Sampling Instants Research Articles

Differential linear matrix inequality in optimal sampled-data control

This paper addresses the design of optimal sampled-data output feedback full order controllers for linear continuous-time invariant systems. First, H2 and H∞ performance indices are determined and expressed through differential linear matrix inequalities (DLMIs). Second, in each scenario, the optimal sampled-data controller of the aforementioned class is determined from a convex programming problem expressed by DLMIs. Theoretical achievements are based on the direct application of the celebrated Bellman’s Principle of Optimality expressed in terms of the dynamic programming equation associated to the time interval corresponding to two successive sampling instants. The design problems to be dealt with are convex and are solved by converting all constraints to LMI and adopting a piecewise linear solution. The possibility of aperiodic sampling is considered and briefly discussed. Finally, academic examples are solved for illustration.

Notice of Violation of IEEE Publication Principles: An Improved Result on Exponential Stabilization of Sampled-Data Fuzzy Systems

This brief paper studies the exponential stabilization problem for the Takagi–Sugeno fuzzy systems with a variable sampling. Different from previous results, the gains of fuzzy state feedback controller adopted in this paper are time-varying during two consecutive sampling instants, which can contribute to the enlargement of the allowable sampling interval by choosing a suitable design parameter. To reduce the design conservativeness, a novel fuzzy time-dependent Lyapunov functional (FTDLF) is put forward to fully exploit the accessible information about the sampling pattern and the fuzzy basis functions. Moreover, a more relaxed constraint condition is presented to ensure the positive definiteness of the FTDLF on sampling intervals. By resorting to the novel FTDLF and the relaxed constraint condition, new exponential stabilization criteria dependent on and independent of upper bounds on time derivatives of fuzzy basis functions are established, by which a larger sampling interval can be achieved. One example is offered to demonstrate the validity and superiorities of the obtained new results.

On aperiodic event-triggered master-slave synchronization of chaotic Lur'e systems

This paper is concerned with master-slave synchronization for chaotic Lur'e systems subject to aperiodic sampled-data. To reduce the communication burden, an aperiodic event-triggered (APET) transmission scheme is introduced to determine the transmission of the latest sampling synchronization data. In order to reduce the design conservatism, a novel time-dependent Lyapunov functional (TDLF) is constructed to fully use the characteristics about sampling behavior, triggering error, and nonlinear part of the system, simultaneously. A more relaxed constraint criterion is then presented to ensure the positivity of the whole functional between two sampling instants. By partially resorting to the TDLF, the APET-based synchronization criterion depending on the upper and lower bounds of the uncertain sampling period is presented. The synchronization criterion based on aperiodic-sampling mechanism is also provided. Finally, a typical example about neural networks is offered to illustrate the benefit and validity of obtained synchronization methodologies.

Global sampled-data output feedback stabilization for a class of uncertain nonlinear systems

This paper investigates the global asymptotical stabilization using sampled-data output feedback (i.e., not all state information is available at the output) for a class of nonlinear systems which have uncontrollable and unobservable linearizations around the origin. A homogeneous version of Gronwall–Bellman inequality is introduced as the essential tool to estimate trajectory of nonlinear sampled-data control systems between two successive sampling instants. With the help of this new tool as well as the homogeneous domination approach, a sampled-data observer-based controller is constructed to globally asymptotically stabilize the origin of the nonlinear system under a homogeneous growth condition.

Driving Cycles Based on Fuel Consumption

Type-approval driving cycles currently available, such as the Federal Test Procedure (FTP) and the Worldwide harmonized Light vehicles Test Cycle (WLTC), cannot be used to estimate real fuel consumption nor emissions from vehicles in a region of interest because they do not describe its local driving pattern. We defined a driving cycle (DC) as the time series of speeds that when reproduced by a vehicle, the resulting fuel consumption and emissions are similar to the average fuel consumption and emissions of all vehicles of the same technology driven in that region. We also declared that the driving pattern can be described by a set of characteristic parameters (CPs) such as mean speed, positive kinetic energy and percentage of idling time. Then, we proposed a method to construct those local DC that use fuel consumption as criterion. We hypothesized that by using this criterion, the resulting DC describes, implicitly, the driving pattern in that region. Aiming to demonstrate this hypothesis, we monitored the location, speed, altitude, and fuel consumption of a fleet of 15 vehicles of similar technology, during 8 months of normal operation, in four regions with diverse topography, traveling on roads with diverse level of service. In every region, we considered 1000 instances of samples made of m trips, where m varied from 4 to 40. We found that the CPs of the local driving cycle constructed using the fuel-based method exhibit small relative differences (<15%) with respect to the CPs that describe the driving patterns in that region. This result demonstrates the hypothesis that using the fuel based method the resulting local DC exhibits CPs similar to the CPs that describe the driving pattern of the region under study.

