Time-varying State Delays Research Articles

Robust local stabilization of discrete time-varying delayed state systems under saturating actuators

This paper deals with discrete time-varying systems with state-delayed and saturating actuators. A robust state feedback control gain is designed through convex methods ensuring the local stability of the time-varying system with interval time-varying state delay. The estimate of the set of admissible initial conditions is characterized by three convex sets allowing less conservative estimates. Through two numerical examples, we compare our approach with others in the literature and illustrate the better behavior of the proposed methods.

Quantification of Flexibility of a District Heating System for the Power Grid

District heating systems (DHS) that generate/consume electricity are increasingly used to provide flexibility to power grids. The quantification of flexibility from a DHS is challenging due to its complex thermal dynamics and time-delay effects. This article proposes a three-stage methodology to quantify the maximum flexibility of a DHS. The DHS is firstly decomposed into multiple parallel subsystems with simpler topological structures. The maximum flexibility of each subsystem is then formulated as an optimal control problem with time delays in state variables. Finally, the available flexibility from the original DHS is estimated by aggregating the flexibility of all subsystems. Numerical results reveal that a DHS with longer pipelines has more flexibility but using this flexibility may lead to extra actions in equipment such as the opening position adjustment of valves, in order to restore the DHS to normal states after providing flexibility. Impacts of the supply temperature of the heat producer, the heat loss coefficient of buildings and the ambient temperature on the available flexibility were quantified.

Mixed control of delayed Markov jump linear systems

This study investigates the state feedback control laws for Markov jump linear systems with state and mode-observation delays. An assumption in this study is that the delay of the mode observation obeys an exponential distribution. Also, the authors raise an unknown time-varying state delay applied in the composition of the state feedback controller. A method of remodelling the closed-loop system as a standard Markov jump linear system with state delay is shown. Furthermore, on the basis of this remodelling, several linear matrix inequalities for designing feedback gains for stabilisation and mixed control are proposed. Finally, the authors apply a numerical simulation for examining the effectiveness of the proposed mixed controller designing method.

Event-Triggered Control of Nonlinear Systems With Time-Varying State Delays

Nonlinear systems with time delays have been object of intense investigation in the last decades for their ability of capturing the behavior of many natural and engineering systems, including ecological, biomedical, industrial, robotic, and networked systems. In this article, a method for the event-triggered stabilization in the sample-and-hold sense of nonlinear time-delay systems with time-varying state delays is presented. The approach exploits control Lyapunov-Razumikhin functions and a spline-based approximation of the functional state feedback, resulting in a finite-memory controller that avoids (by construction) continuous-state monitoring while ensuring also that the minimal interevent time is strictly positive. Examples of application of the illustrated technique highlight the potential of the approach taken.

Observer and fault‐tolerant controller design for discrete‐time multiple state‐delayed T–S fuzzy systems

This study is concerned with observer-based fault estimation (FE) and fault-tolerant controller design for a class of discrete-time Takagi–Sugeno (T–S) fuzzy systems. There exist multiple time-varying state delays, sensor and actuator faults, local non-linear dynamics and exogenous disturbances in the systems. In comparison with the existing results, the approach suggested in this study is more flexible and feasible. By means of the n-step induction FE, a novel fuzzy adaptive descriptor observer is developed to obtain the n-step error functions. Then, an active dynamic output feedback fault-tolerant controller is designed to stabilise the closed-loop fuzzy system. Furthermore, a set of delay-dependent sufficient conditions are provided by the fuzzy Lyapunov function which utilises the form of linear matrix inequalities. The stability results from the observer and the controller in this study have less conservatism compared with the ones from the existence of observers and fault-tolerant controllers. At last, a simulation example is presented to demonstrate the advantages and effectiveness of the approach proposed in the study.

Event-triggered Stabilization of Linear Time-delay Systems by Static Output Feedback Control

In this paper, we study the stabilization problem for a class of linear systems with a time-varying state delay. An event-triggered static output feedback controller is proposed, such that the sampling frequency and the update time of the controller are both lowered. First, we present a novel event-triggering mechanism depending not only on the output but also on an exponential term, with which less sampling is required and Zeno behavior can be excluded at the same time. Some sufficient conditions are then obtained, under which an exponential convergence can be achieved by means of the comparison principle approach. It is further shown that the parameters design can be easily given if the case reduces to the state feedback control. Moreover, two examples are presented to show the effectiveness of the results.

