Sampled-data Systems Research Articles

Zero Assignment via Generalized Sampler: A Countermeasure Against Zero-Dynamics Attack

Networked control systems have advantages such as flexibility, efficiency, but at the same time they are exposed to cyberattacks. Among many lethal attacks, the zero-dynamics attack is a model based attack and it is very hard to detect. In this paper, a new strategy for intrusion detection and defense against zero-dynamics attack is proposed, and it is based on the generalized sampler that takes a weighted average of multiple samples obtained during one sampling interval. By using the generalized sampler instead of the simple sampler, the zeros of the sampled-data system can be placed at arbitrary locations, and if all zeros are placed inside the unit circle, the attack signal becomes no longer effective. This strategy still works even if all the information is exposed to hackers and it is considerably insensitive to the shift of intrinsic zeros. A design procedure for the generalized sampler is provided under mild assumptions. Furthermore, optimal designs for the selection of desired zeros are formulated considering practical issues. Theoretical findings are validated through numerical simulations.

Novel stability criteria for aperiodic sampled-data systems via a time-squared-dependent augmented functional

This paper is focusing on the stability analysis of aperiodic sampled-data systems. The augmented Lyapunov functional is powerful to produce a stability criterion with less conservatism owing to the well construction of coupled relationships among time-dependent states. In this paper, a novel augmented Lyapunov functional involving the time-squared-dependent augmented term is presented under the double-side looped-functional technique, which considers coupled relationships more fully than the current ones. Then, an improved negative definiteness lemma based on adjustable parameters is developed, resulting in a less conservative negative definite condition for the derivative of the Lyapunov functional. Finally, a stability criterion is derived based on the Lyapunov functional and the improved lemma, whose effectiveness is illustrated with four numerical examples and one practical example.

Robust $$\mathcal {L}_{\infty }$$–$$l_{\infty }$$ Sampled-Data Dynamic Output-Feedback Control for Uncertain Linear Time-Invariant Systems Through Descriptor Redundancy

We discuss the robust sampled-data dynamic output-feedback controller design problem for linear time-invariant (LTI) systems subject to parametric uncertainties and $$\mathcal {L}_{\infty }$$ disturbances. The descriptor redundancy-based methods are proposed, and their main features are: (i) sampled-data syntheses are performed in a continuous-time domain; (ii) discrete-time modeling of sampled-data systems, which is adversely affected by uncertainties in LTI plant dynamics, is not required; (iii) linear matrix inequality conditions are presented for asymptotic stability and $$\mathcal {L}_{\infty }$$ – $$l_{\infty }$$ disturbance attenuation.

Integrated stabilisation policy over multipath routing‐enabled network

In this study, a sampled-data networked control system over a multipath routing-enabled network is investigated, where each delivered signal in a path suffers a random delay. For such a system, the mean square stabilisation problem is considered under the joint design of the event-driven strategy on the actuator side and the control policy on the decision-maker side. The contributions of this study are twofold. First, by pre-defining an application time as an event-triggering parameter, the sampled-data system is transformed into a stochastic form with input delay and packet dropout. When the probability distribution F ( ⋅ ) of random delay is known a priori, the close form of packet dropout rate is proposed and a set of necessary and sufficient stabilisation conditions are developed simultaneously. When F ( ⋅ ) is unknown, the reduced system is an uncertain dynamic system. Utilising matrix polynomials, a verifiable criterion is derived for stabilising the uncertain system, which is also necessary and sufficient. Second, for the scalar system, the close form of allowable sampling period bound is developed in terms of F ( ⋅ ) and system parameters.

Stabilisation of multiply-time-delayed sampled-data systems via quasi ℋ∞ control designed with DLMI

This paper considers stabilisation of a class of multiply-time-delayed (MTD) sampled-data systems via variation-of-constant discretisation (VOCD) re-modelling and discrete-time performance control optimisation. More precisely, by utilising the variation-of-constants formula for solutions to functional differential equations, discrete-time re-modelling of sampled-data systems with MTD plants is derived, which yields finite-dimensional linear time-invariant discrete models with augmented states. Based on the VOCD re-modelling, structural features and dynamics of the MTD sampled-data systems are examined in the discrete-time approximation sense, and then stabilisation is achieved by means of the performance controller design with the discrete linear matrix inequalities (DLMI). This provides us with necessary and sufficient conditions in stabilisation and the controller parametrisation is numerically tractable in the DLMI sense. Numerical examples are included to illustrate effectiveness of the proposed method.

