Interconnected Nonlinear Systems Research Articles

Decentralized adaptive tracking control for a class of interconnected nonlinear systems via dynamic high‐gain technique

AbstractIn this article, the problem of decentralized adaptive tracking control for a class of interconnected nonlinear systems is investigated, in which the interconnection term in each subsystem is related to the states of all subsystems. By utilizing the backstepping controller design method and dynamic high‐gain technique, two kinds of decentralized adaptive control schemes are developed. Some dynamic parameters are introduced into the controllers to counteract the effects of interactions among subsystems. Moreover, with the aid of graph theory, it is shown that all signals of the closed‐loop system are bounded. The novelty of the proposed method lies in that the tracking accuracy of each subsystem can be preset without adjusting the controller parameters. Finally, two illustrative examples are presented to demonstrate the efficiency of the proposed schemes.

Decentralized adaptive PI fault tolerant tracking control for strong interconnected nonlinear systems subject to unmodeled dynamics and actuator faults

In this study, a novel decentralized adaptive proportional–integral (PI) fault tolerant tracking control strategy is proposed for a class of strong interconnection nonlinear systems with unmodeled dynamics and actuator faults. The adverse effects generated by unmodeled dynamics could be eliminated by introducing a dynamic signal and the multiplicative actuator faults could be dealt with by using adaptive control technique. In addition, broad learning system (BLS) scheme is used to approximate the unknown nonlinear functions and additive actuator faults, the minimal-learning-parameter (MLP) scheme is used in this study to reduce the number of adaptive update parameters, which resltus in less computation overhead. The decentralized adaptive PI fault tolerant tracking controller including a switching compensation mechanism is designed for the considered interconnected systems, such that all the signals in the closed-loop systems are uniformly ultimately bounded (UUB) and the tracking errors converge to a small residual set. In the end, a chemical reactor example is utilized to illustrate the feasibility and significance of the designed control scheme.

Distributed observer design for interconnected nonlinear systems with faults and disturbances based on dynamic event conditions

AbstractThis study investigated the observer design schemes for interconnected nonlinear systems with actuator faults, sensor faults, external disturbances, and limited measured resources. A novel effective distributed estimation scheme is presented for the interconnected nonlinear system to estimate the states, faults, and lumped disturbances, simultaneously. To save communication resources and to improve information utilization, an adaptive event condition is designed in the sensor channel, and the triggered values are utilized to design the observer. Especially, to handle the sensor fault, the output is separated into two parts, and the estimation is realized with the help of a normal one. In the first part of this study, a class of interconnected nonlinear systems with partial loss of effectiveness of sensor fault is considered, and an event‐based distributed estimation scheme is established. In the second part, a class of more universal feedback interconnected nonlinear with both partial loss sensor fault and bias sensor fault is investigated. An augment system is formulated by an augmented vector composed of state and sensor faults. And then the estimation scheme is realized by utilizing the presented event‐based distributed observer. The convergence abilities of both the two conditions are proved and, finally, the estimation performances of the presented observer are verified by a numerical simulation system and an inverted pendulum system.

A predefined time decentralized adaptive tracking control method for interconnected nonlinear systems

SummaryIn this paper, the problem of predefined time adaptive decentralized tracking control for a class of interconnected nonlinear systems is investigated. Firstly, a time‐varying constraint function is introduced to convert the tracking control problem into one with a constraint on tracking error, which can successfully remove the restriction of initial conditions. Secondly, the asymmetric constraint requirements on tracking error are achieved via defining a novel coordinate transformation function. Then, based on the proposed constraint function and the backstepping method, a decentralized adaptive controller is constructed. Furthermore, it is proved that all signals of the closed‐loop system are globally uniformly ultimately bounded (GUUB) via Lyapunov stability theory. Finally, the effectiveness of the proposed scheme is confirmed by two simulation examples.

Fault Estimation for Switched Interconnected Nonlinear Systems With External Disturbances via Variable Weighted Iterative Learning

The focus of this paper is a fault-estimation issue for switched interconnected nonlinear systems (SINSs) subjected to external disturbances. First, to estimate the fault of all subsystems under external disturbances, a distributed iterative learning observer (DILO) is designed by utilizing related information among subsystems. Then, a novel variable weighted iterative learning (VWIL)-based fault-estimation law is proposed to fast-track the fault signals and weaken the disturbance effects. Subsequently, the convergence conditions are achieved using λ-norm method and mathematical induction. In addition, the gain matrices of the DILO and VWIL law are calculated simultaneously. Finally, simulation results are given to verify the feasibility of the proposed method, which show that accurate fault-estimation results can be obtained after about the 20th iteration.

