State Time Delay Research Articles

Controller design for nonlinear time delay distributed control systems subjected to input saturation nonlinearity and disturbances

This article proposes a state feedback controller synthesis for nonlinear time-delay distributed control systems subjected to input saturation nonlinearity and disturbances. Nonlinear time-delay distributed control system individual states are without time-delay and the states coming from other subsystems have the communication link time-delay. The coupling states time-delay is presumed to be time-varying within a predefined bound. First, we suggest global state feedback controller design and then, we extend the proposed global design technique to more general local state feedback controller scheme by using an auxiliary region of attraction. Linear matrix inequality (LMI)-based solution is anticipated to synthesis global and local state feedback controller by using global and local sector bounded condition, Lyapunov–Krasovskii function, and Lipschitz condition. Which guarantee global and local asymptotic stability of the complete closed-loop system and $$ L_{2} $$ gain reduction of the mapping from $$ d_{p} (t) $$ to $$ z_{p} (t) $$ . Application results are presented to validate the benefits and effectiveness of the anticipated controller design schemes.

Robust Controller Design for Attitude Dynamics Subjected to Time-Delayed State Measurements

Attitude control and time-delay systems are well-developed fields in the control theory, but only a modicum of papers have explored control systems that fall within the intersection of the two. Indeed, combining kinematics and dynamics nonlinearities with sensor and actuator delays reinvigorates the original attitude control problem, typically leading to involved stability arguments based on nonlinear analysis techniques. This paper instead proposes solving the attitude stabilizer design problem by formulating it as a linear matrix inequality feasibility problem. The proposed approach simplifies the stability arguments, without loosing generality; the obtained conditions cope with the general case of rigid bodies that suffer from unknown, heterogeneous, time-varying state measurement delays, and have inertia uncertainties. This methodology is particularly well suited to resource-limited applications, because controllers can be designed offline using computationally efficient tools. Although simple, numerical evidence shows the stability criterion derived in this paper largely outperforms previous results.

Adaptive fault-tolerant control for a class of uncertain switched nonlinear systems with multiple state time delays

ABSTRACTThis paper studies the adaptive fault-tolerant control problem for a class of uncertain switched nonlinear time-delayed systems with mismatching parameter uncertainties, nonlinear functions, external disturbances and actuator failures. By using the estimations of the unknown upper bounds of uncertain parameters, the novel adaptive laws based on state-dependent switching strategy are constructed, and then the effects of multiple state time delays and actuator failures can be eliminated. Moreover, by using the robust technique and multiple Lyapunov functions method, the designed controller can guarantee the asymptotic stability and the desired performances of the switched closed-loop systems in the presence of parameter uncertainties and time-delayed perturbation simultaneously. Finally, simulation results are provided to show the efficiency of the proposed robust adaptive control scheme.

Global stabilization for a class of stochastic nonlinear systems with SISS‐like conditions and time delay

SummaryThe global stabilization problem for a class of stochastic time‐delay nonlinear systems with stochastic‐input‐to‐state‐stable–like conditions is investigated. Different from the existing results, the nonlinear growing conditions are more general, and the existences of the state and input time delays make the work more challenging in the control design and stability analysis. By introducing an appropriate gain‐scaling method and using a homogeneous domain control strategy, a delay‐independent controller is constructed to ensure that the equilibrium at the origin of the closed‐loop system is globally asymptotically stable in probability. Examples are given to show the validness of the proposed method.

Robust Gene Circuit Control Design for Time-Delayed Genetic Regulatory Networks Without SUM Regulatory Logic.

This paper investigates the gene circuit control design problem of time-delayed genetic regulatory networks. In the genetic regulatory networks, the time delays are unknown constants, and the genetic regulatory is not conventional SUM regulatory logic and can be modeled to be an unknown nonlinear function of the time-delayed states of the other genes in a cell. By Lyapunov stability, a novel adaptive gene circuit control design approach is proposed for the genetic regulatory networks, where the unknown time delays are estimated online by adaptive algorithms and the unknown regulatory functions are approximated by neural networks. The design approach in this paper is delay-dependent and has less conservatism than the delay-independent approach. From theoretical analysis, the closed-loop system is asymptotically stable and all the signals in the system converge to an adjustable neighborhood of the origin. Finally, a numerical example is given to show the effectiveness of the new design approach.