Universal Adaptive Neural Network Predictive Algorithm for Remotely Piloted Unmanned Combat Aerial Vehicle in Wireless Sensor Network.

Remotely piloted unmanned combat aerial vehicle (UCAV) will be a prospective mode of air fight in the future, which can remove the physical restraint of the pilot, maximize the performance of the fighter and effectively reduce casualties. However, it has two difficulties in this mode: (1) There is greater time delay in the network of pilot-wireless sensor-UCAV, which can degrade the piloting performance. (2) Designing of a universal predictive method is very important to pilot different UCAVs remotely, even if the model of the control augmentation system of the UCAV is totally unknown. Considering these two issues, this paper proposes a novel universal modeling method, and establishes a universal nonlinear uncertain model which uses the pilot’s remotely piloted command as input and the states of the UCAV with a control augmentation system as output. To deal with the nonlinear uncertainty of the model, a neural network observer is proposed to identify the nonlinear dynamics model online. Meanwhile, to guarantee the stability of the overall observer system, an adaptive law is designed to adjust the neural network weights. To solve the greater transmission time delay existing in the pilot-wireless sensor-UCAV closed-loop system, a time-varying delay state predictor is designed based on the identified nonlinear dynamics model to predict the time delay states. Moreover, the overall observer-predictor system is proved to be uniformly ultimately bounded (UUB). Finally, two simulations verify the effectiveness and universality of the proposed method. The results indicate that the proposed method has desirable performance of accurately compensating the time delay and has universality of remotely piloting two different UCAVs.

H-infinity stability analysis and output feedback control for fuzzy stochastic networked control systems with time-varying communication delays and multipath packet dropouts

The H-infinity stability analysis and delay-dependent Takagi–Sugeno (T–S) fuzzy dynamic output feedback control are proposed for the T–S fuzzy discrete networked control systems with time-varying communication delay and multipath packet dropouts. T–S fuzzy model is employed to approximate the discrete networked control system with time-varying state delay and external disturbance. Stochastic system theory and Bernoulli probability distribution are employed to describe the time-varying communication delay and multipath packet dropouts. Delay-dependent T–S fuzzy dynamic output feedback controller is designed. The delay-dependent T–S fuzzy dynamic output feedback controller is employed to relax the design conditions and enhance the design flexibility. The delay-dependent Lyapunov–Krasovskii functional, stochastic system theory and Bernoulli probability distribution are introduced to guarantee the stochastic mean-square stability and prescribed H-infinity performance. Some slack matrices are introduced to reduce the computation complexity. Finally, simulation examples are presented to show the effectiveness and advantages of the proposed methods.

Neural-network-based adaptive backstepping control for a class of unknown nonlinear time-delay systems with unknown input saturation

In this paper, a neural-network-based adaptive backstepping control scheme is developed for a class of unknown nonlinear systems with unknown time-varying delayed states and unknown saturated delayed input. In the proposed method, radial basis function neural network is adopted to approximate the unknown nonlinear functions. An adaptive backstepping design is employed to compensate for the unknown time-varying delays in states. In addition, to overcome the effects of input delay, an auxiliary dynamic system is constructed. Moreover, a novel adaptive law is used for estimating unknown bounds of saturation function. Using the Lyapunov stability theorem, it is proven that the closed-loop system is semi-globally uniformly ultimately bounded and the tracking error can converge to small desired value by the proper choose of design parameters. Finally, the effectiveness of the proposed method is illustrated by applying it to a chemical reactor recycle system, one-link manipulator actuated by a DC motor and a Brusselator model.

Fault Estimation and Tolerant Control for Discrete-Time Multiple Delayed Fuzzy Stochastic Systems With Intermittent Sensor and Actuator Faults

This article is concerned with observer-based fault estimation (FE) and tolerant controller design for a series of discrete-time Takagi-Sugeno (T-S) fuzzy stochastic systems. There exist multiple time-varying state delays, intermittent sensor and actuator faults, nonlinear dynamics, and exogenous disturbances in the systems. Compared with the results of the existence, this approach suggested in this article is more flexible and feasible. By means of the FE information, a novel fuzzy adaptive descriptor observer is developed to obtain the error dynamics. Then, an active observer-based fault-tolerant controller is designed to stabilize the closed-loop fuzzy system. Furthermore, a set of delay-dependent sufficient conditions are provided by the fuzzy Lyapunov function with the way of linear matrix inequalities (LMIs), which has less conservatism compared with the ones of the existing observers and fault-tolerant controllers. Finally, a simulation example is shown to illustrate the advantages and effectiveness of this approach depicted in this article.

