Sampled-data Systems Research Articles

Computing Safe Sets of Linear Sampled-Data Systems

Leveraging autonomous systems in safety-critical applications requires formal robustness guarantees against uncertainties. We address this issue by computing safe terminal sets with corresponding safety-preserving terminal controllers, which ensure robust constraint satisfaction for an infinite time horizon. To maximize the region of operation, we also construct as large as possible safe initial sets that can be safely steered into the safe terminal set in finite time. We use scalable reachability analysis and convex optimization to efficiently compute safe sets of sampled-data systems. These systems are composed of a physical plant evolving in continuous time and a digital controller being implemented in discrete time. We further verify the effectiveness of our robust control approach using a simple double-integrator system and a vehicle-platooning benchmark.

Stabilization of Interval Type-2 Fuzzy-Based Reliable Sampled-Data Control Systems.

This article investigates the stabilization problem of the Takagi-Sugeno (T-S) fuzzy-based interval type-2 (IT-2) reliable sampled-data control system. Different from the existing studies, the information for the entire sampling interval with a relation of the augmented state vectors is considered for designing the reliable sampled-data control of IT-2 T-S fuzzy systems. In this regard, we construct the suitable looped Lyapunov-Krasovskii functional (LKF) with the information of the fuzzy membership function that feeds back the time derivative of the membership function to derive sufficient conditions. These sufficient conditions are established in the form of linear matrix inequalities (LMIs), which ensure the global asymptotic stability of T-S fuzzy systems under the designed control technique. Finally, the applicability and superiority of developed reliable sampled-data control techniques were validated by three practical systems.

Stability analysis of sampled-data control systems with multiple time-varying delays

This paper deals with the stability analysis of sampled-data control systems with a centralized controller and multiple actuators, where different controller-actuator delays exist. Via the input-delay approach, a sampled-data control system with multiple time-varying delays is modeled as a linear time-delay system. Though some existing criteria for time-delay systems can be applied to analyze the stability of the original system, the results are conservative since these criteria do not consider the sampling effects properly. To reduce the conservatism, a new looped-functional, which takes advantage of the hybrid characteristic of the sampled-data control system model, is proposed. Meanwhile, a new Lyapunov-Krasovskii functional that aims at fully benefiting from the Wirtinger-based inequality and utilizing the relationship information among the states associated with different delays is constructed. Based on the proposed functionals, a new stability condition for sampled-data control systems with multiple time-varying delays is presented in the form of linear matrix inequalities. Numerical examples are given to illustrate the advantages and effectiveness of the proposed method.

Adaptive Sampled-Data Observer Design for a Class of Nonlinear Systems with Unknown Hysteresis

In this paper, a novel adaptive sampled-data observer design is studied for a class of nonlinear systems with unknown Prandtl–Ishlinskii hysteresis and unknown unmatched disturbances based on radial basis function neural networks (RBFNNs). To begin with, we investigate a sampled-data nonlinear system and present sufficient conditions such that the sampled-data nonlinear system is ultimately uniformly bounded (UUB). Then, an adaptive sampled-data observer is designed to estimate the unknown states of the nonlinear system. The unknown hysteresis and the unknown disturbances are approximated by RBFNNs. We also give the learning laws of the weights of RBFNNs, and prove that the estimation errors of the states and the weights are UUB, based on the obtained sufficient conditions and a special constructing Lyapunov–Krasovskii function. Finally, the effectiveness of the proposed design method is verified by numerical simulations.

Exponential stability of bilateral sampled-data teleoperation systems using multirate approach

This paper develops the stability analysis for linear bilateral teleoperation systems exposed to communication constraints and multirate samplers. Dynamics of the master and slave robots are assumed to be continuous-time with discrete-time controllers. The proposed multirate design guarantees the exponential stability of the teleoperation system over a communication networks. Different sampling rates are imposed on position/velocity signals in both master and slave sides and by exerting input-delay approach, the multirate dynamics is transformed into a continuous-time system. Sufficient Krasovskii-based stability criteria are provided to preserve the exponential stability of the linear discrete-time system for asynchronously sampling intervals and update rates. This analysis is formulated as a convex optimization problem in terms of linear matrix inequalities (LMI) to calculate the longest interval between two successive sampling periods. The proposed multirate approach demonstrates that selecting adequate intervals for samplers and proper update rates for actuators has a considerable effect on the stability of the system. In order to validate the stability criteria and present the efficacy of the proposed multirate scheme, pair of two degree of freedom manipulators will be investigated and maximum allowable sampling periods and update rates are computed to preserve the exponential stability for different multirate cases.

