Interconnected Time-delay Systems Research Articles

Improved Full-Error Constrained Control for Unknown Interconnected Time-Delay Nonlinear Systems With Input Saturation

Improved Full-Error Constrained Control for Unknown Interconnected Time-Delay Nonlinear Systems With Input Saturation

Adaptive Decentralized Control for Interconnected Time-Delay Uncertain Nonlinear Systems With Different Unknown Control Directions and Deferred Full-State Constraints.

In this article, the problem of adaptive decentralized control is investigated for a class of interconnected time-delay uncertain nonlinear systems with different unknown control directions and deferred asymmetric time-varying (DTV) full-state constraints. By constructing the novel time-varying asymmetric integral barrier Lyapunov function (TVAIBLF), the conservative limitation of constant integral barrier Lyapunov function (IBLF) or symmetric IBLF is reduced and the need on the prior knowledge of control gains is also avoided, while the deferred constraints directly imposed on the states of system are achieved by introducing the shifting function into the controller design. Furthermore, based on the Nussbaum-type functions, a new adaptive decentralized control strategy for interconnected time-delay nonlinear systems with subsystems having different control directions is proposed via backstepping method. And it is proven that the proposed control method can guarantee that all signals in closed-loop system are bounded and the transform errors asymptotically converge to zero. Finally, the effectiveness of the proposed control strategy is illustrated through the simulation results.

Distributed control of time-delay interconnected nonlinear systems

This paper addresses the distributed control of delayed interconnected nonlinear systems with time-varying delays in both the local subsystems’ dynamics and the physical interconnections among the subsystems. The Takagi–Sugeno fuzzy model with nonlinear consequent parts (N-TS), which is capable to provide less complex representations than standard T–S fuzzy models, is considered to efficiently deal with this class of complex systems. Then, based on Lyapunov–Krasovskii stability arguments, a synthesis condition is proposed to design a distributed control law such that the origin of the closed-loop interconnected system is locally asymptotically stable together with a guaranteed set of admissible initial conditions for which the validity of the N-TS fuzzy model is ensured. Moreover, a quasi-convex optimization procedure is formulated to enlarge the set of admissible initial conditions. The effectiveness of the proposed synthesis condition is validated in two numerical examples, including an interconnected power network with seven generators.

Exponential Stabilization for Time-Delay Nonlinear Interconnected Systems With Unknown Control Directions and Unmodeled Dynamics

An exponential stable control scheme based on state transformation and Lyapunov functions is presented for a class of large-scale nonlinear time-delay interconnected systems subjected to unknown control directions and unmodeled dynamics. By regulating the transformed state, the original system state is regulated to the origin at an exponential rate. By introducing a class of type-B Nussbaum functions, the obstacle caused by multiple unknown control coefficients is successfully overcome. Dynamic gains technique and changing supply function idea are established to tackle time-delay terms and unmodeled dynamics in the system. It turns out that the system state converges to the origin at a prescribed speed, and all the closed-loop signals remain bounded. Finally, simulation results show the effectiveness of the proposed methodology.

Dynamic-based event-triggered neural network control for p-normal interconnected time-delay systems with asymmetric constraints

A decentralized dynamic event-triggered tracking control problem is investigated for a class of p-normal interconnected time-delay nonlinear systems with asymmetric constraints. First, a new event-triggered mechanism (ETM) is constructed by designing a dynamic variable law, which effectively reduces the number of controller updates. The introduced constants provide an obvious solution for the proof of Zeno phenomenon. Second, a barrier Lyapunov function (BLF) is constructed with the help of sign functions to achieve time-varying asymmetric constraints. Meanwhile, we improve the previous neural networks (NNs) approximation scheme and dynamic gain technique in order to handle unknown interconnection functions and time-delay signals, respectively. Then, it is rigorously proved that all signals in the system are bounded, and the error signals are constrained within the time-varying asymmetric bounds. Finally, the feasibility of the scheme is verified by simulation examples.

Multiple Control Functionals for Interconnected Time-Delay Systems

Multiple Control Functionals for Interconnected Time-Delay Systems

Performance analysis for interconnected time-delay systems with networked communication

This paper studies the network-based performance analysis for interconnected time-delay system (ITDS), where each subsystem experiences delays in the state and connects arbitrarily via the packet-based communication network. The ITDS with networked communication is modeled as hybrid systems with memory to incorporate the delay and network-induced imperfections into a unified framework. Based on this model, a general hybrid Lyapunov–Krasovskii functional is constructed. Sufficient linear matrix inequality conditions for the ITDS to be asymptotically stable and L2 stable are proposed, respectively. These conditions are only related to the interconnected structure, the parameters of each subsystem and local network, leading them convenient for feasibility computation. Two examples, including a numerical example and a three-area time-delay power system, are given to show the feasibility of the derived results.

