Sampled-data Systems Research Articles

Fuzzy dynamic output feedback control for nonlinear networked multirate sampled-data systems: An integral inequality method

This paper is devoted to fuzzy dynamic output feedback control for nonlinear networked multirate sampled-data systems based on T-S fuzzy systems. Using asynchronous multirate sampled-data, a multirate fuzzy controller is designed. The resultant closed-loop system is modeled as a perturbed system with two perturbed terms which include multirate sampling and the asynchronous membership functions between the controlled plant and the controller. A novel refined integral inequality is developed, and it improves Jensen's inequality and extends Wirtinger's inequalities by considering the sawtooth structure of time-varying delays. By applying the inequality to the perturbed system and constructing a new storage function, a stability criterion and two fuzzy dynamic output feedback controller design methods are presented for the nonlinear networked multirate sampled-data systems. Finally, three illustrative examples show the effectiveness of the proposed method.

The generalized [formula omitted] controller synthesis problem of sampled-data systems

This paper tackles the generalized H2 controller synthesis problem of sampled-data systems, which is associated with the controller minimizing the induced norm from L2 to L∞. To alleviate the difficulty of the linear periodically time-varying (LPTV) nature of sampled-data systems, we first take an operator-based approach to sampled-data systems via the lifting treatment. We next develop a framework for piecewise constant approximation in the context of the generalized H2 controller synthesis problem after further applying the so-called fast-lifting treatment. An optimal controller for the approximate treatment is also shown to achieve the generalized H2 performance for the sampled-data system that is close enough to its optimal generalized H2 performance, if the fast-lifting parameter N is large enough. This is established by deriving, in a fashion suitable for controller synthesis, upper and lower bounds on the resulting sampled-data generalized H2 performance, where their gap tends to 0 at the rate of 1/N. We further introduce a discretization method of the continuous-time plant, with which the controller synthesis in the approximate fashion can actually be carried out through an equivalent discrete-time counterpart of the generalized H2 controller synthesis problem. Finally, numerical examples are given to validate the overall arguments.

Stability of Zeros for Sampled-Data Models with Triangle Sample and Hold Implemented by Zero-Order Hold

This paper deals with the stability characteristics of zeros for sampled-data models with a class of triangle sample and hold realized by a traditional zero-order hold. For any controlled models in the modern industrial system, using a digital control strategy has been shown to provide the means to achieve the assigned objectives. In this process, one must utilize the sample and hold device to obtain the sampled-data models. Previous studies have shown that the triangle sample and hold can improve the stability properties of zeros of a sampled-data control system compared with zero-order hold. However, it is difficult to use triangle sample and hold in practice. In this paper, an approximated method of using triangle sample and hold is proposed. More importantly, on the basis of that method, we explicitly derive the corresponding accurate sampled-data model of controlled models. In addition, we also provide the expression for sampling zeros and the theorem for the stability of a linear control system in the fast sampling process. The results of this paper show that the proposed method has the same advantages as the accurate one. Finally, theoretical findings are validated through numerical simulations with different considerations.

Exponential stability of sampled-data control systems with enhanced average sampling interval

The stabilisation of the sampled-data control systems is addressed to tolerate large sampling intervals that tend to destroy the system's stability. A new sampling sequence is constructed from two sequences with two different sampling time intervals, where the short one corresponds to a stable system, while the long one produces an unstable system. The decay rate of the state trajectory of the former is utilised to overcome the growth rate of the latter, such that the resulting system with mixed sampling intervals is globally exponentially stable. A sufficient condition for stabilisation is given. It is applicable to the system with a single sampling interval under the missing data scenario. The examples are given to illustrate the proposed results.

Sampled-Data Model Predictive Control

This paper focus on model predictive control (MPC) design in the context of sampled-data control systems with full-state measurements. It is shown that recent results on this area can be successfully generalized to cope with sampled-data MPC. The open-loop plant is subjected to polytopic parameter uncertainty and at sampling times a controlled output variable satisfies a set of convex constraints. A guaranteed H2 performance index with infinity horizon is minimized such as the feedback control preserves asymptotic stability and feasibility. The design conditions are expressed though differential linear matrix inequalities (DLMIs). Continuous-time systems are treated with no kind of discrete-time modeling approximation. Comparisons with classical methods from the literature dealing with continuous-time systems are presented and discussed. Examples are included for illustration.