Further Stability and Stabilization Condition for Sampled-Data Control Systems via Looped-Functional Method

This brief contributes the further results on stability and stabilization conditions for sampled-data-based control systems (SDCSs), which include linear SDCSs and nonlinear SDCSs via looped-Lyapunov functional approach. The improved Lyapunov functional involves the states information such as $x(t_{k})$ and $x(t_{k+1})$ with few slack variables and a tuning parameter. The sufficient conditions are derived for both linear SDCSs and nonlinear SDCSs, whereas Takagi-Sugeno (T-S) approach is employed to express the nonlinear SDCS into T-S fuzzy-based model through fuzzy IF-THEN membership rules. With the derived conditions, the stability region of the proposed SDCSs can be enhanced and their asymptotic stability will be ensured. Finally, the numerical analysis is performed with the existing models and their corresponding performances are provided to validate the less conservatism and superiority of the derived results over the existing ones.

Reachable Set Estimation for Neural Network Control Systems: A Simulation-Guided Approach

The vulnerability of artificial intelligence (AI) and machine learning (ML) against adversarial disturbances and attacks significantly restricts their applicability in safety-critical systems including cyber-physical systems (CPS) equipped with neural network components at various stages of sensing and control. This article addresses the reachable set estimation and safety verification problems for dynamical systems embedded with neural network components serving as feedback controllers. The closed-loop system can be abstracted in the form of a continuous-time sampled-data system under the control of a neural network controller. First, a novel reachable set computation method in adaptation to simulations generated out of neural networks is developed. The reachability analysis of a class of feedforward neural networks called multilayer perceptrons (MLPs) with general activation functions is performed in the framework of interval arithmetic. Then, in combination with reachability methods developed for various dynamical system classes modeled by ordinary differential equations, a recursive algorithm is developed for over-approximating the reachable set of the closed-loop system. The safety verification for neural network control systems can be performed by examining the emptiness of the intersection between the over-approximation of reachable sets and unsafe sets. The effectiveness of the proposed approach has been validated with evaluations on a robotic arm model and an adaptive cruise control system.

Contract-Based Design of Symbolic Controllers for Safety in Distributed Multiperiodic Sampled-Data Systems

This article presents a symbolic control approach to the design of distributed safety controllers for a class of continuous-time nonlinear systems. More precisely, we consider systems made of components where each component is equipped with a sampled-data controller with its own sampling period, resulting globally in a distributed multiperiodic sampled-data system. Moreover, controllers receive partial information on the state of the other components. We propose a component-based approach to controller synthesis, which relies on the use of abstractions and continuous-time assume-guarantee contracts. The abstractions describe the dynamics of the system from the point of view of each component based on the information structure, whereas assume-guarantee contracts specify guarantees that a component must satisfy if assumptions on the other components are met. We show that our approach makes it possible to decompose a global safety control problem into local ones that can be solved independently. We then show how symbolic control techniques can be used to synthesize controllers that enforce the local control objectives. Illustrative applications in building automation and vehicle platooning are shown.

Ripple-Free Data-Driven Dual-Rate Controller Using Lifting Technique: Application to a Physical Rotation System

This study proposes a data-driven approach for controlling a dual-rate sampled-data system using the lifting technique, where the sampling interval of the plant output is longer than the holding interval of the control input. In the proposed method, the structure of the dual-rate controller is linearized to its controller parameter, and the controller parameter is optimized using noniterative correlation-based tuning. Furthermore, intersample ripples are eliminated because the difference in the control inputs between sampled outputs is weighted. The effectiveness of the proposed method is demonstrated through numerical and experimental examples.