Local stabilization of nonlinear discrete-time systems with time-varying delay in the states and saturating actuators

Although most of the control design methods assume unbounded control signals, real systems do have saturating actuators, which may degenerate closed-loop performance or even lead to unstable behavior. Additionally, the delay is generally almost ubiquitous in processes, that is also imposing performance and stability constraints. Our main contribution is to provide a controller design methodology for the stabilization of delayed systems under saturating actuators. Specifically, we address the design of non-Parallel Distributed Compensation (non-PDC) state feedback fuzzy control laws that locally stabilize a class of nonlinear discrete-time systems with state time-varying delay and saturating actuators. The proposed non-PDC control law depends on the current state xk and the state delayed by d¯ samples. Based on the Lyapunov–Krasovskii approach, we characterize the safe region of initial conditions through two sets: an ellipsoidal one for the current state vector, and another set for the delayed state vectors. Through two convex optimization procedures, we can maximize the estimate of the region of attraction of the closed-loop control system. Additionally, a relaxation method inspired by the Frank-Wolfe algorithm is introduced, yielding better estimates of the region of attraction. The achievements are compared with other finds in the literature, illustrating the efficiency of this proposal.

Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations

Network control system (NCS) is a distributed real-time feedback control system with the continuous development of network technology. It is generally composed of network, controller, actuator and sensor. It has brought great convenience to people in many fields, but it also has many problems, which makes the research of control system more complicated. Recently, there have been some efforts to tackle the reliable guaranteed cost controller design problem, and some good results have also been obtained for the continuous-time and for the discrete-time. However, there have been few results in the literature of an investigation for the reliable guaranteed cost controller design of nonlinear uncertain systems with time-varying state delay and actuator failure. This paper concerns the reliable guaranteed cost control problem of uncertain systems with time-varying state delay and nonlinear perturbations for a given quadratic cost function. The problem is to design a reliable guaranteed cost state feedback control law which can tolerate actuator failures, such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound. Firstly, the existence condition of reliable guaranteed cost control law is given by constructing Lyapunov stability function and using linear matrix inequality (LMI). Secondly, the design method of the optimal reliable guaranteed cost controller is given by solving the convex optimization problem with LMI constraints, which minimizes the upper bound of guaranteed cost for closed-loop systems. In the end, the numerical simulation result illustrates the effectiveness of the proposed method.

Consensus Tracking Control of Uncertain Multiagent Systems With Sampled Data and Time-Varying Delay.

In this article, the adaptive consensus tracking control is developed for uncertain multiagent systems with time-varying state delay in the case that leader's state is accessible at sampling instants. By proposing a distributed sampled observer with hybrid form, adaptive tracking controller with the complementary term is designed for first-order multiagent systems, and then is extended to high-order multiagent systems with the aid of dynamic surface control. Through the complementary term, the effects of parameter estimation error as well as dynamical terms with time-varying delays are eliminated and thus less conservative condition on time delays is required. It is proved that, under criteria in terms of linear matrix inequalities (LMIs), tracking error and estimation error exponentially converge to zero for first-order systems, and to a sufficiently small neighborhood of zero for high-order systems.

A Novel Delay-Independent Robust Adaptive Controller Design for Uncertain Nonlinear Systems With Time-Varying State Delay

Abstract In this paper, two novel adaptive control strategies are presented based on the linear matrix inequality for nonlinear Lipschitz systems. The proposed approaches are developed by creatively using Krasovskii stability theory to compensate parametric uncertainty, unknown time-varying internal delay, and bounded matched or mismatched disturbance effects in closed-loop system of nonlinear systems. The online adaptive tuning controllers are designed such that reference input tracking and asymptotic stability of the closed-loop system are guaranteed. A novel structural algorithm is developed based on linear matrix inequality (LMI) and boundaries of the system delay or uncertainty. The capabilities of the proposed tracking and regulation methods are verified by simulation of three physical uncertain nonlinear system with real practical parameters subject to internal or state time delay and disturbance.