Active Disturbance Rejection Control for Uncertain Nonlinear Systems With Sporadic Measurements

This paper deals with the problem of active disturbance rejection control (ADRC) design for a class of uncertain nonlinear systems with sporadic measurements. A novel extended state observer (ESO) is designed in a cascade form consisting of a continuous time estimator, a continuous observation error predictor, and a reset compensator. The proposed ESO estimates not only the system state but also the total uncertainty, which may include the effects of the external perturbation, the parametric uncertainty, and the unknown nonlinear dynamics. Such a reset compensator, whose state is reset to zero whenever a new measurement arrives, is used to calibrate the predictor. Due to the cascade structure, the resulting error dynamics system is presented in a non-hybrid form, and accordingly, analyzed in a general sampled-data system framework. Based on the output of the ESO, a continuous ADRC law is then developed. The convergence of the resulting closed-loop system is proved under given conditions. Two numerical simulations demonstrate the effectiveness of the proposed control method.

Add-On Type Data-Driven Ripple-Free Dual-Rate Control Design Based on the Null Space of Steady-State Step Responses

In the present study, a data-driven ripple-free design is proposed for a dual-rate sampled-data control system in which the sampling interval of the plant output is longer than the holding interval of the control input. The objective of the present study is to improve the steady-state intersample response without changing the sampled response and without using the plant model. To achieve the objective directly from controlled data, an add-on input based on the null space of steady-state step responses to an existing control system is used. The open-loop or closed-loop system to obtain the step response is assumed to be stable. In the present study, a two-degree-of-freedom design is given that redesigns the intersample output response independently of the steady-state sampled output response. In a numerical example, the proposed method is applied to a linear time-invariant single-input single-output stable system, where intersample ripples are eliminated using the add-on input that is independent of the existing sample output response in steady state.

A sampling-period-partitioning approach for stability analysis of sampled-data systems with constant delay

This paper is concerned with the stability of sampled-data systems with constant delay. Firstly, by dividing the interval of sampling periods in two subintervals, two separate looped functionals are employed in each of these subintervals. Then, a new Lyapunov functional that combines classical Lyapunov functionals and looped-functionals is constructed. Furthermore, several zero equalities which consider the intrinsic relationships of state vectors in the system are introduced into the derivative of the constructed functional, and some stability criteria with less conservatism are obtained in forms of linear matrix inequalities (LMIs). Finally, two numerical examples are carried out as to verify the effectiveness and advantages of our method.

Stability of infinite-dimensional sampled-data systems with unbounded control operators and perturbations

We analyze the robustness of the exponential stability of infinite-dimensional sampled-data systems with unbounded control operators. The unbounded perturbations we consider are the so-called Desch–Schappacher perturbations, which arise, e.g., from the boundary perturbations of systems described by partial differential equations. As the main result, we show that the exponential stability of the sampled-data system is preserved under all Desch–Schappacher perturbations sufficiently small in a certain sense.

Delay-Dependent Stability Improvement for Networked Control Systems: a Sampled Data Approach

This paper concerns the stability conditions and controller design for sampled-data networked control systems (NCSs) model subject to network communication delays, the main objective is to guarantee the maximum allowable upper bounds of network-induced time-varying delays that keep the NCSs stable. First, Lyapunov-Krasovskii functional with simple and double-integral terms is constructed considering both upper and lower bounds of network delay. Then, less conservative Linear Matrix Inequalities (LMIs) stability conditions are established using null terms to introduce free weighting matrices based on the Leibniz-Newton formula. Furthermore, Finsler's lemma is used for the relaxation of the obtained LMI's stability conditions using slack decision variables. It is also used to decouple Lyapunov-Krasovskii matrices from the system ones. The application of the proposed approach for different NCSs gives higher upper delay bounds compared with other methods.

Sensors Allocation and Observer Design for Discrete Bilateral Teleoperation Systems with Multi-Rate Sampling.