Distributed Model Predictive Control of Time-Delay Systems

In this paper, a new approach to distributed MPC of linear interconnected time-delay systems is proposed. The general case of time-delay in both the states and the control inputs is considered. The approach includes representation of the interconnected time-delay dynamics in the augmented state space and reformulation of the centralized MPC problem into a Quadratic Programming framework. The latter this is solved distributedly by using the dual gradient method for optimization. The suggested approach would be appropriate for embedded distributed MPC and is illustrated on a simulation example of two interconnected time-delay systems.

Interval type-2 fuzzy decentralised event-triggered H ∞ control for nonlinear interconnected systems with time delays

This paper studies the interval type-2 fuzzy decentralised event-triggered control design problem for the nonlinear time-delay interconnected systems. The considered plant is first represented by an interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy time-delay interconnected system and then an event-triggered mechanism is established through using the sampled states. By using the PDC algorithm, a fuzzy decentralised event-triggered controller is developed. Furthermore, the asymptotic stable conditions with a performance of closed-loop system are obtained, which are formulated in the form of linear matrix inequalities. Finally, an example of the nonlinear Tuned Mass Damper system with time delays is given to illustrate the effectiveness of the proposed fuzzy decentralised controller.

Decentralized full-state constrained adaptive tracking control for interconnected time delay systems with input saturation

In this article, the problem of decentralized full-state constrained adaptive tracking control is investigated for interconnected time delay systems with input saturation. The extreme learning machine is applied to approximate the unknown nonlinear function in the design process. By selecting the appropriate Lyapunov–Krasovskii function, the time delay interconnection term could be compensated. A unified barrier function is introduced to ensure that the constraints imposed on all states are not violated. The Nussbaum function is introduced to deal with the problem of input saturation. By applying adaptive backstepping procedures, a novel decentralized full-state constrained adaptive tracking control strategy is proposed for the considered interconnected time delay systems. In terms of Lyapunov stability theory, it is proved that all the signals of the closed-loop systems are semi-global ultimately uniformly bounded and all state variables could be constrained within the time varying asymmetric boundaries. Finally, the effectiveness of the proposed scheme is illustrated by a simulation example of a two-stage chemical reactor.

Decentralised fault-tolerant tracking control for interconnected nonlinear time delay systems using dynamic event triggering mechanism

In this study, a novel decentralised fault-tolerant control strategy is developed for a class of interconnected nonlinear time delay systems with unmeasurable state variables and actuator faults by using dynamic event triggering mechanism. The interconnected system model includes nonlinear time delay functions and unstructured uncertainties, which could be identified by the radial basis function neural networks approximation technique. The adaptive nonlinear observer is designed for each interconnected subsystem to obtain the estimated values of unmeasurable state variables and unknown system faults simultaneously. Then, a decentralised fault-tolerant tracking controller is designed for the considered interconnected time delay systems using both backstepping control procedures and a dynamic event triggering mechanism, which has the smaller event trigger frequency by comparing the traditional static event-triggered control scheme, such that the tracking error signals converge to a small neighbourhood near the origin and all the signals of the closed-loop system are globally bounded. Finally, a chemical reactor example is given to illustrate the feasibility and significance of the designed control scheme.

Sliding Mode Load Frequency Regulator for Different-Area Power Systems with Communication Delays

In this article, a sliding mode control (SMC) is proposed to deal with the frequency deviation problem in interconnected time-delay power systems (ITDPS) with two source power generations. First, the proportional and integral switching surface is used for each area to guarantee the frequency deviation reach zero in normal operating conditions. Then, the stability of the system is ensured with a new Linear Matrix Inequality (LMI) via Lyapunov stability theory. In addition, the SMC law is designed to guarantee the finite time eachability of the system. Finally, impacts of certain physical constraints affecting dynamic performance of the power network such as time-delay is proposed to consider the signal delay in the controller. Effectiveness of the suggested method is validated by simulation studies on the load frequency control under time-delays in the two-area, the step load disturbance and the mismatched uncertainty.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

Decentralised state-feedback prescribed performance control for a class of interconnected nonlinear full-state time-delay systems with strong interconnection

This paper investigates the problem of the state-feedback control design for a class of interconnected nonlinear full-state time-delay systems with strong interconnection and prescribed performance. Based on the dynamic gain approach and Lyapunov-Krasovskii method, it overcomes the rigorous restriction that the interconnected time-delay functions should satisfy linear growth condition. Compared with the existing results, the main contribution is that the dynamic gain approach is extended to state-feedback control for interconnected time-delay systems, and it is strictly proved that the closed-loop system is globally bounded stable with the proposed decentralised control strategy. The problem of the strong interconnection terms is solved by combining the backstepping approach and graph theory. Furthermore, the expected transient and steady-state performance of the output can be guaranteed by considering prescribed performance control into such strongly interconnected systems. Finally, simulation is performed and the results show the effectiveness of the proposed method.