Decentralized adaptive finite‐time fault‐tolerant control for a class of high‐power interconnected nonlinear systems via graph theory

SummaryThis article investigates the decentralized adaptive finite‐time fault‐tolerant control (FTC) for unknown strong interconnected nonlinear systems with high‐powers and actuator faults. The powers are the ratio of positive odd rational integers and may be different, which makes the presented scheme different from existing work on interconnected nonlinear systems. The considered interconnections are governed by some boundary functions that grow nonlinearly in the states of all subsystems. First, the difficulty brought by high powers to controller design is overcome by introducing the adding one power integrator method. Then, based on backstepping method and FTC theory, a decentralized adaptive algorithm is proposed without approximate structure (neural network, fuzzy logic, etc.), which adaptively compensates the impact of actuator faults. Besides, with the aid of algebraic graph theory, the system is stable under practical finite‐time concept. Finally, the effectiveness of the theoretical findings are validated by conducting two simulation examples.

Adaptive backstepping control for nonlinear interconnected systems with prespecified-performance-driven output triggering

This paper considers a class of nonlinear large-scale interconnected systems and proposes an event-triggered decentralized controller by using adaptive output feedback backstepping. To save the communication resource, the output measurements are transmitted to the controller based on a novel double-events-triggered (DET) mechanism driven by transient performance request. Due to the use of triggered mechanism, only discontinuous output signals can be utilized such that the derived virtual controls are discontinuous, of which the derivatives cannot be computed as often done in standard backstepping design procedure. To overcome this difficulty, a new error signal decomposition and compensation mechanism is proposed to quantify and compensate for the difference between the virtual controls derived by using the event-triggered measurement signals and the real-time system outputs. Through a nonsmooth stability analysis where the closed-loop stability is considered under different conditions of output data transmissions, it is shown that the tracking error remains within a prespecified performance bound all the time. In contrast to the existing backstepping results addressing event-triggered outputs, the designed DET mechanism does not require the virtual control signals to be reversely transmitted to the sensor side from the controller side and guarantees the communication burden can be reduced under tracking performance guarantees.

Sliding-mode surface-based decentralized event-triggered control of partially unknown interconnected nonlinear systems via reinforcement learning

This paper studies a sliding-mode surface (SMS)-based decentralized event-triggered control problem for a class of partially unknown interconnected nonlinear systems within an identifier-critic neural networks framework. By assigning an especial cost function associated with SMS for each nominal subsystem, the original control issue is equivalently converted into designing a number of optimal controllers updating under an event-triggered manner, which considerably saves the communication resources. To derive these optimal event-based control policies, the corresponding Hamilton-Jacobi-Bellman equations are solved via the reinforcement learning algorithm. Different from traditional reinforcement learning algorithms, the identifier-critic network framework can obviate the requirement for the knowledge of system internal dynamics, and remove the errors generated by approximating actor networks. The weight vector in the critic network is updated through the gradient descent method and the experience replay technology, such that the persistence of excitation condition is relaxed. Under the proposed SMS-based decentralized control scheme, the considered system has a faster control response while minimizing the cost function. After that, according to the Lyapunov stability theory, all signals of the interconnected nonlinear systems are strictly proved to be bounded. Finally, the validity of the proposed control scheme is demonstrated via a simulation example.

Extended dissipative filter design for discrete-time interconnected fuzzy systems with time-varying delays subject to cyber attacks

This article addresses the problem of extended dissipative filtering design for the class of nonlinear interconnected systems with time-varying delays under the cyber attacks. The dynamics of proposed interconnected systems (ISs) is modeled by the Takagi-Sugeno fuzzy (TSF) IF-THEN rules. The relevant practical model is used to describe the network connectivity between the plant and the filter. In addition, to develop the filter for nonlinear systems in more practical sense, the sensor delays and the influence of cyber attacks are taken into account during the signal transmission. In order to verify that the developed closed-loop system is asymptotically stable with extended dissipative, sufficient conditions are derived by constructing the delay-dependent Lyapunov-Krasovskii functional (LKF) and employing the summation inequalities through the linear matrix inequalities (LMIs) approach. The outcomes of theoretical results can be used to analyze the various performances like H∞ performance, (Υ1,Υ2,R)−α−dissipativity, passivity, mixed H∞/passivity, and l2−l∞ performance in a single framework. At last, a numerical example is presented to demonstrate the proposed method and to validate the theoretical findings in a practical sense.