Regional stabilization of nonlinear sampled-data control systems: A quasi-LPV approach

This paper addresses the asymptotic stabilization of a class of continuous-time nonlinear systems under a sampled-data control. The proposed approach is based on a quasi linear parameter varying (quasi-LPV) model for the nonlinear system and the use of a parameter dependent looped-functional to deal with the aperiodic sampling effects. Explicitly taking into account that the model parameters are functions of the state and therefore are bounded only in a given region of the state space, quasi-LMI conditions are proposed to compute a regional stabilizing nonlinear state feedback control law under aperiodic sampling. These conditions are then incorporated in convex optimization problems to compute the control law aiming at the maximization of an estimate of the region of attraction of the origin or the maximization of an upper bound on the intersampling time, with a guaranteed region of stability.

Resilient Distributed Voltage Synchronization of CI Networks Under Denial of Service Attacks

This brief proposes a resilient distributed sampled-data control method to achieve the voltage synchronization of connected inverter (CI) networks against denial of service (DoS) attacks. In practical CI networks, the continuous communication among cooperative and connected inverters may be result in high communication traffic, which is also vulnerable to the DoS attacks. To this end, the proposed distributed resilient sampled-data control method can synchronize CIs' output voltages to track the reference state exponentially, even if the sparse communication is subject to DoS attacks. Specifically, in order to effectively deal with the time-varying sampling and against malicious attacks simultaneously, the sampled-data CI system is transformed into the switched time-delay CI system. By employing the Lyapunov stability theory, and the Jensen's Inequality method, the criteria for sampling interval boundedness considering DoS attacks is derived for the stable operation of closed-loop CI system. Finally, simulation results are carried out in MATLAB/SimPower Systems to verify the effectiveness of the proposed control method.

The Affordable Care Act Young Adult Mandate and Suicidal Behavior.

This article aimed to determine the association between the Affordable Care Act young adult mandate and suicidal behavior. From 2007 to 2013, we used the Nationwide/National Inpatient Sample and National Poison Data System to examine suicide attempt, and Centers for Disease Control and Prevention Wide-Ranging Online Data for Epidemiologic Research to examine suicide. We aggregated each outcome by quarter/year and conducted a difference-in-differences linear regression to compare young adults aged 19 to 25 years with those 27 to 29 years before and after implementation. There were not statistically significant associations between the mandate and suicide attempt inpatient hospitalizations (unstandardized beta coefficient [b] = -0.72, p = .12, standard error [SE] = 0.42) and percentage of poisoning cases due to suspected suicidal intent (b = 0.23, p = .19, SE = 0.16). There was a statistically significant association when examining suicide prevalence (b = -0.03, p = .01, SE = 0.001). The results suggest that health insurance may buffer against but is unlikely to reverse the increasing suicide rate.

Sampling Dependent Stability Results for Aperiodic Sampled-Data Systems

This paper investigates sampling dependent stability for aperiodic sampled-data systems by employing a Lyapunov-like functional that is time-dependent, and not imposed to be definite positive. Based on the system information on the sampling interval wholly rather than partly, a new Lyapunov-like functional is constructed, which extends existing ones by introducing the integral of the system state and the cross terms among this integral and the sampled state. To take advantage of the integral of the system state, integral equations of the sampled-data system are explored when estimating the derivative of the extended functional. By the Lyapunov-like functional theory, a new sampling dependent stability result is obtained for sampled-data systems without uncertainties. Then, the stability result is applied to sampled-data systems with polytopic uncertainties and a robust stability result is derived. At last, numerical examples are given to illustrate that the stability results improve over some existing ones.

