Nonlinear Delay Systems Research Articles

Decentralized Output-Feedback Adaptive Event-Triggered Control for Interconnected Nonlinear Delay Systems with Actuator Failures

This paper investigates decentralized adaptive event-triggered fault-tolerant control for interconnected nonlinear delay systems with actuator failures. The actuator failures suffered include loss of effectiveness and bias faults. A control scheme based on the K-filter is proposed, which effectively compensates for the effects of unknown actuator failures. A hyperbolic tangent function and neural network are introduced to approximate the unknown interconnection function and nonlinear delay function. By introducing the dynamic surface control method, the “explosion of complexity” issue is addressed. Furthermore, our proposed controller can ensure that all states of the corresponding closed-loop system are semi-globally uniformly ultimately bounded and that the tracking error can converge to a small neighborhood of zero. Meanwhile, Zeno behavior can be effectively avoided. Finally, the validity of the proposed control scheme is verified using a simulation example.

Stability of highly nonlinear neutral stochastic delay system with both stable and unstable subsystems

AbstractThe article addresses the exponentially stable conditions of the highly nonlinear neutral stochastic delayed system (HNNSDS) that contains unstable subsystems apart from stable ones under Markov switching. By the application of the mode‐dependent average dwell time (MDADT) as well as Lyapunov function approach, the general switching condition still satisfies even when the partial Lyapunov coefficients are negative. In addition, the degree of instability is combined with the study of switching signals. On this basis, the case when the system contains only stable subsystems is also investigated. A well‐known switching condition is obtained, establish the foundation of the comparison with more complex cases involving unstable subsystems. The simulation processes are eventually provided to verify rationality of the obtained criteria.

Stability analysis for nonautonomous impulsive hybrid stochastic delay systems

In this paper, the problems on the existence and uniqueness, and the input-to-state stability for the global solution of nonlinear nonautonomous impulsive stochastic delay systems with Markovian switching are considered. The existence and uniqueness for the global solution of such systems is studied by using the Lyapunov function, the theory of stochastic analysis, and the function of the impulsive density. In order to overcome the difficulty stemming from the simultaneous presence of the indefinite derivative for the Lyapunov function, the bounded external disturbances, and a nonnegative and bounded time-varying delay, one impulsive generalized Halanay inequality of integral version is established. The input-to-state stability, the integral input-to-state stability, the stochastic input-to-state stability and the eλt(λ>0)-weighted input-to-state stability for the global solution of nonlinear nonautonomous impulsive stochastic delay systems with Markovian switching are investigated, respectively. One example is provided to illustrate the effectiveness of the theoretical results obtained.

Boundedness and stability of nonlinear hybrid neutral stochastic delay differential equation with Lévy jumps under different structures

This paper investigates the boundedness and stability of a class of nonlinear hybrid neutral stochastic differential delay systems with Lévy jumps and different structures. The coefficients in this system satisfy the local Lipschitz condition and a suitable Khasminskii-type condition, and the state space of the system is separated into two subsets, the existence uniqueness, asymptotic boundedness, and exponential stability of the system are obtained by designing a new Lyapunov function and applying the M-matrix technique as well as dealing with the non-differentiable delay function. Different with the existing work, we not only consider the neutral term, but also the case of the delay function being bounded and non-differentiable. At last, numerical examples are performed to manifest the obtained results.

Exponential Stability of Stochastic Nonlinear Delay Systems Subject to Multiple Periodic Impulses

Exponential Stability of Stochastic Nonlinear Delay Systems Subject to Multiple Periodic Impulses

Stability in Distribution of Highly Nonlinear Hybrid Stochastic Delay Systems by Delay Feedback Control

Stability in Distribution of Highly Nonlinear Hybrid Stochastic Delay Systems by Delay Feedback Control

Adaptive multi-dimensional Taylor network tracking control of time-varying delay nonlinear systems subject to input saturation

For the tracking control problem of a class of nonlinear systems with input saturation constraint and time-varying delay, an adaptive tracking control scheme based on multi-dimensional Taylor network (MTN) is designed, and the proposed control scheme has the advantages of simple structure and small computation. A Gaussian error function is introduced to transform the input saturation into a linear model with bounded error. The Lyapunov-Krasovskii function is constructed, and the nonlinearity of the system is approximated using MTN, and an adaptive control strategy is constructed based on the backstepping method. The results show that the proposed control method can both ensure that all signals in the closed-loop system are bounded and achieve convergence of the tracking error to a small neighborhood near the origin. Numerical simulations verify the effectiveness of the method.

