Large-scale Time-delay Systems Research Articles

A new distributed robust H∞ control strategy for a class of uncertain interconnected large-scale time-delay systems subject to actuator saturation and disturbance

In the realm of large-scale systems, the complexity of controller design has long been exacerbated by the proliferation of decision variables and inherent conservatism. This study introduces a novel approach to address these challenges, presenting a new distributed robust controller design methodology tailored for large-scale systems grappling with disturbances, uncertainties, and actuator saturations. The primary objectives include reducing conservatism, minimizing decision variables, and significantly curtailing computation time. To surmount these hurdles, the research leverages descriptive and reciprocally convex methods, formulating the design procedure using linear matrix inequalities. This enables the adjustment of uncertain parameters and robust disturbance rejection, thereby ensuring stability in large-scale systems. Additionally, a feedback control law is proposed to accommodate saturation constraints and ensure the closed-loop system’s stability. Notably, the effectiveness of the proposed control scheme is demonstrated through the evaluation of a full-car active suspension system, which is partitioned into interconnected subsystems to a large-scale system. Comparative analyses underscore the superior performance and technical advancements offered by the proposed methodology over existing approaches.

An improved robust distributed [formula omitted] control method for uncertain interconnected large-scale time-delayed systems

In modern industries, systems have become increasingly large-scale and complex, comprising multiple interconnected subsystems where the performance of each subsystem impacts the others. Ensuring stability and performance under uncertainties, external disturbances, and time delays is crucial for such systems. This paper proposes a new distributed control method that stabilizes a specific type of time-varying input-delayed large-scale system in the presence of uncertainties and external disturbances. The proposed method employs Jensen’s inequality to reduce the number of decision variables and uses reciprocally convex and descriptive methods to minimize conservatism and decrease computation time. The performance of the proposed method is evaluated on a full-car model with an active suspension system as a novel approach to controlling large-scale systems. This paper describes how to divide a large-scale full-car system into several interconnected subsystems, for the first time. The results indicate the potential of the proposed controller in enhancing the performance of the system in comparison with other previous control methods.

A partial solution operator discretization-based method for small signal stability analysis of time-delay power systems

To analyze the small signal stability of large-scale time-delay power systems (TDPSs), critical oscillation modes are required to be reliably computed. The solution operator discretization with pseudo-spectral collocation (SOD-PS)-based method has been proposed to indirectly calculate critical eigenvalues from the solution operator’s discretization matrix. However, dimension of the discretization matrix is dozens of times the number of system state variables, and thus limits the efficiency of SOD-PS. To resolve this, SOD-PS is evolved into partial SOD-PS (PSOD-PS) in this paper by applying the idea of partial spectral discretization (PSD). Specifically, only the discretization of retarded states is reserved instead of discretizing all system states in delay interval. The resultant partial discretization matrix exhibits very low order, which is close to the number of system state variables. In addition, the rotation-and-multiplication preconditioning technique is studied to efficiently capture oscillation modes with damping ratios less than the given threshold. Specifically, the preconditioning technique is implemented by two ways and their consistency is derived in detail. Both theoretical analyses and intensive tests on the 16-machine 68-bus test system, a real-life 516-bus provincial transmission system of China and the 33028-bus ultra-high-voltage (UHV) interconnected system of China verify the accuracy and efficiency of the presented PSOD-PS.

Adaptive tracking control of uncertain large-scale nonlinear time-delay systems with input saturation

This paper investigates the adaptive tracking control problem of uncertain large-scale nonlinear time-delay systems with input saturation. Unknown constants and continuous functions with respect to output or delayed output are allowed in the nonlinear interconnected functions. The dynamic gain control technique is used to study the tracking control problem of considered system, which simplifies design process and form of controller. By introducing a full-order state observer and three dynamic equations, output feedback tracking control scheme is constructed to ensure that all signals of the closed-loop system are globally uniformly ultimately bounded (GUUB). In addition, the tracking error can converge to a small neighbourhood around the origin by selecting appropriate parameters. Finally, a practical example is presented to illustrate the feasibility of the proposed control scheme.

