Nonlinear Time-delay Systems Research Articles

Event-Triggered Control of Switched Nonlinear Time-Delay Systems With Asynchronous Switching.

This article investigates the event-triggered switching control (ETSC) of switched nonlinear time-delay systems (SNTDSs) with asynchronous switching. First, we study the input-to-state stability (ISS) and integral ISS (iISS) for SNTDSs with asynchronous switching, where switching instants are generated based on the designed event-triggered mechanism. Among existing works on the ETSC, systems behavior at event-triggered instants is neglected. In fact, whenever an event is triggered, the systems mode will jump suddenly such that a switch is imposed to the systems, leading to the change of subsystems. Moreover, asynchronous switching behavior may occur between the actual subsystem and its corresponding controller. These facts bring great challenges for the event-triggered mechanism design and ISS analysis. To tackle these problems, a new Lyapunov-based event-triggered mechanism with adjustable parameters is designed to establish the relationship between systems switches and event triggers, and exclude the Zeno phenomenon. The analysis of the asynchronous switching behavior can be implemented and some ISS and iISS criteria of SNTDSs are derived utilizing the merging switching technique. Finally, two numerical examples, including a practical stirred tank reactor system, are presented to show the validity of the proposed methods.

Event-Triggered State Observer Design for a Class of Nonlinear Time-Delay Fractional-Order Systems

Event-Triggered State Observer Design for a Class of Nonlinear Time-Delay Fractional-Order Systems

A Lyapunov--Krasovskii Method for Semiglobal Stabilization of a Class of Time-Delay Nonlinear Systems With Uncontrollable Linearization by Linear Feedback

A Lyapunov--Krasovskii Method for Semiglobal Stabilization of a Class of Time-Delay Nonlinear Systems With Uncontrollable Linearization by Linear Feedback

Non-singular control strategies for a class of strict-feedback nonlinear time-delay systems

This paper focuses on the non-singular control for strict-feedback nonlinear time-delay systems. The boundedness of all the signals of the closed-loop system is rigorously proved by introducing a class of Lyapunov-Krasovskii functionals, including exponential functions. Besides, novel auxiliary functions with continuous derivatives are proposed to construct the control law to avoid the discontinuity of the virtual controllers. Besides, the amount of computation is reduced by applying the new auxiliary functions when the other control methods require loads of calculations for handling singular problems. In the end, numerical examples are given to validate the effectiveness of the proposed control scheme.

Decentralized Implicit Inverse Control for Large-Scale Hysteretic Nonlinear Time-Delay Systems and Its Application on Triple-Axis Giant Magnetostrictive Actuators.

This article proposes fuzzy-logic systems (FLSs)-based decentralized adaptive implicit inverse control scheme for a class of large-scale nonlinear systems with time delays and multihysteretic loops. Our novel algorithms feature hysteretic implicit inverse compensators designed to effectively mitigate multihysteretic loops in large-scale systems. In this article, hysteretic implicit inverse compensators can replace the traditional hysteretic inverse models, which are exceedingly difficult to construct, and no longer necessary. The authors provide three contributions: 1) a searching mechanism to obtain the approximate value of the practical input signal from the so-called hysteretic temporary control law; 2) the arbitrarily small L∞ norm of the tracking error attained by utilizing the proposed initializing technique, which applies the combination of FLSs and a finite covering lemma to deal with time delays; and 3) the construction of a triple-axis giant magnetostrictive motion control platform, which validates the effectiveness of the proposed control scheme and algorithms.

Output Feedback Stabilization of High-Order Nonlinear Time-Delay Systems With Low-Order and High-Order Nonlinearities

In this paper, the output feedback stabilization of a class of high-order nonlinear time-delay systems with more general low-order and high-order nonlinearities is investigated. By constructing the new Lyapunov-Krasovskii functional and reduced-order observer, based on homogeneous domination theory together with the adding a power integrator method, an output feedback controller is developed to guarantee the equilibrium of the closed system globally uniformly asymptotically stable.