Set-Valued Feedback Control and Its Application to Event-Triggered Sampled-Data Systems

Motivated by challenges in feedback control with event-triggered control input updates, this article studies an ellipsoidal set-valued feedback control problem for linear time-invariant (LTI) discrete-time (DT) systems, and its application to event-triggered control systems. First, a state feedback controller based on the set-valued information is designed for LTI DT systems with disturbances. Then, the stability of the closed-loop system is analyzed, and the state of the closed-loop system is shown to be uniformly ultimately bounded in an ellipsoidal set. Based on the proposed set-valued feedback controller, we consider the case when the event-triggering condition (ETC) is described by an ellipsoidal set for an event-triggered control system. To ensure the requirements on control performance and communication rates simultaneously, an optimal ETC design problem is formulated and its optimal solution is provided. Finally, simulation examples are given to show the effectiveness of the proposed method.

Intersample Modeling of the Converter Output Admittance

The stability of the converter-grid interconnection can be studied by analyzing the product of the converter output admittance and the grid impedance. For reliable stability analysis, it has been of interest to obtain accurate converter output admittance models for a wide range of frequencies, ideally also around and above the Nyquist frequency of the converter system. This article presents a modeling method for the output admittance of power converters defined in the Laplace domain that takes into account the discrete nature of the control system. The modeling method is based on analyzing the intersample behavior of sampled-data systems, a class of systems that includes the modern digitally controlled power converters. The proposed method is compared to conventional admittance modeling methods, and its accuracy is validated by means of simulations and experiments.

Global sampled-data stabilization for a class of nonlinear systems with arbitrarily long input delays via a multi-rate control algorithm

In this paper, the problem of global sampled-data stabilization is investigated for high-order nonlinear systems with arbitrarily long input delays. Based on the Lie algebra technique in nonlinear control theory, a discrete-time predictor-based multi-rate sampled-data state feedback control law with a series expansion form is proposed to ensure that the resulting system is globally asymptotically stable under some conditions. Compared with the existing methods, the proposed control algorithm just needs to know the approximate prediction of state variables, and the faster decrease of Lyapunov function may be provided for each subsystem. Performance of approximate versions of the proposed controller is given by theoretical analyses. It is showed that the approximate controllers achieve practical stability of the sampled-data closed-loop system. Finally, the obtained stabilization results are applied to a trajectory tracking problem for a high-order planar system.

Constant speed lines–curves—NURBS reference pulse IPOs (part I)

The reference pulse system avoids most of the constraints introduced by the sampled-data system. The bottleneck of the reference pulse system is the non-constant feedrate of the incremental step IPOs. The wrong initialized software DDA-IPOs make these IPOs unusable. The three conditions to apply the reference pulse system are the small incremental step, the small execution time per step, and the constant speed along the curve. Cascading an ultra-fast 3-lines algorithm “PRM-cs” to the current reference pulse IPO quickly converts this IPO to a constant speed reference pulse IPO. This applies to 2D-lines, 3D-lines, 2D-curves, and 2D-NURBS. The PRM-cs measures, in real time, the length of the discrete curve and the PRM-cs is completely new. The 2D-IPOs are perfect or nearly-perfect, but the current 3D-lines are mostly imperfect, meaning that the accuracy is much less (e.g., 37% worse) than the accuracy of the perfect or best 3D-line IPOs. The accuracy of the imperfect 3D-lines is also bounded; therefore, they can be used as constant speed 3D-line IPOs when the production manager agrees. The global definition (given by the Digital Analytic Geometry) of a discrete 3D-line is imperfect, too. The three causes of the imperfect 3D-lines will be given. All lines and curves have major axis segments. The major axis principle holds for the actual 3D-line IPOs but that is generally wrong. All existing pulse-rate or PRM-IPOs use a wrong initialization, which deteriorates the accuracy, but the new PRM-cs and the updated PRM-IPO use the right initialization. The new constant speed listSIM-IPO can be used in real time for every 2D and 3D-curve and it can be used as a benchmark for every IPO. The third-degree Trident NURBS shows that the constant speed MIDP-IPO is flexible, that it can be used for NURBS, that it can be used for conics, and that it calculates the gradient (direction vector) in real time. The paper shows that the reference pulse method is much better than the existing sampled-data methods.