An Input–Output Approach to Anti-windup Design for Sampled-Data Systems with Time-Varying Delay

A methodology for designing anti-windup compensators is investigated, for sampled-data systems with delays and actuator saturation. More precisely, criteria for the existence of an anti-windup compensator that ensure simultaneously stability and an $$H_{\infty }$$ norm bound in closed-loop are developed, thanks to the use of a three-term approximation of the delays, of the scaled small gain theorem, and of a Wirtinger-based inequality. The criteria are in the form of a set of linear matrix inequalities: an optimization algorithm is proposed to maximize the estimated domain of attraction that can be easily implemented. Some simulation examples are also provided to demonstrate the superiority of the proposed approach.

Estimation with unknown inputs and uncertainties for sampled-data systems based on quasi sliding mode

In this work, we consider the problem of simultaneously estimating the system states and unknown inputs in a linear sampled-data system, whose dynamics is influenced by external disturbances and uncertainties. Hardware limitations prevent an estimation scheme for a sampled-data system from achieving finite-time convergence, which is a typical property of existing sliding mode observers for dynamical continuous-time systems, because the sampling period is finite. Due to the sampling process, an approximate implementation of such an observer, designed for a continuous-time system, may not retain the desired performance in the sampled-data context. In this paper, we present an observer which takes advantage of the quasi-sliding motion concept to simultaneously estimate the state variables and the unknown input signals in a sampled-data context. A theoretical study is conducted to formally justify the convergence properties of the observer whilst simulation results are provided to show the efficiency of the proposed scheme.

Controller Optimization for Multirate Systems Based on Reinforcement Learning

The goal of this paper is to design a model-free optimal controller for the multirate system based on reinforcement learning. Sampled-data control systems are widely used in the industrial production process and multirate sampling has attracted much attention in the study of the sampled-data control theory. In this paper, we assume the sampling periods for state variables are different from periods for system inputs. Under this condition, we can obtain an equivalent discrete-time system using the lifting technique. Then, we provide an algorithm to solve the linear quadratic regulator (LQR) control problem of multirate systems with the utilization of matrix substitutions. Based on a reinforcement learning method, we use online policy iteration and off-policy algorithms to optimize the controller for multirate systems. By using the least squares method, we convert the off-policy algorithm into a model-free reinforcement learning algorithm, which only requires the input and output data of the system. Finally, we use an example to illustrate the applicability and efficiency of the model-free algorithm above mentioned.

Input-output Approach and Scaled Small Gain Theorem Analysis to Sampled-data Systems with Time-varying Delay

Input-output Approach and Scaled Small Gain Theorem Analysis to Sampled-data Systems with Time-varying Delay

Fuzzy optimal control for nonlinear systems with time-varying delay via sampled-data controller

This work is devoted to a fuzzy sampled-data optimal control problem for nonlinear systems with time-varying delay in Takagi–Sugeno fuzzy form. Based on the Lyapunov–Krasovskii functional theory, some novel stability criteria are established. A fuzzy sampled-data controller is developed to ensure that the fuzzy closed-loop sampled-data control system is asymptotically stable and the guaranteed cost performance is also minimized. It is shown that the obtained results are less conservative in the stability analysis. Two examples of the computer-simulated truck-trailer system and the continuous stirred tank reactor system are provided to show the effectiveness and the merits of the proposed design.

Stability Analysis of Load Frequency Control Systems With Sampling and Transmission Delay

To analyze the delay-dependent stability of a load frequency control (LFC) system with transmission delays, the continuous-time model with delay is usually adopted. However, practical LFC is actually a sampled-data system, where the power commands sent to generation units are updated every few seconds. It is therefore desirable to analyze the delay-dependent stability of LFC when sampling is introduced. This paper undertakes stability analysis of LFC with both sampling and transmission delay. The model of the LFC system is first modified to consider sampling and transmission delay separately. Based on Lyapunov stability theory and linear matrix inequalities, a new stability criterion for linear systems with both sampling and transmission delay is proposed using the Wirtinger-based integral inequality and its affine version. The proposed criterion is applicable for both time-invariant and time-varying transmission delays. Case studies are undertaken on both single-area and two-area LFC systems to verify the effectiveness and advantage of the proposed method.