Design of generalized dissipativity state estimator for static neural networks including state time delays and leakage delays

This paper discusses the issue of generalized dissipativity index for state estimation of static neural networks (SNNs) including leakage delays and state time delays. The integral terms in the time derivative of the Lyapunov–Krasovskii functionals (LKFs) are estimated by the well-known Wirtinger based integral inequality approach. As a result, a novel delay-dependent extended dissipativity state estimation condition is exploited based on the estimated error system is extended dissipative. The notion of the extended dissipativity based state estimation methodology is launched to investigate the L2−L∞ state estimation, H∞ state estimation, passivity state estimation, mixed H∞ and passivity state estimation, and (Q,S,R)−γ-dissipativity state estimation of SNNs by choosing free weighting matrices. Therefore, a new scheme is put forward to quantify multi-dynamic behaviors of SNNs in a combined structure by introducing of the free weighting matrices. The main scope of the addressed problem is to design state estimation criterion to estimate the neuron states such that, in the presence of both leakage delays and state time delays, the dynamics of the estimator error system is extended dissipative. In comparison with some recent results, much better and more dynamic behavior is performed by our methodology, which is immensely assisted from proposing a leakage delays and gain matrix in the system model. The advantage of the established methodology is explored by numerical examples and comparison results also are made along with the previous results.

Adaptive control for uncertain nonlinear time-delay systems in a lower-triangular form

In the presence of uncertain time-varying control coefficients, structuring parameter uncertainty and unknown state time delay, this paper proposes a continuous feedback control scheme for highly nonlinear systems without extra nonlinear growth restriction. An expansion of the backstepping method is presented based on dynamic gains and tuning functions. By Lyapunov–Krasovskii functionals, a delay-free controller is designed to regulate the original system states to zero with the other states being globally bounded.

The stability analysis of nonlinear switched systems with time delay in input and states with stable and unstable subsystems

Time delay and sampling appear in many industrial systems. It is irrefutable that applying measurement delay with controls can cause the sampling of control laws with the delay in the behavior of nonlinear control systems. As a result, in this paper, the stability of nonlinear time varying switched system with time delay in the input and the states of the system is studied in two modes by a new Lyapunov Krasovskii functional (LKF). Firstly, if all subsystems of the proposed nonlinear switched system with time delay are stable. Then, if some of the subsystems of the proposed switched system are unstable. This paper is organized in two steps. In the first step, the upper bound for the time delay under sufficient conditions in the nonlinear systems with time delay in input and states is obtained. In this step, the Uniformly Globally Asymptotic Stability is proved for nonlinear systems with the presence of time delay. In the second step, with a proper Lyapunov Krasovskii functional, the global exponential stability of the proposed switched system is proved. Also, finally a proper observer is designed for our proposed switched system in two stable and unstable modes.

Optimal control problems with time delays: Two case studies in biomedicine.

There exists an extensive literature on delay differential models in biology and biomedicine, but only a few papers study such models in the framework of optimal control theory. In this paper, we consider optimal control problems with multiple time delays in state and control variables and present two applications in biomedicine. After discussing the necessary optimality conditions for delayed optimal control problems with control-state constraints, we propose discretization methods by which the delayed optimal control problem is transformed into a large-scale nonlinear programming problem. The first case study is concerned with the delay differential model in [21] describing the tumour-immune response to a chemo-immuno-therapy. Assuming L¹-type objectives, which are linear in control, we obtain optimal controls of bang-bang type. In the second case study, we introduce a control variable in the delay differential model of Hepatitis B virus infection developed in [7]. For L¹-type objectives we obtain extremal controls of bang-bang type.

Complex Scaling Approach for Stability Analysis and Stabilization of Multiple Time-Delayed Systems

Based on complex scaling, the paper copes with stability analysis and stabilization of linear time-invariant continuous-time systems with multiple time delays in state, control input, and measured output, under state and/or output feedback. More specifically, the paper establishes stability criteria for exponential/asymptotical stability with Hurwitz complex scaling being applied to the related characteristic polynomials. The stability conditions are necessary and sufficient, delay-dependent, and independent of feedback structures and open-loop poles distribution. The criteria can be implemented graphically with locus plotting or numerically without it; moreover, no prior frequency sweeping is involved, and the contour and locus encirclement orientations can be self-defined. Exploiting the complex scaling approach and embracing its technical merits, it is considered to design static state feedback control for robustly stabilizing time-delayed systems. A small-gain interpretation for the suggested stabilization is also elaborated. Examples are included to illustrate the main results.