Novel Robust Estimation-Based Control of One-Sided Lipschitz Nonlinear Systems Subject to Output and Input Delays

This paper highlights the design of a controller established on estimated states for one-sided Lipschitz (OSL) nonlinear systems subject to output and input delays. The controller has been devised by involving Luenberger-like estimated states. The stability of the time-delayed nonlinear system is reckoned by assuming a Lyapunov functional for delayed dynamics and for which a delay-range dependent criterion is posed with a delay ranging between known upper and lower bounds. The time derivative of the functional is further exploited with linear matrix inequality (LMI) procedures, and employing Wirtinger’s inequality for the integral terms instead of the traditional and more conservative Jensen’s condition. Moreover, a sufficient and necessary solution is derived for the proposed design by involving the tedious decoupling technique to attain controller and observer gain simultaneously. The proposed methodology validates the observer error stability between observers and states asymptotically. The solution of matrix inequalities was obtained by employing cone-complementary linearization techniques to solve the tiresome constraints through simulation tools by convex optimization. Additionally, a novel scheme of an observer-based controller for the linear counterpart is also derived for one-sided Lipschitz nonlinear systems with multiple delays. Finally, the effectualness of the presented observer-based controller under input and output delays for one-sided Lipschitz nonlinear systems is validated by considering a numerical simulation of mobile systems in Cartesian coordinates.

Empirical study of robust/developed PID control for nonlinear time-delayed dynamical system in discrete time domain

In addition to the high nonlinearity of liquid dynamics inside a tank, a study was conducted to overcome loading/unloading liquid storage tank control problems. In this study, the author developed a nonlinear control system to conquer both nonlinearity and the significant time delay arising from using a pressure-difference-based level sensor. To this end, this study proposes the implementation of nonlinear state dependent (SDP-PID+) control using the SDP transfer function model as a class of nonlinear descriptions of dynamical systems. By incorporating additional robust (plus) compensators alongside the traditional P-, I-, and D-compensators, the robust SDP-PID controller utilizes the complete state feedback to create a time-varying state variable feedback (SDP-SVF) control law. This approach effectively mitigates the effects of the discrete-time SDP-TF. It introduces the pole placement tuning approach, which renders significant performance using the laboratory test rig TPS8.2.2.4, for automatic liquid level control.

Finite region stability and networked predictive control for 2-D nonlinear time-delayed systems with quantization, packet dropouts and random disturbances

In this paper, we focus on the finite region stability (FRS) and networked predictive control (NPC) problems for two-dimensional (2-D) networked control systems (NCS) with time delays, quantization errors, packet losses and random disturbances described by the Roesser model. The random packet dropouts and disturbances are modeled as Bernoulli process, and the sufficient conditions of FRS and finite region boundedness (FRB) for 2-D NCS are obtained by using the expectation to process the Lyapunov function difference, so as to better study the transient performance of the systems. According to the recursive formula, an active compensation scheme for time delays of NPC is proposed, which takes into account quantization errors, packet losses, nonlinearity and interferences. Introducing FRS and FRB into 2-D NCS and considering the above factors in NPC scheme are new attempts made in this paper. An example is used to demonstrate the validity of the conclusions in the end.

Output-mask-based adaptive NN control for stochastic time-delayed multi-agent systems with a unified event-triggered approach

This paper investigates a class of output-mask-based adaptive neural network (NN) tracking control for nonlinear stochastic time-delayed multi-agent systems (STMASs) based on a unified event-triggered approach. The output signal relies on an output mapping acted as a mask, defined as a privacy-protection-like method, so that the internal state of one agent cannot be identified by other distrustful eavesdroppers or attackers. Moreover, the construction of a unified event-triggered control scheme retains the advantages of the saturation threshold triggering strategy, incorporates distributed errors, and increases the flexibility of thresholds. Furthermore, for stochastic time-delay multi-agent systems, the initial value limitation of the conventional first-order filter is removed by a first-order Levant differentiator, and a new estimation term in the fuzzy observer is established to solve the nonlinear fault. The unknown function in pure-feedback form is addressed via combining Butterworth low-pass filter and radial basis function neural networks (RBF NNs). Finally, the boundedness of all signals in the closed-loop systems is demonstrated, and the effectiveness of the proposed algorithm is verified by some simulation results.