Characterization of semiglobal stability properties for discrete-time models of non-uniformly sampled nonlinear systems

Discrete-time models of non-uniformly sampled nonlinear systems under zero-order hold relate the next state sample to the current state sample, (constant) input value, and sampling interval. The exact discrete-time model, that is, the discrete-time model whose state matches that of the continuous-time nonlinear system at the sampling instants may be difficult or even impossible to obtain. In this context, one approach to the analysis of stability is based on the use of an approximate discrete-time model and a bound on the mismatch between the exact and approximate models. This approach requires three conceptually different tasks: (i) ensure the stability of the (approximate) discrete-time model, (ii) ensure that the stability of the approximate model carries over to the exact model, (iii) if necessary, bound intersample behaviour. Existing conditions for ensuring the stability of a discrete-time model as per task (i) have some or all of the following drawbacks: are only sufficient but not necessary; do not allow for varying sampling rate; cannot be applied in the presence of state-measurement or actuation errors. In this paper, we overcome these drawbacks by providing characterizations of, i.e. necessary and sufficient conditions for, two stability properties: semiglobal asymptotic stability, robustly with respect to bounded disturbances, and semiglobal input-to-state stability, where the (disturbance) input may successfully represent state-measurement or actuation errors. Our results can be applied when sampling is not necessarily uniform.

Global practical stabilisation of a class of switched nonlinear systems via sampled-data control

ABSTRACT This paper investigates a global practical stabilisation problem of a class of switched nonlinear systems via sampled-data control, where all the subsystems are assumed to be in non-strict feedback form and all the -subsystems are not required to be input-to-state stable. Since the system states are unmeasurable and the output can only be measured at the sampling instants, an observer is designed to estimate the state. By adopting the multiple Lyapunov function method and the backstepping technique, a virtual controller is constructed, then a sampled-data controller is obtained by discretizing the designed virtual controller. With appropriate choice of a switching law and an allowable sampling period, it is proved that the designed sampled-data controller renders the corresponding closed-loop system to be globally practically stable. Finally, two examples are presented to illustrate effectiveness of the proposed methods.

Master–slave structure‐based capacitor voltage measuring technique for hybrid modular multilevel converters

The measurement of the capacitor voltage of each sub-module (SM) is a crucial part of achieving robust control of modular multilevel converters (MMCs). This study proposes a master-slave structure-based capacitor voltage measuring technique (MS-MT) for hybrid MMCs, in which the SM capacitor voltages are calculated using nine processes at the corresponding sampling instants according to the changing rule of the arm AC-side voltage and SM operation states. In MS-MT, the master sensor is used to measure the overall arm voltage while the slave sensor, which measures the full bridge, is used additionally to improve accuracy. Furthermore, MS-MT performs well even under pre-charging and DC short-circuit fault conditions, for the reason that a single SM short-circuit fault can be detected during above two conditions by comparing the voltages measured by the two sensors. Compared with the direct measuring technique, which has low measurement errors, and the overall measuring technique, which requires less hardware cost, MS-MT inherits both advantages. Finally, extensive simulation and experimental results validate the effectiveness of the proposed MS-MT.

A Min–Max Approach to Event- and Self-Triggered Sampling and Regulation of Linear Systems

This paper presents both an event- and a self-triggered sampling and regulation scheme for continuous time linear dynamic systems by using zero-sum game formulation. A novel performance index is defined wherein the control policy is treated as the first player and the threshold for control input error due to aperiodic dynamic feedback is treated as the second player. The optimal control policy and sampling intervals are generated using the saddle point or Nash equilibrium solution, which is obtained from the corresponding game algebraic Riccati equation. To determine the optimal event-based sampling scheme, an event-triggering condition is derived by utilizing the worst case control input error as the threshold. To avoid the additional hardware for the event-triggering mechanism, a near optimal self-triggering condition is derived to determine the future sampling instants given the current state vector. To guarantee Zeno-free behavior in both the event- and self-triggered closed-loop systems, the minimum intersample times are shown to be lower bounded by a nonzero positive number. Asymptotic stability of the closed-loop system is ensured using Lyapunov stability analysis. Finally, simulation examples are provided to substantiate the analytical claims.