This study addresses sensor allocation by analyzing exponential stability for discrete-time teleoperation systems. Previous studies mostly concentrate on the continuous-time teleoperation systems and neglect the management of significant practical phenomena, such as data-swap, the effect of sampling rates of samplers, and refresh rates of actuators on the system’s stability. A multi-rate sampling approach is proposed in this study, given the isolation of the master and slave robots in teleoperation systems which may have different hardware restrictions. This architecture collects data through numerous sensors with various sampling rates, assuming that a continuous-time controller stabilizes a linear teleoperation system. The aim is to assign each position and velocity signals to sensors with different sampling rates and divide the state vector between sensors to guarantee the stability of the resulting multi-rate sampled-data teleoperation system. Sufficient Krasovskii-based conditions will be provided to preserve the exponential stability of the system. This problem will be transformed into a mixed-integer program with LMIs (linear matrix inequalities). These conditions are also used to design the observers for the multi-rate teleoperation systems whose estimation errors converge exponentially to the origin. The results are validated by numerical simulations which are useful in designing sensor networks for teleoperation systems.

Deterministic learning from neural control for a class of sampled-data nonlinear systems

This study investigates the deterministic learning and control issues for uncertain sampled-data nonlinear systems (SDNSs). The problem of how to acquire/learn knowledge from adaptive control for SDNSs with uncertain affine terms is studied. To be specific, an appropriate neural network-based (NNB) control strategy is first presented to ensure tracking performance. To further realize learning, the exponential stability (ES) of the integrated closed-loop system coupled with the estimation error of the NN weights is considered. As the uncertain affine term prevents learning from occurring, the integrated system is converted into a discrete linear time-varying (DLTV) perturbed system by employing the state conversion technique. Tracking convergence allows the persistent excitation condition (PEC) of the NNs to be established, which guarantees the ES of the integrated DLTV system. Thus, accurate modeling of closed-loop sampled dynamics is obtained. By reutilizing the experiential knowledge obtained, a knowledge-based controller is constructed for high-performance control. Finally, simulations are performed to verify the presented strategy.

Admissibility Analysis of a Sampled-Data Singular System Based on the Input Delay Approach

This study investigates the sampled-data admissibility problem for a singular system. The objective of this paper is to design a sampled-data controller to ensure the admissibility of a singular system and to construct an appropriate Lyapunov–Krasovskii functional (LKF) to get less conservative results for the sampled-data singular system. To accomplish these objectives, the system is converted into a time-delay system by the input delay approach firstly, and both lower and upper bounds of the delay are considered. Secondly, by introducing a suitable LKF, the admissibility criteria are obtained. Then, when estimating the derivative of the LKF, a relaxation variable is introduced by the method of reciprocally convex inequality, and it is proved that the conservatism is reduced. Finally, two numerical examples are given to prove that the designed sampled-data controller can ensure the states of the systems under the influence of external interference.

Bidirectional fragmentation approach on the stability analysis of sampled-data linear systems

In this paper, a novel stability analysis method for continuous-time linear systems with aperiodic sampling is presented by using a partitioned looped-functional approach. Based on the Lyapunov function with a new looped-functional, the stability condition is derived by using a bidirectional fragmentation of a sampling interval from to , which is divided into two sides forward and backward directions based on time t. For the bidirectional regions, the new looped functional is constructed by taking into account relations between states defined at the fragmented time and the sampling time. The improvement using the proposed scheme is shown through the comparisons with existing methods.

Zonotopic Filtering for Uncertain Nonlinear Systems: Fundamentals, Implementation Aspects, and Extensions [Applications of Control

This tutorial provides a comprehensive perspective on the study of zonotopic filtering for nonlinear uncertain dynamical systems. Unlike stochastic methods that characterize the states by means of random vectors, set-based observers estimate deterministic sets that are guaranteed to contain the system states. Among many classes of sets, the focus here is on zonotopes due to their appealing properties that pursue a good tradeoff between precision and computational cost. We start by reviewing the fundamentals of zonotopic filtering together with illustrative examples. As nonlinear systems bring up many challenges for this topic, we choose one of the first nonlinear zonotopic observers proposed in the literature to guide a series of discussions. After presenting this algorithm and understanding its limitations, we extend it by incorporating state inequality constraints. In addition, we motivate the use of linear programs when solving minimum-volume intersections. Additionally, we give a practical discussion on the implementation of discrete-time zonotopic algorithms for sampled-data nonlinear dynamical systems. To better introduce the zonotopic approaches, we briefly review unscented Kalman filtering to trace parallels between the stochastic and set-theoretic frameworks. Then the presented algorithms are experimented and compared in a case study involving a quadrotor unmanned aerial vehicle.