A new approach for dynamic output feedback control design of time-delayed nonlinear systems

This paper introduces a full-order dynamic output-feedback (DOF) controller for discrete-time nonlinear systems with time-varying delays represented by Linear Parameter-Varying (LPV) systems. The controller design is carried out by developing delay-dependent Linear Matrix Inequality based conditions using Lyapunov–Krasovskii stability arguments. A notable characteristic of the proposed approach is that the dynamic controller gains are directly obtained, without the need for variable transformations, equality constraints, or iterative algorithms. This feature sets it apart from many existing approaches in the literature and simplifies the design process. Furthermore, the proposed approach guarantees the local asymptotic stability of the origin of the closed-loop system and provides an estimated admissible initial condition region. The correct operation of the system is ensured once the state trajectories initiated within the admissible initial condition region remain enclosed in the validity domain of the LPV model. Numerical examples are provided to illustrate the potential and effectiveness of the proposed conditions.

Event-Triggered Impulsive Control for Input-to-State Stabilization of Nonlinear Time-Delay Systems.

This article investigates the event-triggered impulsive control (ETIC) problem for a class of nonlinear time-delay systems subject to exogenous disturbances. An original event-triggered mechanism (ETM) which utilizes the information of system state and external input is constructed based on Lyapunov function approach. To achieve the input-to-state stability (ISS) of the considered system, some sufficient conditions are presented, in which the underlying relationship among ETM, exogenous input, and impulse action is established. Furthermore, the possible Zeno behavior induced by the proposed ETM is excluded simultaneously. As an application, the design criterion of ETM and impulse gain is put forward for a class of impulsive control systems with delay according to the feasibility of some linear matrix inequalities (LMIs). Finally, two examples with numerical simulations are provided to confirm the effectiveness of the developed theoretical results, where the synchronization issue of delayed Chua's circuit is considered.

Implicit Function Theorem for Nonlinear Time-Delay Systems With Algebraic Constraints

Implicit Function Theorem for Nonlinear Time-Delay Systems With Algebraic Constraints

On the digital event-based control for nonlinear time-delay systems with exogenous disturbances

In this paper, the stabilization problem of nonlinear time-delay systems in presence of known exogenous disturbances and by means of quantized sampled-data event-based controllers is investigated. In particular, nonlinear systems with state delays are studied. Known exogenous disturbances affecting the plant dynamics are considered in order to address, for instance, tracking control problems commonly studied by considering the stabilization problem of the corresponding tracking error system in which the chosen reference signal appears as a known exogenous signal. The stabilization in the sample-and-hold sense theory is used as a tool to provide sufficient conditions for the existence of a suitably fast sampling and of an accurate quantization of the input/output channels such that: the quantized sampled-data implementation of continuous-time controllers, updated through a proposed event-based mechanism, guarantees the semi-global practical stability property, with arbitrarily small final target ball of the origin, of the related closed-loop system. A spline approximation methodology is used in order to: (i) cope with the problem of the possible non-availability in the buffer of suitable past values of the system variables needed for the digital implementation of the controller; (ii) consider approximations related to the hardware implementation of the signal describing the known exogenous disturbance (e.g., the chosen reference signal). The provided results include the case of non-uniform quantization of the input/output channels and the case of aperiodic sampling. Applications are presented in order to validate the results, one of which concerning a single-link flexible joint robot arm with time delays.