Identification of continuous‐time switched linear systems from low‐rate sampled data

This study is about the identification problem of continuous-time switched linear systems from low-rate sampled data. The main problem in the identification of such systems, when the sampling rate is low, is that the sampling instances do not coincide with the switching times. Therefore, some of the measured samples are generated from more than one subsystem. This problem was first observed during the sampling of a step-up DC–DC converter at the rate of 100 kHz. The current study aims to explain the theoretical aspects of the identification problem of continuous-time switched linear systems, and to offer a new method for estimating of subsystem parameters plus the switching times. The proposed method accurately determines the switching times which might be between two consecutive sampling instances. The results obtained from the proposed method are used to determine the switching times and parameters of an experimental DC–DC boost converter.

Optimal and Robust Sampled-Data Control of Markov Jump Linear Systems: A Differential LMI Approach

This paper addresses the problem of designing optimal sampled-data state feedback control for continuous-time Markov jump linear systems. Stability and performance robustness against polytopic uncertainty acting on the system parameters including the transition rate matrix are analyzed. The main goal is to characterize the optimal solution of this class of problems in the context of ${\mathcal H}_2$ and ${\mathcal H}_\infty$ performances. The theoretical achievements are based on the direct application of the celebrated Bellman's Principle of Optimality expressed in terms of the dynamic programming equation applied to the time interval corresponding to two successive sampling instants. The design conditions are expressed through differential linear matrix inequalities. Examples are solved for illustration.

Networked State Estimation With Delayed and Irregularly Spaced Time-Stamped Observations

We analyze the performance of a networked multisensor continuous-discrete Kalman filter in the presence of random observation delay and irregular sampling. The primary cause for irregular intersample intervals is the occasional loss of information packets. Additional causes include lack of synchrony between sensors, difference in their sampling rates, and the superposition of multiple sampling patterns. We rely on time stamping of all sensor packets to accurately determine, at the estimation hub, both transmission delay and sensor sampling instants. We relate the average (steady-state) error covariance to two moment-generating functions: 1) we provide lower and upper bounds on the average error covariance in the presence of irregular sampling, expressed in terms of the moment-generating function of the sampling intervals; 2) we obtain a stability condition that depends on the region of convergence of this moment-generating function; and 3) we derive an expression for the added error caused by transmission delay, which depends on the moment-generating function of the delay. We also demonstrate that the average error covariance depends primarily on the average sampling interval, with a very minor dependence on the variance and higher order moments of the multisensor intersample interval.

‐disturbance attenuation for LPV systems under sampled‐data control

SummaryThis paper focuses on the synthesis of sampled‐data linear parameter‐varying (LPV) control laws. In particular, the problem of disturbance attenuation for continuous‐time LPV systems under aperiodic sampling is addressed. It is explicitly assumed that the LPV controller is updated only at the sampling instants while the plant parameter can evolve continuously between two sampling instants. The proposed approach is based on a polytopic model for the LPV system and the use of a parameter‐dependent looped‐functional to deal with the aperiodic sampling effects. From these ingredients, conditions in a quasi‐LMI form (ie, they are LMIs provided a scalar parameter is fixed) are derived to compute a stabilizing control law ensuring an upper bound on the closed‐loop system ‐gain. These conditions are then incorporated to convex optimization problems aiming at either minimizing the ‐gain upper bound or maximizing the allowable sampling interval for which stability is ensured. Numerical examples illustrate the proposed methodology.

An Interpolation Technique for Input Constrained Robust Stabilization

This paper presents an interpolation technique of two given robust stabilizing gains for input constrained uncertain systems. The proposed interpolated feedback gain is computed at every sampling instance by solving an optimization problem with a single decision variable. Use of the interpolated feedback gain can bring about not only large invariant set but also good control performance. Moreover, it is shown that the feasible and invariant set yielded by the proposed control is the convex hull of the two invariant sets by the known controls. The simulation results show that the proposed interpolation based feedback gain indeed results in both large invariant set and good control performance.

On the Asymptotic Hyperstability of Linear Time-Invariant Continuous-Time Systems under a Class of Controllers Satisfying Discrete-Time Popov’s Inequality

This paper is concerned with the property of asymptotic hyperstability of a continuous-time linear system under a class of continuous-time nonlinear and perhaps time-varying feedback controllers belonging to a certain class with two main characteristics; namely, (a) it satisfies discrete-type Popov’s inequality at sampling instants and (b) the control law within the intersample period is generated based on its value at sampling instants being modulated by two design weighting auxiliary functions. The closed-loop continuous-time system is proved to be asymptotically hyperstable, under some explicit conditions on such weighting functions, provided that the discrete feed-forward transfer function is strictly positive real.