Global output‐feedback adaptive regulation for planar time‐delay nonlinear systems with polynomial growth

AbstractThis paper addresses the problem of the global adaptive regulation via output feedback for a class of uncertain planar time‐varying delay nonlinear systems with an unknown control coefficient and unmeasured states dependent growth. The growth rate is the form of an unknown constant multiplying polynomial of output, and the upper bounds of unknown control coefficient and unknown time‐varying delay are both not required to be known. A systematic non‐identifier‐based output‐feedback control scheme is developed by combining the idea of universal control, backstepping technique, and Lyapunov–Krasovskii theorem. The global regulation of nonlinear systems and the global boundedness of the closed‐loop system can be simultaneously achieved by the designed controller based on a dynamic high‐gain observer and a proper update law. A practical example illustrates the efficiency of the proposed method.

Robust exponential arbitrary time control of nonlinear systems with input delay

In this study, we aim to present an exponential arbitrary-time control scheme for nonlinear systems subjected to input time delay and additive disturbances. To this end, a new finite-time controller was developed for certain nonlinear systems, which ensures exponential tracking in a time independent of initial conditions. Due to the presence of unknown disturbances, predictors cannot be directly used to control the system, being a challenging issue. Therefore, to utilize predictor feedback in disturbed nonlinear input delay systems, a disturbance observer was designed. The proposed disturbance observer guarantees the exponential arbitrary time estimation of unknown disturbances. Next, an adaptive exponential arbitrary time controller was designed for the system using the proposed disturbance observer. In addition, the Lyapunov theorem was utilized to prove the disturbance observer and tracking errors converged to the origin in an arbitrary time. In the end, the state tracking error was analyzed accurately. It was ensured that the upper bound of the tracking error was bounded and converged to zero in the adjusted arbitrary time. Ultimately, the main results of this study will be illustrated and validated by simulation and experimental results.

Finite‐time robust simultaneous stabilization control for two nonlinear singular time‐delay systems

AbstractIn this paper, the finite‐time simultaneous stabilization problem of two nonlinear singular time‐delay Hamiltonian systems is investigated. Firstly, the two general nonlinear singular time‐delay Hamiltonian systems are transformed into their Hamiltonian differential‐algebraic forms by equivalent transformation, respectively, they are then converted to two strictly dissipative Hamiltonian forms via the state feedback method, and two strictly dissipative Hamiltonian systems are extended into a Hamiltonian one. Based on which, a suitable Hamiltonian function is constructed to analyze the finite‐time simultaneous stability and finite‐time robust simultaneous stabilization problem. Finally, an illustrative example is given to show the effectiveness of the results obtained. It should be pointed out that since there does not exist a finite‐time stability criterion on the nonlinear singular delay system, we adopt a new double compound asymptotic method.

ANALYSIS OF GLOBAL EXPONENTIAL STABILITY FOR NONLINEAR IMPULSIVE STOCHASTIC SYSTEMS WITH DELAY USING REGULARIZATION TECHNIQUES

The W-transform in the form of the regularization techniques, based on inverse-positive matrices, is used to obtain verifiable global stability conditions for linear and nonlinear stochastic delay systems with random coefficients and impulses at random times. The results are conveniently formulated in terms of coefficients of the systems. Several examples illustrating the main results are offered.

Tracking Control of Heterogeneous Multiagent Systems With Intrinsic Nonlinear Dynamics in Noisy and Time-Delayed Environments.

This article investigates the tracking control problem of heterogeneous multiagent systems (MASs) with intrinsic nonlinear dynamics in noisy and time-delayed environments. First, a stability criterion for nonlinear stochastic delay systems with multiplicative noise and time-varying delay is proposed by applying the appropriate Lyapunov-Krasovskii functional. Then, based on the proposed stability criterion, sufficient conditions are derived for mean square (m.s.) and almost sure (a.s.) tracking of heterogeneous MASs with intrinsic nonlinear dynamics. Afterward, the above sufficient conditions further degenerate to integrator heterogeneous MASs. In particular, when the time-delay vanishes, the explicit conditions are obtained for the integrator heterogeneous MASs in the form of scalar inequalities, which can intuitively reflect the relationship between noise intensity and control gains. Finally, simulation results validate the effectiveness of the proposed control protocol.