$$\varepsilon $$-Embedding Model Reduction Method for Time-Delay Differential Algebra Systems

A new model order reduction (MOR) method for large-scale time-delay differential algebra systems is proposed herein. The presented MOR algorithm is based on parametric moment matching and $$\varepsilon $$ -embedding. By selecting an appropriate projection matrix, this process generates reduced-order models that preserve the structure of the original time-delay differential algebra system. Additionally, moment-matching results and error estimations are provided. Finally, two numerical circuits are tested to illustrate the effectiveness of the proposed MOR method.

Decentralized Adaptive Neural Approximated Inverse Control for a Class of Large-Scale Nonlinear Hysteretic Systems With Time Delays

This paper proposes a decentralized neural adaptive dynamic surface approximated inverse control (DNADSAIC) scheme for a class of large-scale time-delay systems with hysteresis nonlinearities as input. The decentralized control problem under the case only the outputs are measurable is solved by utilizing the radial basis function neural networks approximator and the hysteresis approximated inverse compensator. Also, with the help of finite covering lemma, the traditional Krasovskii functionals are dropped when coping with the delays, leading to the removal of the assumptions on the functions with time-delay states and the acquisition of the arbitrarily small ${L}_{{\infty }}$ tracking performance of each hysteretic subsystem with time delays. The analysis of stabilities guarantees all the signals of the closed-loop systems are semiglobally uniformly ultimately bounded. Simulation results illustrate the efficiency of the proposed DNADSAIC scheme.

Absolute stability of large-scale time-delay Lurie indirect control systems with unbounded coefficients

We study the absolute stability of large-scale time-delay Lurie indirect control systems with unbounded coefficients. Based on Lyapunov-Krasovskii functional approach, we derive some novel absolute stability conditions for this class of Lurie systems with a single nonlinearity. These conditions are particularly suitable for large-scale time-delay Lurie systems with unbounded coefficients. At the same time, they are also effective for such systems with bounded or constant coefficients. Furthermore, we extend the results obtained to multiple nonlinearities. The effectiveness of the proposed methods is illustrated via two numerical examples.

An LMI-based functional estimation scheme of large-scale time-delay systems with strong interconnections

In this paper, the problem of distributed functional state observer design for a class of large-scale interconnected systems in the presence of heterogeneous time-varying delays in the interconnections and the local state vectors is considered. The resulting observer scheme is suitable for strongly coupled subsystems with multiple time-varying delays, and is shown to give better results for systems with very strong interconnections while only some mild existence conditions are imposed. A set of existence conditions are derived along with a computationally simple observer constructive procedure. Based on the Lyapunov–Krasovskii functional method (LKF) in the framework of linear matrix inequalities (LMIs), delay-dependent conditions are derived to obtain the observer parameters ensuring the exponential convergence of the observer error dynamics. The effectiveness of the obtained results is illustrated and tested through a numerical example of a three-area interconnected system.

Adaptive fuzzy decentralized control for uncertain large-scale nonlinear time-delay systems with virtual control functions

In this paper, the adaptive fuzzy decentralized tracking control problem is investigated for a class of uncertain large-scale nonlinear systems, interacted through their outputs with completed unknown time-varying delays. The novel contribution is to remove the common assumptions on the unknown time delays by the proposed delay replacement technique, so that the controller design is not dependent on these assumptions any more, and thus, added flexibility in decentralized control design is achieved. Furthermore, the approximation and replacement errors are handled by the adaptive technique. All closed-loop signals are proved to be semiglobal uniform ultimate boundedness, and the tracking errors are guaranteed to converge to a small residual set around the origin. The simulation studies illustrate the effectiveness of the control scheme.