Distributed Saturated Impulsive Control for Local Consensus of Nonlinear Time-Delay Multiagent Systems With Switching Topologies

In this paper, the local consensus problem of nonlinear time-delay multi-agent systems with switching topologies via distributed saturated impulsive control is discussed and the maximum domain of attraction is well estimated. Specifically, we develop a new estimation approach that is quite distinct from the contractive invariant set to estimate the domain of attraction. Moreover, a novel composite impulsive-instant-dependent Lyapunov function is constructed and an improved convex hull representation with more slack variables is adopted to minimize the conservativeness. And then, some delay-independent sufficient criteria in the form of bilinear matrix inequalities that guarantee local consensus of nonlinear time-delay multi-agent systems are obtained by means of the Lyapunov-Razumikhin technique and proof by contradiction. Through appropriate transformation, some linear matrix inequalities-based optimization problems constrained by the proposed local consensus criteria are formulated, and the corresponding numerical solutions are solved by the Yalmip. Finally, a simulation example is given to confirm the validity and superiority of the proposed theoretical results.

Nonlinear causal network learning via Granger causality based on extreme support vector regression.

For complex networked systems, based on the consideration of nonlinearity and causality, a novel general method of nonlinear causal network learning, termed extreme support vector regression Granger causality (ESVRGC), is proposed. The nonuniform time-delayed influence of the driving nodes on the target node is particularly considered. Then, the restricted model and the unrestricted model of Granger causality are, respectively, formulated based on extreme support vector regression, which uses the selected time-delayed components of system variables as the inputs of kernel functions. The nonlinear conditional Granger causality index is finally calculated to confirm the strength of a causal interaction. Generally, based on the simulation of a nonlinear vector autoregressive model and nonlinear discrete time-delayed dynamic systems, ESVRGC demonstrates better performance than other popular methods. Also, the validity and robustness of ESVRGC are also verified by the different cases of network types, sample sizes, noise intensities, and coupling strengths. Finally, the superiority of ESVRGC is successful verified by the experimental study on real benchmark datasets.

Observer-Based Adaptive Fuzzy Quantized Control for Fractional-Order Nonlinear Time-Delay Systems with Unknown Control Gains

This paper investigates the observer-based adaptive fuzzy quantized control problem for a class of fractional-order nonlinear time-delay systems with unknown control gains based on a modified fractional-order dynamic surface control (FODSC) technique and an indirect Lyapunov method. First, a fractional-order, high-gain state observer is constructed to estimate unavailable state information. Furthermore, the Nussbaum gain technique and a fractional-order filter are adopted to cope with the problem of unknown control gains and to reduce the computational complexity of the conventional recursive procedure, respectively. Moreover, through integration with the compensation mechanism and estimation model, the adaptive fuzzy quantized controllers and adaptive laws are designed to ensure that all the signals of the closed-loop system are bounded. In the end, the proposed controller is applied to a numerical example and a single-machine-infinite bus (SMIB) power system; the simulation results show the validity, superiority, and application potential of the developed control strategy.

Input-to-state exponential stability of switched nonlinear time-delay systems having stable/unstable subsystems

This research introduces new approaches to the Lyapunov–Krasovskii methodology to ensure the input-to-state exponential stability of switched nonlinear time-delay systems with stable and unstable subsystems. New average dwell-time bounds are provided by using the trade-off among the activation times of the stable and unstable subsystems. As illustrative examples, two systems representing neuronal population phenomena with additive and multiplicative inputs are analyzed. As two examples show, these criteria apply to a broad class of switched nonlinear time-delay systems.

Stabilization of time-delay nonlinear systems using Takagi-Sugeno fuzzy models

We propose a controller design method for time-delay nonlinear systems with delays affecting both the states and the inputs, represented by Takagi-Sugeno fuzzy models with nonlinear consequents. To handle the nonlinearities in the consequents we assume that they are slope-bounded. Linear matrix inequality conditions are formulated to design the controller. The obtained results are compared to state-of-the-art approaches and illustrated on two examples.

Adaptive Dynamic Surface Control for Uncertain Nonlinear Time-Delay Cyber-Physical Systems Under Injection and Deception Attacks

Adaptive Dynamic Surface Control for Uncertain Nonlinear Time-Delay Cyber-Physical Systems Under Injection and Deception Attacks