Sampled-Data Consensus of Linear Time-Varying Multiagent Networks With Time-Varying Topologies.

The main purpose of this article is to investigate the consensus of linear multiagent networks with time-varying characteristics under sampled-data communications, where the time-varying characteristics include both time-varying topologies and the node's linear time-varying dynamics. By using the decoupling method, we prove that the sampled-data consensus problem of multiagent networks is equal to the stability problem of sampled-data systems. Then, the globally asymptotical consensus is investigated for multiagent networks with time-varying characteristics by virtue of the Lyapunov function method. It should be noted that when the Lyapunov function method is utilized to investigate the stability problem of control systems, it is always assumed that the derivative of the constructed Lyapunov function is not more than zero. This assumption is removed here and as a replacement, the average value of the derivative of the Lyapunov function in a period to be negative is needed.

Stability analysis of perturbed infinite-dimensional sampled-data systems

This paper addresses the stability analysis of infinite-dimensional sampled-data systems under unbounded perturbations. We present two classes of unbounded perturbations preserving the exponential stability of sampled-data systems. To this end, we investigate the continuity of strongly continuous semigroups with respect to their generators, considering the uniform operator topology.

Novel analysis of sampled-data systems stabilised by a pulsed control signal

In this work, a little known control technique known as pulsed control law or switched control law is studied. In general, this linear control technique has reported enlarging the stabilising sampling period region of a sampled-data system. However, in previous works no dynamic justification has been given. Here, using a different approach to work previously done, it is shown that in a sampled-data system exposed to large stabilising sampling periods, the control law applied as a ZOH contributes to moving the system faster away from the origin as the next sampling time is approaching. It is shown that this is the dynamic reason behind the effectiveness of the pulsed control law reported in previous works. In addition, our analysis allows us to deduce conditions based on the spectrum of a linear system matrix to justify the phenomena reported previously.

Stability analysis of sampled-data control system and its application to electric power market

The stability of sampled-data systems is investigated using a new type of Lyapunov functional. The interval from the sampling point t k to t k+1 is assumed to be a sampling interval. By fully utilizing the characteristic information on the whole sampling interval, a new two-sided closed-loop Lyapunov functional is proposed, which utilizes the information on both the intervals from the sampling point t to t k and from t to t k+1 . Based on the two-sided closed-loop Lyapunov functional and modified free-matrix-based inequality, a less conservative stability criterion is derived for a sampled-data control system, and three numerical examples are provided to verify the effectiveness and reduced conservativeness of the proposed method. Furthermore, the proposed method is applied to solve the stability problem of electric power markets, and the practical significance of reducing the conservativeness is discussed.

Design of [formula omitted] stable fixed-order decentralised controllers in a network of sampled-data systems with time-delays

A methodology is proposed for the design of sampled-data fixed-order decentralised controllers for Multiple Input Multiple Output (MIMO) Linear Time-Invariant (LTI) time-delay systems. Imperfections in the communication links between continuous-time plants and controllers arising due to transmission time-delays, aperiodic sampling, and asynchronous sensors and actuators are considered. We model the errors induced due to the control imperfections using an operator approach leading to a simple L2 stability criterion. A frequency domain-based direct optimisation approach towards controller design is proposed in this paper. This approach relies on the minimisation of cost functions, for stability and robustness against control imperfections, as a function of the controller or design parameters. First, the proposed method towards controller design is applied to generic MIMO LTI systems with time-delays. Second, when the delay system to be controlled has the structure of a network of coupled quasi-identical subsystems, we use a scalable algorithm to design identical decentralised controllers through network structure exploitation. Quasi-identical subsystems are identical subsystems that have non-identical uncertainties or control imperfections. By exploiting the structure, we improve the computational efficiency and scalability with the number of subsystems. The methodology has been implemented in a publicly available software, which supports system models in terms of delay differential algebraic equations. Finally, the effectiveness of the methodology is illustrated using a numerical example.