A Probability Theory Approach to Stability Analysis of Networked Sampled-Data Systems With Consecutive Packet Dropouts

In this brief note, a probability theory approach is proposed to investigate the stability analysis issue for a class of networked sampled-data systems with packet dropouts. The continuous-time linear system under consideration is first transformed into a discrete-time system, where the system matrix of the discrete-time system is characterized by stochastic characteristic. Then, by the matrix exponential computation, an equivalent discrete-time stochastic system is established. Based on this, a controller is designed by the law of total expectation, which guarantees the stochastic stability of the closed-loop stochastic system. Finally, a numerical example and an example using power grid with IEEE 4-bus line are used to verify the effectiveness and applicability of the proposed design algorithm.

Synchronization of Sampled-data Coupling Nonlinear Systems in Time-varying Networks

This paper investigates synchronization in time-varying networks of nonlinear systems with sampled-data couplings. In particular, we consider the synchronization problem of systems with a time-varying network structure realized by switching between multiple network structures, including the completely disconnected network. Throughout this paper, we derive a synchronization condition for sampled-data network systems with such a time-varying network structure by introducing a concept of the average dwell time. Finally, we show a numerical simulation result to illustrate the validity of the derived condition.

Robust Quantized Sampled–Data Stabilization for a Class of Lipschitz Nonlinear Systems With Time–Varying Uncertainties

In this letter, a robust quantized sampled-data controller is provided for a class of nonlinear systems affected by time-varying uncertainties, actuation disturbances and measurement noises. Sufficient conditions based on linear matrix inequalities and ensuring the existence of the proposed robust quantized sampled-data controller are given. Quantization of both state measurements and input signals is simultaneously considered. Input-to-state stability redesign technique is used in order to attenuate the effects of bounded actuation disturbances and of bounded observation errors. It is proved that, under suitably fast sampling and accurate quantization of the input/output channels, the proposed controller achieves the semi-global practical stability, with arbitrarily small final target ball, of the related quantized sampled-data closed-loop system provided that the observation errors do not affect (or affect marginally) the robustification term added in the controller and, that the bounds of the actuation disturbances as well as of the observation errors are a priori known. The theory here developed includes also the cases of time-varying sampling intervals and of non-uniform quantization of the input/output channels as well as the stability analysis of the inter-sampling system behavior. The provided results are validated through an example of one-link manipulator.

Control Barrier Functions in Sampled-Data Systems

This paper presents conditions for ensuring forward invariance of safe sets under sampled-data system dynamics with piecewise-constant controllers and fixed time-steps. First, we introduce two different metrics to compare the conservativeness of sufficient conditions on forward invariance under piecewise-constant controllers. Then, we propose three approaches for guaranteeing forward invariance, two motivated by continuous-time barrier functions, and one motivated by discrete-time barrier functions. All proposed conditions are control affine, and thus can be incorporated into quadratic programs for control synthesis. We show that the proposed conditions are less conservative than those in earlier studies, and show via simulation how this enables the use of barrier functions that are impossible to implement with the desired time-step using existing methods.

Trajectory Tracking for Discrete-Time Port-Hamiltonian Systems

This paper presents a regulator for nonlinear, discrete-time port-Hamiltonian systems that lets the state track a reference signal. Similarly to continuous-time approaches, the synthesis is based on the mapping via state-feedback of the open-loop error system to a target one in port-Hamiltonian form, and with an asymptotically stable origin that corresponds to the perfect tracking condition. The procedure is formally described by a matching equation that, in continuous-time, turns out to be a nonlinear partial differential equation (PDE). This is not the case for sampled-data systems, so an algebraic approach is proposed. The solution is employed to construct a dynamical regulator that performs an “approximated” mapping. The stability analysis relies on Lyapunov arguments.