Adaptive Neural Network Control for Uncertain Switched Nonlinear Systems With Time Delays

This paper is concerned with the problem of adaptive neural network (NN) tracking control for a class of uncertain switched nonlinear systems with time delays. Compared with the existing results, a new common Lyapunov function with switched adaptive parameters is constructed. The unknown functions with time-delay state are compensated by using appropriate Lyapunov–Krasovskii functionals in the design. To guarantee transient performance of switched systems with time delays, the prescribed performance bound (PPB) method is utilized. Based on convex combination technique, a novel adaptive NN tracking control method under state-dependent switching law is proposed. It is shown that under the proposed control and switching laws, all the signals of the closed-loop system are bounded and the tracking error is preserved within PPB. Finally, the simulation example is given to demonstrate the effectiveness of the proposed control scheme.

Global Asymptotic Stability for a New Class of Neutral Neural Networks

In the present world, due to the complicated dynamic properties of neural cells, many dynamic neural networks are described by neutral functional differential equations including neutral delay differential equations. These neural networks are called neutral neural networks or neural networks of neural-type. The differential expression not only defines the derivative term of the current state but also explains the derivative term of the past state. In this paper, global asymptotic stability of a neutral-type neural networks, with time-varying delays, are presented and analyzed. The neural network is made up of parts that include: linear, non-linear, non-linear delayed, time delays in time derivative states, as well as a part of activation function with the derivative. Different from prior references, as part of the considered networks, the last part involves an activation function with the derivative rather than multiple delays; that is a new class of neutral neural networks. This paper assumes that the activation functions satisfy the Lipschitz conditions so that the considered system has a unique equilibrium point. By constructing a Lyapunov-Krasovskii-type function and by using a linear matrix inequality analysis technique, a sufficient condition for global asymptotic stability of this neural network has been obtained. Finally, we present a numerical example to show the effectiveness and applicability of the proposed approach.

Response of a Harmonically Forced Dry Friction Damped System Under Time-Delayed State Feedback

Nonlinear dynamics, control, and stability analysis of dry friction damped system under state feedback control with time delay are investigated. The dry friction damped system is harmonically excited, and the nonlinearities in the equation of motion arise due to nonlinear damping and spring force. In this paper, a frequency domain-based method, viz., incremental harmonic balance method along with arc-length continuation technique (IHBC) is first employed to identify the primary responses which may be present in such system. The IHBC is then reformulated in a manner to treat the dry friction damped system under state feedback control with time delay and is applied to obtain control of responses in an efficient and systematic way. The stability of uncontrolled responses is obtained by Floquet's theory using Hsu' scheme, and the stability of the controlled responses is obtained by applying a semidiscretization method for delay differential equation (DDE).

Asynchronous output regulation with passivity control for a class of switched stochastic delay systems

In this study, the problem of output regulation with passive performance control is investigated for a class of switched stochastic delay systems by using an average dwell time approach. It is assumed that the system under consideration is subject to the existence of time delays in both states and the regulators switching signal which causes asynchronous switching between candidate regulators and subsystems. By construction of a Lyapunov–Krasovskii (L–K) functional, sufficient conditions for the existence of the corresponding regulators are derived from the cases where the states are measurable and unmeasurable, respectively. Then, a switching signal is designed based on the upper bounds of the time delays. Finally, simulation examples are provided to illustrate the feasibility and efficiency of the proposed method.

An asymptotic method for quasi-integrable Hamiltonian system with multi-time-delayed feedback controls under combined Gaussian and Poisson white noises

In the present paper, we consider an approximate approach for predicting the responses of the quasi-integrable Hamiltonian system with multi-time-delayed feedback control under combined Gaussian and Poisson white noise excitations. Two-step approximation is taken here to obtain the responses of such system. First, based on the property of the system solution, the time-delayed system state variables are approximated by using the system state variables without time delay. After this approximation, the system is converted to the one without time delay but with delay time as parameters. Then, stochastic averaging method for quasi-integrable Hamiltonian system under combined Gaussian and Poisson white noises is applied to simplify the converted system to obtain the averaged stochastic integro-differential equations and generalized Fokker–Planck–Kolmogorov equations for both non-resonant and resonant cases. Finally, two examples are worked out to show the detailed procedure of proposed method for the illustrative purpose. And the influences of the time delay on the responses of the systems are also discussed. In addition, the validity of the results obtained by present method is verified by Monte Carlo simulation.