Periodic event-triggered robust output feedback control for nonlinear uncertain systems with time-varying disturbance

This paper investigates the periodic event-triggered robust output feedback control problem for a class of nonlinear uncertain systems subject to time-varying disturbance. By means of the feedback domination approach and disturbance compensation technique, a new framework of periodic event-triggered robust control strategy is developed in the form of output feedback, which encompasses a discrete-time event-triggering transmission scheme that is only intermittently monitored at sampling instants and a discrete-time output feedback controller consisting of a set of linear difference equations. The proposed robust method may reduce the communication resource utilization as compared to the non-event triggering schemes while maintaining a desirable closed-loop system performance even in the presence of a general class of time-varying disturbance and nonlinear uncertainties. The closed-loop system under the proposed control scheme is actually modeled as a hybrid system, and it is shown that the global practical stability of the closed-loop hybrid system is guaranteed by selecting a sufficiently large scaling gain and a sufficiently small sampling period. Finally, the experimental results on a DC–DC buck power converter are presented to illustrate the effectiveness of the proposed control approaches.

Non-uniform Multi-rate Estimator based Periodic Event-Triggered Control for resource saving

This paper proposes a systematic non-uniform multi-rate estimation and control framework for a periodic event-triggered system which is subject to external disturbance and sensor noise. When the disturbance dynamic model is available, and in order to efficiently estimate the state variable and disturbance from non-uniform slow-rate measurements, a time-varying Kalman filter is designed. When the disturbance dynamic model is not available, a disturbance observer is proposed as an alternative approach. Both the Kalman filter and the disturbance observer are proposed in a non-uniform multi-rate format. Such disturbance estimation enables faster controller updating in spite of slower measurement. Interlacing techniques are used in the control system to uniformly distribute the computational load at each fast sampling instance. Compared to the conventional time-triggered sampling paradigm, the control solution is able to reduce the resource utilization, while maintaining a satisfactory control performance. The proposed control solution will reduce the number of transmissions among devices, which enhances the energy and computational efficiency. Simulation results are provided to validate the effectiveness and benefits of the proposed control algorithms.

Periodic event-triggered control of nonlinear systems using overapproximation techniques

In event-triggered control, the control task consisting of sampling the plant’s output and updating the control input is executed whenever a certain event function exceeds a given threshold. The event function typically needs to be monitored continuously, which is difficult to realize in digital implementations. This has led to the development of periodic event-triggered control (PETC), in which the event function is only evaluated periodically. In this paper, we consider general nonlinear continuous event-triggered control (CETC) systems, and present a method to transform the CETC system into a PETC system. In particular, we provide an explicit sampling period at which the event function is evaluated and we present a constructive procedure to redesign the triggering condition. The latter is obtained by upper-bounding the evolution of the event function of the CETC system between two successive sampling instants by a linear time-invariant system and then by using convex overapproximation techniques. Using this approach, we are able to preserve the control performance guarantees (e.g., asymptotic stability with a certain decay rate) of the original CETC system.

Networked control of a power system: A non-uniform sampling approach

This article deals with the damping of low-frequency power systems oscillations using a networked controller on a smart grid. We assume that the network channel is band-limited and has random communication delay whose probability distribution can be found. To mitigate the effect of delay on control system performance, the measurements from the system are sampled at a random and non-uniform period but the inputs are updated at a faster and constant rate. This makes the closed-loop control system a stochastic switching system. A framework to analyze the mean square stability of the closed-loop system is developed and a switching observer-based controller is designed to ensure the stability of the system at random sampling instants. A case study has been performed using the Western-System-Coordinating-Council (WSCC) 3-machines, 9-bus system for verification of the technique. The contribution of the paper is a bandwidth efficient delay compensation technique and its application to power systems stability enhancement in a smart grid.

Leader-Following Consensus of Multi-Agent Systems With Switching Networks and Event-Triggered Control

This paper addresses the event-based leader-following consensus of a class of multi-agent systems with switching networks. Fully distributed event-triggered functions are proposed to select the sampling instants automatically. Detailed algorithms are given to design the feedback gains and coupling strength. The positive lower bound of the sampling intervals is captured to exclude Zeno behaviours. Finally, simulations are also carried out to verify the effectiveness of the event-triggered control scheme.