampling time considering a given set of admissible initial conditions.

Exploring the Role of Sampling Time in String Stabilization for Platooning: An Experimental Case Study

In this article, we investigate the behavior of vehicle platoons operating in a predecessor-following configuration, implemented through sampled-data control systems. Our primary focus is to examine the potential influence of the sampling time on the string stability of the platoon. To address this, we begin by designing a string-stable platoon in continuous time. Subsequently, we consider the controller discretization process and proceed to simulate and implement the designed control strategy on an experimental platform at a scaled-down level. Through experimental testing and some theoretical results, we analyze the effects of different sampling times on the string stability performance of the platoon. We observe that an inappropriate selection of the sampling time can lead to a degradation in string stability within the platoon, making the choice of the sampling time crucial in maintaining the desired string stability properties. These findings highlight the importance of carefully considering the sampling time in the implementation of control systems for platooning applications.

On the reinforcement learning extended state observer for a class of uncertain sampled-data control systems

On the reinforcement learning extended state observer for a class of uncertain sampled-data control systems

Continuous-time approach of sampled-data systems

This paper studies the continuous-time behavior of sampled-data control systems. In these systems, a discrete-time control law is applied to a continuous-time system model using sampling and zero-order hold. Traditionally, sampled-data systems are modeled in discrete-time, and thus, the intersample dynamics cannot be examined. This paper shows that the classical methods (such as the d2c function of MATLAB) for obtaining continuous-time models can be inaccurate between the sampling instants, even when Shannon’s sampling theorem is satisfied. In this paper, a new method is also presented which can be used to characterize the continuous-time dynamics of sampled-data control systems. The new continuous-time system model including the intersample behavior is derived analytically from the discrete-time model, and the results are verified by simulations.

New Stabilization Conditions for Fuzzy-Based Sampled-Data Control Systems Using a Fuzzy Lyapunov Functional

This paper focuses on the stabilization problem of Takagi-Sugeno fuzzy systems via a sampled-data controller using a fuzzy dependent functional. By employing a property of convex combination, a new approach to deal with the time derivatives of the fuzzy membership functions (FMFs) in the stabilization conditions is proposed, and less conservative conditions are derived in the form of linear matrix inequalities (LMIs). Moreover, the proposed approach introduces a switching function which opens up possibilities to use a switched controller and take advantage of its benefits well known in the literature. Therefore, two sampled-data control strategies are proposed, where the first one is a fuzzy controller and the second is a robust switched controller, that does not require the expressions of the FMFs to implement the control law, which guarantees the robustness of the controlled system in cases where the FMFs depend on uncertain parameters. Finally, the effectiveness of the proposed strategies is verified by two examples.

Resilient Control for Multiagent Systems With a Sampled-Data Model Against DoS Attacks

To reduce the computational burden and resist the denial-of-service (DoS) attacks, a resilient distributed sampled-data control scheme is proposed for multiagent systems. The agent states are sampled periodically by the sensors. DoS attacks disrupt the data communication from transmitters to controllers randomly or periodically with a limited duration time. Information on DoS attacks can be obtained by introducing novel logic processors embedded in corresponding controllers. Next, the problem of resilient control can be converted into one concerned with the upper and lower bound of the sampling interval of an aperiodic sampled-data control system. Some sufficient criteria for developing resilient distributed controllers are derived using the novel looped Lyapunov functional approach and the free-matrix-based inequality method. Finally, two illustrative examples, unmanned aerial vehicles and the two-mass-spring systems, are provided to demonstrate the efficiency of the proposed resilient distributed sampled-data control protocols against the DoS attacks.

Stability analysis of sampled-data systems with sector-bounded input nonlinearity

This work proposes a method for the stability analysis of aperiodic sampled-data control systems with sector and slope bounded input nonlinearities. The stability conditions are derived by using a hybrid system representation and a timer-dependent Lur'e type Lyapunov function. Considering a polynomial timer-dependence, the stability conditions are cast in sum-of-squares optimization problems aiming at computing the largest range of sampling intervals or the largest sector bounds on the nonlinearity for which the origin of the closed-loop system is globally asymptotically stable.

Using partial sampled-data information for synchronization of chaotic Lur’e systems and its applications: an interval-dependent functional method

This paper is concerned with the synchronization problem of chaotic Lur’e systems by using partial sampled-data information. First, a useful lemma is established on the basis of discrete-time Lyapunov theory and interval estimate methods, which contributes to the stability of partial sampled-data control (PSC) systems. According to the features of the designed control scheme, a single-interval-dependent functional and a double-intervals-dependent functional are constructed by utilizing the corresponding interval information, respectively. Unlike the previous Lyapunov functional methods, the proposed functionals are essentially continuous and then some additional constraint conditions are removed. Then, based on several inequality methods, two sufficient criteria dependent on the controller gain, sampling period, and allowable data loss ratio (ADLR), are respectively developed to guarantee the global synchronization of Lur’e systems. Additionally, the quantitative analysis about the ADLR is discussed. Compared with the existing results, the developed interval-dependent functional techniques are beneficial to enlarging the ADLR. Finally, illustrative examples and an application to image encryption are given to demonstrate the advantages and effectiveness of the proposed control strategy.

Periodic sampled-data-based dynamic model control of switched linear systems

Sampled-data control as an effective mean of digital control has shown its prominent superiority in most practical industries and a zero-order holder (ZOH) is often introduced to maintain continuity of control in the field of sampled-data control system. However, it decreases the control accuracy in a certain extent since the state will be held invariably within each sampling interval. In order to improve the control accuracy, this paper proposes a dynamic model-based control strategy instead of ZOH for a class of switched sampled-data control systems. The model, which is built by abstracting the plant knowledge, is located at the controller side. The controller is set up based on the model state and it provides control input to the switched system. A fixed sampling period is adopted, under which a hybrid-dwell time switching condition is revealed by taking into account asynchronous switching. With reasonable design of switching condition, exponential stability of the closed-loop system can be guaranteed. Finally, advantages of our proposed method are presented through a numerical example by comparing with the result of ZOH-based control.