Output feedback control of linear systems with input, state and output delays by chains of predictors

In this paper, we consider the control problem of linear systems with state time-delays when the control signal is affected by a possibly time-varying delay. The problem is solved by a chain of predictors under the assumption that a stabilizing control exists for the case of no input delay. This solution is then extended to the case of partial information when only delayed output is available. Both the input and the output delays may have arbitrary bounds. With respect to previous approaches to the same problem appeared recently in the literature the method proposed here has a simpler structure and in particular it does not need the computation of distributed terms. As a by-product we show that it is possible to derive an observer for a system with state and output delays from an observer for the same system without output delays.

Adaptive neural dynamic surface control for a general class of stochastic nonlinear systems with time delays and input dead-zone

This paper investigates adaptive tracking control for a more general class of stochastic nonlinear time-delay systems with unknown input dead-zone. For the considered system, the drift and diffusion terms contain time-delay state variables. In control design, Lyapunov-Krasovskii functionals are employed to handle unknown time-delay terms. Then, unknown nonlinear functions are approximated by RBF neural networks, and the dynamic surface control (DSC) technique is utilized to avoid the problem of explosion of complexity. At last, based on the Lyapunov stability theory, a robust adaptive controller is designed to guarantee that all closed-loop signals are bounded in probability and the tracking error converges to a small neighborhood of the origin. The simulation example is presented to further show the effectiveness of the proposed approach.

Modified function projective feedback control for time-delay chaotic Liu system synchronization and its application to secure image transmission

This paper is devoted to synchronize time-delay Liu chaotic system in order to develop a secure image transmission system. An adaptive modified function projective synchronization (MFPS) method is proposed to control the behavior of the uncertain Liu chaotic system in the presence of time-delay state variables and uncertainty in system parameters. The stability and convergence of the present method are analyzed by means of Lyapunov stability theorem. Numerical simulations were used to validate the effectiveness of the proposed MFPS method. Furthermore, a novel image cryptosystem is generated for secure image transmission. Image data is embedded within the response signals and is transmitted to the receiver. The image data can be extracted at the receiver by using of the drive signals. The proposed image cryptosystem was applied to a plain image, and also, performance of the image cryptosystem was evaluated by some mathematical tools and the results were satisfactory, in both cases.

A new online delay estimation-based robust adaptive stabilizer for multi-input neutral systems with unknown actuator nonlinearities

This paper studies the problem of actuator-nonlinearities compensation in the multi-input uncertain neutral systems. The neutral systems with different unknown time-varying delays, unmodeled dynamics, nonlinear perturbations and disturbances are considered. A new methodology based on the online estimation of the delays to compensate for the effects generated by dead-zone and saturation, acting in series on a system's input are presented. The online estimations of the unknown delays are accomplished by adaptive laws that guarantee the exponential stabilities of the estimated delays. In the presence of state time delay, derivative state time delay, unmodeled dynamics, nonlinear perturbations, disturbances and both input dead-zone and saturation, the asymptotic stability of the closed-loop system is ensured and the state response converge to the origin. Finally, the practicability and the efficacy of the proposed approach is demonstrated via a numerical example.

State constrained optimal control problems with time delays

In a recent, related, paper, necessary conditions in the form of a Maximum Principle were derived for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions covered fixed end-time problems and, under additional hypotheses, free end-time problems. These conditions improved on previous conditions in the following respects. They provided the first fully non-smooth Pontryagin Maximum Principle for problems involving delays in both state and control variables, only special cases of which were previously available. They provide a strong version of the Weierstrass condition for general problems with possibly non-commensurate control delays, whereas the earlier literature does so only under structural assumptions about the dynamic constraint. They also provided a new ‘two-sided’ generalized transversality condition, associated with the optimal end-time. This paper provides an extension of the Pontryagin Maximum Principle of the earlier paper for time delay systems, to allow for the presence of a unilateral state constraint. The new results fully recover the necessary conditions of the earlier paper when the state constraint is absent, and therefore retain all their advantages but in a setting of greater generality.