Event-Triggered Sampling Problem for Exponential Stability of Stochastic Nonlinear Delay Systems Driven by Le ´vy Processes

Event-Triggered Sampling Problem for Exponential Stability of Stochastic Nonlinear Delay Systems Driven by Le ´vy Processes

Fuzzy-Sliding-Mode Strategy for Multi-Channel Nonlinear Delay System With Disturbance

Fuzzy-Sliding-Mode Strategy for Multi-Channel Nonlinear Delay System With Disturbance

Analysis of Functional and Neutral Differential Equations via Lyapunov Functionals

We employ Lyapunov types functions and functionals and obtain sufficient conditions that guarantee the boundedness and the exponential decay of solutions, stability and exponential stability of the zero solution in nonlinear delay and neutral differential systems. The theory is illustrated with several examples. 2000 Mathematics Subject Classification: Primary 39A13, 39A23; Secondary 34K42

Stability for nonlinear delay systems: Self-triggered impulsive control

This paper studies the stability problem of nonlinear delay systems in the framework of self-triggered impulsive control (STIC), where a class of self-triggered mechanisms is designed based on comparison approach. Different from the traditional event-triggered impulsive control (ETIC), in this paper the next impulse instant can be predicted at the previous impulse instant, and there is no need for state monitoring between two adjacent impulse instants. Under the proposed STIC strategy, some sufficient conditions for non-Zeno behavior and asymptotical stability of nonlinear delay systems are presented, respectively. Finally, two numerical examples are carried out to illustrate the effectiveness of the theoretical results.

The finite-time boundedness and control analysis of switched nonlinear time-varying delay systems based on auxiliary matrices

This paper explores the finite-time boundedness and controller problem of switching nonlinear delay systems. The time delay is considered as time-varying delay rather than constant delay. First of all, an appropriate Lyapunov–Krasovskii functional (LKF) which contains three integral terms is selected. The upper and lower bounds of these integral terms are given by segmenting the time delay interval. Meanwhile, the auxiliary matrix method is used to separate the Lyapunov matrix from the system matrix. Moreover, a new state-dependent switching law is designed to switch between subsystems according to the change of the magnitude of the LKF. Based on the above methods, the first step is to research the finite-time bounded analysis of delayed system without control input. Then, a sufficient condition is obtained to ensure the finite-time boundedness of switched systems with control input. Further, by designing an observer-based H∞ controller, the closed-loop system with time-varying delay is bounded and has H∞ performance index ν by using the Finsler’s Lemma and Singular Value Decomposition (SVD). Simultaneously, the controller and observer gains are designed. Finally, two simulations are used to verify the effectiveness and feasibility of the proposed methods.

Lyapunov conditions for exponential stability of nonlinear delay systems via impulsive control involving stabilizing delays

The problem of global exponential stability (GES) for nonlinear delay impulsive systems is investigated in this paper. By extending the traditional comparison principle, delay effects on continuous and discrete dynamics of the system are estimated, based on which, the internal relationship between delays, parameters of impulsive control, and continuous dynamics of the system is revealed. Then some sufficient criteria are obtained for GES, which quantitatively shows the beneficial influences of delays in impulses on the system performance. Finally, two numerical examples are given to illustrate the effectiveness of the proposed result.

Periodically intermittent control for stochastic nonlinear delay systems with dynamic event‐triggered mechanism

AbstractIn this article, the mean‐square exponential stability of the stochastic nonlinear delay systems with dynamic event‐triggered mechanism under periodically intermittent control scheme is concerned. First, to avoid Zeno behavior, the triggered mechanism contains with a fixed positive lower bound for the inter‐execution time is constructed. Then, an auxiliary system with dynamic event‐triggering mechanism under continuous control is introduced. Combining the Lyapunov theorem with Halanay inequality, the sufficient conditions and the mean‐square exponential stability of the auxiliary system are obtained. In addition, by using the comparison theorem, the exponential stability of the system under intermittent control is also proved. Meanwhile, the lower bound of the duty cycle for a fixed period under intermittent controller is obtained. Furthermore, we apply the theoretical results to the consensus of stochastic nonlinear delay networked multi‐agent systems (MASs) with dynamic event‐triggered mechanism. Finally, numerical examples are given to verify the effectiveness of the proposed methods.

Finite‐time input/output‐to‐state stability of nonlinear stochastic switched time‐varying systems with mode‐dependent average dwell time

AbstractThis article investigates the finite‐time input/output‐to‐state stability (FTIOSS) of stochastic switched nonlinear delay systems (SSNDS). This article extends the well‐known concepts of input/output‐to‐state stability to finite‐time control problems. By using the finite‐time stable function and generalized function, we establish an unified FTIOSS criteron for stochastic switched systems, where both stable and unstable switching signals are considered. Compare with the existing works, the main advantage is that the constructed Lyapunov function (LF) is permitted to own indefinite‐derivative. Meanwhile, the Razumikhin technique and the mode‐dependent average‐dwell time (MDADT) approach are introduced to guarantee the FTIOSS of the system. The efficacy of the obtained results is demonstrated by an example.