Normalization and stabilization of neutral descriptor hybrid systems based on P-D feedback control

This paper is concerned with the problem of normalization and stabilization of neutral descriptor hybrid systems with neutral and time-varying state delays. By designing mode-dependent delayed proportional-derivative state feedback and mode-dependent delayed proportional-derivative output injection controllers, respectively, the stabilization problem of neutral descriptor hybrid systems is transformed into the stability problem of normal neutral hybrid systems via normalization technique. Sufficient conditions are provided in terms of linear matrix inequalities by constructing mode-dependent and delay-dependent Lyapunov–Krasovskii functional. Simulation examples including a partial element equivalent circuit system are employed to verify the usefulness and validity of the controllers design method.

Static anti-windup compensator for nonlinear systems with both state and input time-varying delays

In this work, the design on static anti-windup compensator (SAWC) for a class of nonlinear systems with saturation constraint is presented, in which both state time-varying delay and input one are involved. First, by utilizing an augmented Lyapunov–Krasovskii functional (LKF), sector condition, and L2 gain reduction for exogenous input, a sufficient condition on local stability is presented in terms of linear matrix inequalities (LMIs), which is later extended to the global stability issue. During the discussions, an improved dynamical Lyapunov method is initially proposed and it can fully utilize the individual and mutual information on both state and input delays. Especially, some effective techniques are utilized to given more tighter estimations on the LKF’s derivatives. In all, these treatments above can result in much less conservatism. Finally, some comparisons and simulations are presented in two numerical examples under the proposed SAWC.

Prediction-based super twisting sliding mode load frequency control for multi-area interconnected power systems with state and input time delays using disturbance observer

A shift in paradigm from dedicated to open communication channels in power systems has made them prone to constant and time-varying delays. This paper tackles a novel load frequency control (LFC) problem in the presence of constant and time-varying delays in state and control input under load disturbances. The presence of time delays can deteriorate the performance of the controller or even destabilise the system. The above problem is addressed through a prediction-based super twisting sliding mode control (ST-SMC) using a state and disturbance observer. The proposed design achieves finite-time convergence of frequency and tie-line power deviation. The said design is validated under ramp and random step disturbance, with nonlinearities like generation rate constraints and governor deadband, with an integration of renewable energy and also with IEEE 39 bus power system. The closed-loop stability is proven thanks to candidate Lyapunov function and verified by simulations.

Global regulation of high-order feedforward and non-feedforward systems with unknown time-varying delays in states and input

In this paper, the global regulation problem is considered for a class of high-order nonlinear systems with unknown time-varying delays. More specifically, the considered systems consist of a chain of power integrators with high-order nonlinearity and there are unknown input and state delays. From the system structural point of view, the high-order feedforward nonlinearity is further extended to include non-feedforward terms. In our controller design, our controller is a memoryless one which does not use any past input values such that any a priori information on time-varying delays is not needed. The global regulation of the controlled system is analyzed by using the Razumikhin theorem and adding a power integrator method.

ISS Robust Stabilization of State-Delayed Discrete-Time Systems With Bounded Delay Variation and Saturating Actuators

We address the problem of robust input-to-state stabilization of parameter-varying discrete-time systems with time-varying state delay, saturating actuators, and subject to $\ell _2$ -limited disturbance. It is assumed that the delay belongs to a known interval and its maximum variation between two consecutive instants is taken into account. The proposed convex delay-dependent conditions for the synthesis of robust state feedback controllers ensure local input-to-state stability of the closed-loop system for a set of initial conditions and for energy-bounded disturbance signals. However, the computed controllers do not require the real-time knowledge of the delay. The approach is based on the rewriting of the saturating and delayed system in terms of a switching uncertain augmented delay-free system with a dead-zone nonlinearity and on the application of the generalized sector condition. To illustrate the efficiency of our approach, we compare it by means of numerical examples with others found in the literature.

Stabilization of Discrete-Time Delayed Systems in Presence of Actuator Saturation Based on Wirtinger Inequality

This paper examines the stability analysis of discrete-time control systems particularly during the event of actuator saturation and time-varying state delay. With the help of Wirtinger inequality along with Lyapunov-Krasovskii functional gain of state feedback controller is determined for stabilization of above system. The saturation nonlinearity is represented in the terms of convex hull. A new linear matrix inequality (LMI) criterion is settled with reciprocally convex combination based inequality which is dependent on delay. The proposed criterion is less conservative in concern to increase the delay bound and a controller is also simulated for real time problem of missile control system in this paper. It is also attained that projected stability criterion is less conservative compared to other outcomes. Furthermore, an optimization procedure together with LMI constraints has been proposed to maximize the attraction of domain.