Chattering-Free Reference Sliding Variable-Based SMC

The paper addresses the problem of chattering elimination in sliding mode control for sampled data dynamical systems and proposes an innovative control scheme. The key to the proposed control method is utilizing a pregenerated nonswitching type reference sliding variable profile to control the disturbed plant. As sampled data systems contain sample-and-hold devices in their input and output channels, we carry out a discrete time analysis. We consider the discretization effects on the controller in two aspects: the pace of convergence of the system and the ultimate band width. Consequently, in the reference sliding variable generator, we analyse two reaching laws, differently adapting to changes of the controller’s frequency. We prove that this approach not only minimizes the chattering phenomenon but also provides a reduction of the quasi-sliding mode band width, which in general case remains of O(T) order. Furthermore, the proposed control method incorporates a disturbance compensation algorithm, which results in the ultimate band width of O(T2) order. Finally, we also show that a certain selection of the sliding plane guarantees limitation of all the state variables’ errors to O(T2) order as well. Therefore, the proposed control algorithm significantly improves the system’s robustness.

Less conservative results for stability of sampled-data systems with constant delay

In this paper, the stability problem of the sampled-data system with communication delay is investigated. By construction with the functionals combining Lyapunov-Krasovskii functional and loop functionals, a less conservative result is derived in linear matrix inequalities. And then, by using the relations of state vectors belonging to augmented vectors and the integration between sampling times and communication delay in the system, several zero equalities are introduced. Based on the proposed result, improved stability criteria are investigated by using the zero equalities. Finally, some numerical examples are utilized to confirm the superiority and effectiveness of the results by comparing them with the existing ones.

Event-Triggered Reliable Dissipative Filtering for Delayed Neural Networks with Quantization

This paper investigates the event-triggered reliable dissipative filtering for delayed neural networks with quantization. First, an event-triggered scheme is introduced to save limited network resources, by which whether or not sampled signals should be transmitted to the quantizer depends on a predefined event-triggered condition. Second, with the event-triggered scheme, a new unified sampled-data filtering error system is established to deal with the issue of dissipative filtering for the neural networks with quantization. Third, by using the Lyapunov–Krasovskii functional method, a sufficient criterion is obtained to ensure asymptotic stability and strict $$({\mathscr {Q}},{\mathscr {S}},{\mathscr {R}})$$ - $$\alpha $$ -dissipativity for the filtering error system. Then, based on solutions to a set of linear matrix inequalities, both proper event-triggered parameters and filter parameters can be co-designed. Finally, the effectiveness and the superiority of the proposed method are verified by numerical simulation via two examples.

Discrete‐time adaptive control of uncertain sampled‐data systems with uncertain input delay: a reduction

This study proposes a discrete-time adaptive control approach for uncertain single-input single-output linear time-invariant sampled-data systems with uncertain, constant input time delay that has a known upper-bound, without explicitly estimating the time delay. To cope with the unknown time delay, a reduction approach similar to that proposed by Artstein in 1982 is used, which results in a delay-free system that simplifies the control law design. In addition, the proposed control approach is capable of coping with bounded exogenous disturbances. A rigorous stability analysis shows that the proposed control approach drives the system output to a bound around the reference signal asymptotically, in the presence of an exogenous disturbance. Moreover, simulation results are shown to verify the approach.

On construction of sampling patterns for preserving observability/controllability of linear sampled-data systems

ABSTRACT In this paper, we design a new nonequidistant sampling pattern such that the property of controllability and observability of the linear continuous time systems is preserved during the procedure of the sample and zero-order hold operation. The idea behind the strategy comes from Kronecker's theorem and it is proven that new construction is more effective by requiring less number of sampling times which guarantees controllability and observability of sampled-data system in two dimensional space. Moreover, we provide one application in the concept of controllability of the pendulum in two dimensional space and obtain corresponding digital controls which make the corresponding sampled-data system controllable. Finally, the research is extended to different type of sampling patterns which are compared with the constructed sampling pattern separately.

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.