Fuzzy Graph Modeling and Clustering Analysis of Nonlinear Dynamical Systems

Analyzing stability and designing control strategies for interconnected nonlinear dynamical systems poses mathematical challenges due to combinatorial growth in complexity. This paper develops a methodology integrating fuzzy graph theory with spectral clustering techniques to enable tractable certification of stability properties. Fuzzy similarity relations between state variables model imprecise couplings within the nonlinear dynamics. Representing these relations through graph adjacency matrices facilitates partitioning strongly connected states using spectral algorithms. Stability of the overall fuzzy state graph is inferred from the spectral radii of decoupled fuzzy subgraphs. The graph-theoretic abstraction provides a coarse-grained lens into nonlinear stability properties while circumventing computational barriers. The fuzzy graph modeling and spectral partitioning pipeline ultimately streamlines control synthesis targeting local clustered subdynamics. Case studies on power network stabilization, swarm navigation, and process operations showcase scalable applications to high-dimensional complex systems. The integrated fuzzy graph and spectral clustering approach provides a systematic toolkit for analysis and control of heavily interconnected nonlinear dynamical systems across engineering domains.

Analysis of operating characteristics of interconnected operation of thermal grids with bidirectional heat trade

This study analyzed the effects of bidirectional heat trade of extra heat on the overall operational efficiency of interconnected thermal grids with empirical correlation formulation. A decision support operational simulation tool was developed to assess the technical-, and techno-economic performance of the complex and highly non-linear interconnected thermal grid system. From the techno-economic feasibility analysis for the test case of a hypothetical new thermal grid with a peak heat demand of 60 MWh, it was analyzed that the operating profit could be secured only for the gas engine, estimated to be about 8%. Moreover, the sensitivity analysis revealed that fuel price has the most dominant effect on operating profit in that the gas engine can attain 21% of operating profits as the fuel price is assumed to decrease by 20%. This study demonstrated the possibility of attaining favorable operational benefits with interconnected operation between thermal grids in terms of technological and techno-economic aspects with a newly proposed approach with empirical correlation formulation.

Quantized neural adaptive finite-time preassigned performance control for interconnected nonlinear systems

Quantized neural adaptive finite-time preassigned performance control for interconnected nonlinear systems

Neural network‐based decentralized adaptive fault‐tolerant control for a class of nonlinear interconnected systems with unknown input powers

SummaryThis article studies the output tracking control for a class of interconnected nonlinear systems with actuator faults, where each subsystem has unknown powers. Based on Lyapunov stability theory, a neural‐network‐based decentralized adaptive fault‐tolerant control scheme is proposed so that each tracking error can be constricted in a small adjustable neighborhood of the origin. In existing results, interconnections and actuator bias faults have been addressed. But the systems' input powers are required to be a known positive integer and preferably one. So in our article, we relax the restrictions and consider more general systems whose input powers are extended to larger than one and unknown at the same time. Finally, two numerical simulation examples are shown to explain the validity of control strategy proposed in our article.

Event-triggered optimal decentralized control for stochastic interconnected nonlinear systems via adaptive dynamic programming

This paper presents an event-triggered adaptive dynamic programming (ETADP) algorithm to study the optimal decentralized control issue of interconnected nonlinear systems subject to stochastic dynamics. By developing a performance index function for augmented auxiliary subsystem, the primordial control issue is converted into deriving an array of optimal control policies sampling in an aperiodic pattern. Then, an ETADP algorithm is introduced under an identifier-actor-critic network framework, where the identifier aims to determine the stochastic dynamic, the critic aims to assess the system performance and the actor aims to implement the control action. A remarkable feature is that the actor-critic updating laws are constructed through the negative gradient method of a positive function, which is designed in the light of the partial derivative of a Hamilton–Jacobi-Bellman equation. Under the provided weight tuning rule, the traditional ADP algorithm can be significantly simplified. The stability of the close-loop system is verified through direct Lyapunov theory, and a numerical simulation is given to confirm the effectiveness of the optimal control scheme.

Stability of networked nonlinear systems: Generalization of small-gain theorem and distributed testing

This paper studies the stability problem for networked control systems. A general result is presented to determine either global uniform boundedness (GUB), global asymptotic stability (GAS) or input-to-state stability (ISS), for interconnected nonlinear systems. This result checks stability in terms of a scalar called the network gain, hence we call the result the network gain theorem. The result generalizes the previously known matrix small-gain theorem and cyclic small-gain theorem for ISS. As in these results, our theorem does not assess the stability of a given networked system, but of a whole family of networked systems satisfying certain common assumption. An advantage of our stability condition is that it is not only sufficient, but also necessary, in the sense that, if not met, there exists an unstable networked system within that family. To complement our theoretical result, we propose a fully distributed algorithm to compute the network gain. We present simulation results to illustrate the proposed algorithm.