Decentralised adaptive output feedback stabilisation for stochastic time-delay systems via LaSalle-Yoshizawa-type theorem

ABSTRACTThis paper deals with the decentralised output feedback stabilisation problem for a class of large-scale stochastic time-delay nonlinear systems. A general theorem is firstly given to guarantee the global existence and uniqueness of the solution for stochastic time-delay systems. In addition, a stochastic version of the well-known LaSalle-Yoshizawa theorem with time-varying delay is initially proposed for the controller design and stability analysis. Then, for a class of large-scale stochastic systems with time-varying delays, totally decentralised adaptive delay-dependent controllers are designed by using K-filter and backstepping approach. Via LaSalle-Yoshizawa-type theorem and constructing a general Lyapunov function, it is shown that all signals in the closed-loop system are bounded almost surely and the solution is almost surely asymptotically stable. Finally, a simulation example is given to illustrate the effectiveness of the results of this paper.

Decentralised fault compensation of time‐delayed interactions and dead‐zone actuators for a class of large‐scale non‐linear systems

An approximation-based decentralised adaptive fault compensation (FC) problem is addressed for large-scale non-linear time-delay systems with unknown faults in both time-delayed C 1 non-linear interconnections and non-symmetric dead-zone actuators. Error surfaces constrained by prescribed performance bounds, which characterise the convergence rate and maximum overshoot of control errors, are presented to provide predefined bounds of control errors. Then, we design a memoryless decentralised FC control system using the constrained-surfaces-based dynamic surface design methodology, without constructing a dead-zone inverse and requiring the information about dead-zone parameters and time-delayed interactions. For the compensator design, the function approximation technique using neural networks is applied to adaptively estimate unknown non-linear effects and changes in model dynamics because of time-delayed interaction and dead-zone actuator faults. It is shown from Lyapunov stability theorem that all the error surfaces are preserved within the prescribed performance bounds and finally converge to an adjustable neighbourhood of the origin. Therefore guaranteed transient performance is achieved at the moment the faults occur.

Decentralised robust stabilisation of uncertain large-scale interconnected time-delay systems with unknown upper bounds of uncertainties

The problem of decentralised robust stabilisation is considered for a class of uncertain large-scale time-delay interconnected dynamical systems. In the paper, the upper bounds of delayed state perturbations, uncertainties, interconnection terms, and external disturbances are assumed to be completely unknown, and the delays are assumed to be any non-negative constants. For such a class of uncertain large-scale time-delay interconnected systems, a new method is presented whereby a class of adaptation-free decentralised local robust state feedback controllers can be constructed. In addition, it is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed to be uniformly ultimately bounded. Finally, as an application to the practical mechanical systems, some simulations of a numerical example are provided to demonstrate the validity of the theoretical results.

Decentralized adaptive neural output feedback control of a class of large-scale time-delay systems with input saturation

A decentralized adaptive neural output feedback control scheme is presented for a class of large-scale time-delay systems with saturating inputs. The observer is constructed to estimate the immeasurable states of the system and the auxiliary system is designed to compensate the nonsmooth nonlinearities of input saturation constraints. Also, the control strategy is developed by the backstepping recursive method combining with neural networks (NNs) for the approximation of the unknown functions and dynamic surface control (DSC) technique for the well known ‘explosion of complexity’ problem. The advantage of this scheme is that it only relies on the output information of the system and there is no requirement for exact priori knowledge about the system parameters. It is proved that the control approach guarantees all signals in the closed-loop system uniformly ultimately bounded. Simulation results are provided to demonstrate the effectiveness and usefulness of the proposed strategy.

Adaptive decentralized NN control of large-scale stochastic nonlinear time-delay systems with unknown dead-zone inputs

In this paper, the problem of adaptive decentralized neural network (NN) control for a class of large-scale stochastic nonlinear time-delay systems with unknown dead-zone inputs is investigated. Neural networks are utilized to approximate unknown nonlinear functions, and an adaptive decentralized controller is constructed by incorporating the minimal learning parameters algorithm into backstepping design procedure. It is proved that the proposed control scheme guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded in probability. Finally, a numerical example is provided to demonstrate the effectiveness of the present results.