Distributed functional observers for fractional-order time-varying interconnected time-delay systems

Our main purpose in this paper is to design distributed functional observers for a class of fractional-order time-varying interconnected time-delay systems. The contributions of this paper conclude three aspects. First, we propose novel functional observers for subsystems of the fractional-order time-varying interconnected time-delay systems. The designed distributed functional observers in this paper work for a wider class of interconnected time-delay systems in the sense that when some existing design methods cannot be applied to estimate linear functions of the state vector, the distributed functional observers in this paper can still estimate linear functions of the original state vector. Then, we establish existence conditions for the proposed functional observers. Finally, we provide effective algorithms for computing unknown observer matrices.

Asymptotic stability analysis and model reduction for spatially interconnected time-delay systems

This paper deals with problems of asymptotic stability analysis and model reduction for spatially interconnected continuous time-delay systems. The well-posedness, asymptotic stability, and contractiveness of spatially interconnected continuous-time state-delay systems are appropriately defined. The Lyapunov–Krasovskii method is extended for asymptotic stability analysis of spatially interconnected continuous time-delay systems in infinite-dimensional space. A sufficient condition based on the given system matrices is presented in terms of linear matrix inequalities to check the well-posedness, asymptotic stability, and contractiveness. We then obtain a sufficient condition for the existence of a delay-free reduced-order system for a given spatially interconnected continuous time-delay system. Employing the elimination lemma and the cone complementary linearization algorithm, we can obtain a delay-free reduced-order system. Finally, two examples are used to demonstrate the effectiveness and applicability of the proposed method.

A weighted distributed predictor-feedback control synthesis for interconnected time delay systems

The paper investigates the control design of interconnected time delay systems by means of distributed predictor-feedback delay compensation approaches and event-triggered mechanism. The idea behind delay compensation is to counteract the negative effects of delays in the control-loop by feeding back future predictions of the system state. Nevertheless, an exact prediction of the overall system state vector cannot be obtained providing that each system has only knowledge of their local data regarding the system model and state variables. Consequently, predictor-feedback delay compensation may lose effectiveness if the coupling between subsystems is sufficiently strong. To circumvent this drawback, the proposed distributed predictor-feedback control incorporates extra degree of freedom for control synthesis by introducing new weighting factors for each local prediction term. The design of the weighting factors is addressed, together with the event-triggered parameters, by an algorithm based on Linear Matrix Inequalities (LMI) and the Cone Complementarity Linearization (CCL). Simulation results are provided to show the achieved improvements and validate the effectiveness of the proposed method, even in the case that other control strategies fail to stabilize the closed-loop system.

Distributed Functional Interval Observers for Nonlinear Interconnected Systems With Time-Delays and Additive Disturbances

In this article, a novel distributed functional interval observer design method is developed for nonlinear interconnected time-delay systems with additive disturbances in the outputs. The traditional distributed functional state observer is replaced by two distributed ones corresponding to two bounds (upper and lower bound) of functions of the state variables which need to be estimated. The structures of the functional interval observer for each subsystem are first proposed and then existence conditions are provided and formulated in terms of linear programmings (LPs). Finally, three examples are provided to illustrate the feasibility of the propounded theories.

Distributed finite frequency fault detection observer design for spatially interconnected time-delay systems with interconnected chains

This paper proposes an $$H_{-}/H_{\infty }$$ fault detection observer method for a class of spatially interconnected time-delay systems (SITSs) with interconnected chains in finite frequency domain. As one of the main contribution, a delay-dependent generalized Kalman–Yakubivich–Popov (GKYP) lemma for SITSs with interconnected chains is proposed. Based on the giving GKYP lemma, sufficient conditions for the existence of the observers to guarantee the fault sensitivity and disturbance robustness in finite frequency domain are presented. Finally, an example is provided to demonstrate the effectiveness of the proposed method.

Global decentralized output feedback control for interconnected time delay systems with saturated PI hysteresis

In this paper, a global decentralized adaptive output feedback control is proposed for a class of nonlinear interconnected time delay systems, in which each subsystem covers unknown parameters, the unmeasured states dependent nonlinearities, and unknown saturated PI hysteresis. By constructing modified dynamic high-gain observers, together with backstepping technique, the unmeasured states dependent nonlinearities that fail to match global Lipschitz condition can be well disposed and global stability of the overall closed-loop system is obtained. With the aid of a new adaptive law, the restrictive assumption requiring known bounds of the time-varying delays in the existing literature is removed. Furthermore, based on the prescribed performance technique, it can be proved that both steady state and prespecified transient tracking performance are able to be guaranteed.

Fault detection for discrete spatially interconnected systems with time-delay over finite frequency domains

This paper investigates the problem of fault detection observer design for discrete spatially interconnected time-delay systems (SITSs) in finite frequency range. Firstly, a delay-dependent generalised Kalman–Yakubivich–Popov (GKYP) lemma for SITSs is proposed. Then, by the giving GKYP lemma, a distributed fault detection observer design method can be derived by solving a set of linear matrix inequalities (LMIs). Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.