Input‐to‐state practical stability for nonautonomous nonlinear infinite‐dimensional systems

AbstractIn this article, we are concerned with the input‐to‐state practical stability (ISpS) of nonautonomous nonlinear infinite‐dimensional systems. Sufficient conditions of ISpS are provided based on Lyapunov functions and a nonlinear inequality. We characterize ISpS in terms of uniform practical asymptotic gain property. We show that for a class of admissible inputs the existence of an ISpS‐Lyapunov function implies the ISpS of a system in Banach spaces. These results are used to study the input‐to‐state practical stability of a certain class of nonautonomous semilinear evolution equations. Furthermore, we provide a small‐gain theorem for nonautonomous nonlinear interconnected systems. An example is used to illustrate the application of the developed method.

Decentralized Adaptive Fuzzy Finite-Time Event-Triggered Control for Interconnected Nonlinear Systems Subject to Input Saturation

This article investigates the decentralized adaptive finite-time command filter control for interconnected nonlinear systems subject to input saturation by event-triggered (ET) output feedback. In practice, some subsystems may be distributed distantly, making it difficult for a centralized controller to acquire feedback signals from them. On the other hand, the finite-time control scheme with a nonsmooth controller could be used for accelerating the system convergence rate. However, with this control scheme, it is difficult to exclude Zeno behavior directly by using the existing methods. To overcome these obstacles, we consider a decentralized control scheme and exploit the property of hyperbolic tangent functions and the approximation capability of fuzzy logic systems to handle interconnected nonlinear functions. Furthermore, we develop a new switching-type finite-time ET mechanism in the presence of asymmetric input saturation. Under the developed decentralized controller, all system states are bounded as well as the tracking error converges to a compact set near the origin in a finite time. Meantime, the function's one-sided differentiability is employed to avoid Zeno phenomenon. Finally, two practical examples are provided to demonstrate the effectiveness and advantages of the presented approach.

Event-triggered adaptive decentralised control of interconnected nonlinear systems with Bouc-Wen hysteresis input

ABSTRACT This article presents an event-based adaptive decentralised output feedback control scheme for interconnected systems with Bouc-Wen hysteresis and unmeasured system states. To reduce some unnecessary data transmissions, a novel dynamic threshold adjustable event-triggering mechanism is proposed. In contrast with the traditional static threshold event-triggering mechanism, communication efficiency is greatly enhanced. Then, a neural networks-based observer is constructed to address the problem of unmeasured states, and the dynamic surface control method is used to address the ‘explosion of complexity’ that comes up when traditional backstepping design processes are used. Meanwhile, the Nussbaum function is introduced to eliminate the effect of unknown hysteresis. By resorting to the Lyapunov stability theory, it can be verified that all signals in the close-loop system are uniformly ultimately bounded. Finally, a simulation example is given to verify the effectiveness of the developed control scheme.

An Event-Triggered Predefined Time Decentralized Output Feedback Fuzzy Adaptive Control Method for Interconnected Systems

This article investigates the event-triggered predefined time output feedback control design problem for nonlinear interconnected systems with nonstrict feedback control structures. Compared with the existing event-triggered output feedback control design schemes, the most significant contribution of this article is that the system stability time can be preset directly. Fuzzy logic systems (FLSs) and FLSs-based state observer deal with unknown nonlinear dynamics and unmeasured states. Combining with dynamic surface control technology and event-triggered mechanism based on switching threshold strategy, an event-triggered predefined time decentralized output feedback control method is proposed, in which a predefined time filter is designed to solve the computational complexity problem. In addition, the algebraic loop problem and control singular problem are also solved, respectively, by applying the property of fuzzy basis function and L’Hospital’s rule. Utilizing the predefined time Lyapunov stability theory, the system stability analysis is given. Finally, the effectiveness and practicability of the proposed control method are verified by practical system simulation cases.

Event-Triggered output feedback adaptive control for nonlinear switched interconnected systems with unknown control coefficients

This paper proposes an event-triggered adaptive control scheme for switched nonlinear interconnected systems with unknown control coefficients and unknown backlash hysteresis. Firstly, unknown interconnected terms and unknown nonlinearities of the system are approximated through fuzzy logic systems. By introducing the Nussbaum function and choosing an appropriate Lyapunov function, an event-triggered output feedback controller is developed. The proposed control scheme can guarantee that the whole states are semi-globally uniformly ultimately bounded, meanwhile, the elimination of Zeno behavior is ensured. Eventually, the effectiveness of the method is verified by simulation results.