Decentralized Variable Structure Control for Uncertain Large-Scale Time-Delayed Systems: A New Approach

In this paper, a novel decentralized variable structure control (DVSC) scheme is proposed for a class of large-scale time-delayed systems (LSSs) with mismatched interconnections and uncertainties. New invariance conditions are derived such that each subsystem in the switching surface is completely invariant to both delay interconnections and uncertainties. It also shows that the stability of each closed-loop subsystem is guaranteed. By constructing auxiliary function and applying matrix norm inequality technique, the developed DVSC law for the interconnected system is realized independently through the delay terms. Moreover, the chattering around the switching surface can be reduced by the proposed design approach. Illustrative example is given to verify the validity of the developed controller.

Delay dependent stability of linear time-delay systems

This paper deals with the problem of delay dependent stability for both ordinary and large-scale time-delay systems. Some necessary and sufficient conditions for delay-dependent asymptotic stability of continuous and discrete linear time-delay systems are derived. These results have been extended to the large-scale time-delay systems covering the cases of two and multiple existing subsystems. The delay-dependent criteria are derived by Lyapunov's direct method and are exclusively based on the solvents of particular matrix equation and Lyapunov equation for non-delay systems. Obtained stability conditions do not possess conservatism. Numerical examples have been worked out to show the applicability of results derived.

Computing the H2 norm of large-scale time-delay systems

The H2 norm of an appropriately defined transfer function plays an important role in the field of systems and control, as a robustness measure with respect to noise or external disturbances. For a time-delay system the H2 norm of a transfer function can be approximated by rewriting the time-delay system as an infinite-dimensional linear system and applying a spectral discretization to become a system without delay. The H2 norm of this (larger) standard LTI system can be calculated by solving a Lyapunov equation. Downside of this method is the fact that the discretized model is of dimension nN, with n the size of the original time-delay system and N the number of discretization points. Therefore, a Krylov based model order reduction technique will be applied, which allows to reduce the order of the discretized model further down to a chosen value k <<nN and where the transfer function of the reduced order model matches several moments (function value and derivatives) at zero and infinity with the transfer function of the original time-delay system. In this paper, we describe in detail the procedure allowing to transform a large-scale time-delay system into a standard linear system of small dimension and show how the H2 norm of the resulting system is an accurate approximation for the H2 norm of the original time-delay system. We predict the error behavior of the approximation and demonstrate this on an application.

Controller Design of Multiinput Multioutput Time-Delay Large-Scale System

The paper presents a novel feedback linearization controller of nonlinear multiinput multioutput time-delay large-scale systems to obtain both the tracking and almost disturbance decoupling (ADD) performances. The significant contribution of this paper is to build up a control law such that the overall closed-loop system is stable for given initial condition and bounded tracking trajectory with the input-to-state-stability characteristic and almost disturbance decoupling performance. We have simulated the two-inverted-pendulum system coupled by a spring for networked control systems which has been used as a test bed for the study of decentralized control of large-scale systems.

A Stability Condition with Delay-Dependence for a Class of Switched Large-Scale Time-Delay Systems

By using the time-switched method and the comparison theorem, we derived a criterion of delay-dependent stability for the switched large-scale time-delay systems. To guarantee the exponential stability for the switched large-scale time-delay systems with stability marginλ, the total activation time ratio of the switching law is determined. An example is used to illustrate the effectiveness of our result.

On Delay Independent Stabilization Analysis for a Class of Switched Large-Scale Time-Delay Systems

In view of the state-driven switching method, the sufficient stability conditions with delay independence will be derived for the switched large-scale time-delay systems. A new stability criterion of switched large-scale time-delay systems is deduced by Lyapunov stability theorem. The method can be applied to cases when all individual switched systems are unstable. Finally, one example is exploited to illustrate the proposed schemes.