Interconnected Nonlinear Systems Research Articles

Output-Feedback Control of Interconnected Nonlinear Systems With Both State and Input Delays Based on Truncated Prediction

In this paper, we investigate decentralized output-feedback control of interconnected nonlinear systems with both state and input delays. Unlike existing related works, in this paper, both the state delays and the input delay of each subsystem are unknown and different from each other. In order to achieve global asymptotic stability of the interconnected nonlinear system based on output feedback, we construct a finite-dimensional observer based on the output information to asymptotically estimate the state information. Simultaneously, based on a truncated prediction of the system state over the delay period, a novel decentralized observer-based output-feedback controller is proposed for each subsystem. Then, under the framework of Lyapunov-Krasovskii functional, a set of conditions for the global asymptotic stability of the closed-loop system is determined. Finally, a simulation example is given to verify the effectiveness of the proposed control scheme.

Decentralized discrete adaptive sliding mode control for interconnected nonlinear systems

This article presents a study on controlling a class of large-scale systems composed of interconnected subsystems. The systems are represented by discrete block-oriented models with unknown parameters. This article proposes a novel adaptive sliding mode control strategy to address the tracking control problem and minimize the impact of interconnection. This approach leverages the robustness of sliding mode control against unmodeled dynamics and disturbances with the advantages of adaptive control. To adapt the system’s parameters, a recursive parametric estimation algorithm using least-squares techniques is employed. The proposed method offers benefits such as robustness against parameter uncertainties, handling of nonlinearities, improved tracking accuracy, and reduced chattering phenomena. The effectiveness of the method is demonstrated through the evaluation of two simulation examples.

Adaptive fuzzy decentralized optimal control for interconnected nonlinear systems with unmodeled dynamics via mixed data and event driven method

In this work, based on the adaptive critic learning algorithms and fuzzy logic systems, the decentralized optimal control problem for interconnected nonlinear systems with unmodeled dynamics is investigated by applying a mixed data and event driven method. By introducing a modified performance index function for each auxiliary subsystem, the considered control problem of the whole interconnected system can be transformed into a group of event-driven optimal control problems of the auxiliary subsystems. Then, a three-layer neural network (NN) identifier is employed to reconstruct the completely unknown functions. Based on the obtained data-driven model, a single-critic NN is developed to solve the modified HJB equation. Meanwhile, a novel adaptive controller is designed by fuzzy logic systems to deal with the dynamical uncertainties cased by the unmodeled dynamics. Finally, a robot arm example is given to verify the effectiveness of the proposed control method.

Adaptive fuzzy output-Feedback control of switched large-Scale systems with fast time-Varying delay

In this paper, an adaptive fuzzy decentralized output-feedback control is developed for the uncertain switched large-scale interconnected nonlinear system, which contains fast time-varying delays and unknown nonconstant control coefficients. By introducing and proving a new lemma, an improved analysis method is given based on the Lyapunov-Krasovskii (LK) functional, and it gets rid of the dependence of LK functional design on the bound of the derivative of the delay. Immeasurable states are estimated by co-designing the decentralized state observer and the innovative compensation system, which eliminates a widely adopted but strict assumption that the unknown control coefficient must be constant. By comprehensively designing the state observer, the compensation system and LK functionals, a novel adaptive fuzzy decentralized output-feedback control law is proposed, and stability of the closed-loop system is guaranteed theoretically based on an improved average dwell time. Finally, the effectiveness is further verified by complete simulation experiments.

Event‐triggered adaptive control for a class of switched nonlinear interconnected systems

SummaryIn this article, the adaptive event‐triggered control issue is researched for a kind of switched nonlinear interconnected systems subject to unknown backlash‐like hysteresis and control coefficients. The fuzzy logic systems (FLSs) are employed to approximate the unknown nonlinear functions. To deal with the unknown control coefficients, the Nussbaum method and adaptive control are introduced. The proposed event‐triggered controller can effectively lessen the communication burden, meanwhile, the Zeno behavior is eliminated. It is guaranteed that the system outputs can track the reference signals and all the system signals are semi‐globally uniformly ultimately bounded (SGUUB). Finally, the simulation results verify the effectiveness of this control scheme.

On the Admissibility and Stability of Multiagent Nonlinear Interconnected Positive Systems With Heterogeneous Delays

Many multi-agent interconnected systems include typical nonlinearities which are highly sensitive to inevitable communication delays. This makes their analysis challenging and the generalization of results from linear interconnected systems theory to those nonlinear interconnected systems very limited. This paper deals with the analysis of Multi-Agent Nonlinear Interconnected Positive Systems (MANIPS). The main contributions of this work are two fold. Based on Perron-Frobenius theorem, we first study the “admissibility” property for MANIPS, and show that it is a fundamental requirement for this category of systems. Then, using admissibility/positivity properties and sequences of functions theory, we propose a suitable Lyapunov function candidate to conduct the analysis of the dynamical behavior of such systems. We show that the stability of MANIPS is reduced to the positiveness property (i.e. negative or positive definiteness) of a new specific matrix-valued function ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {Z}$</tex-math></inline-formula> ) that we derive in this paper. Furthermore, the obtained results generalize the existing theory. The quality of the results achieved are demonstrated through the applications of the developed theory on cells with multi-stage maturation process dynamical models.

Time-/Event-Triggered Adaptive Neural Asymptotic Tracking Control of Nonlinear Interconnected Systems With Unmodeled Dynamics and Prescribed Performance.

This article proposes two adaptive asymptotic tracking control schemes for a class of interconnected systems with unmodeled dynamics and prescribed performance. By applying an inherent property of radial basis function (RBF) neural networks (NNs), the design difficulties aroused from the unknown interactions among subsystems and unmodeled dynamics are overcome. Then, in order to ensure that the tracking errors can be suppressed in the specified range, the constrained control problem is transformed into the stabilization problem by using an auxiliary function. Based on the adaptive backstepping method, a time-triggered controller is constructed. It is proven that under the framework of Barbalat's lemma, all the variables in the closed-loop system are bounded and the tracking errors are further ensured to converge to zero asymptotically. Furthermore, the event-triggered strategy with a variable threshold is adopted to make more precise control such that the better system performance can be obtained, which reduces the system communication burden under the condition of limited communication resources. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed control scheme.

Design of distributed preview tracking controller for nonlinear interconnected systems with time‐delay

AbstractThe focus of this article is to design a distributed preview tracking controller for a class of nonlinear interconnected systems with time‐delay. By constructing the error systems with the information of previewable reference signal, and defining an performance index, the original preview tracking problem is converted into the control problem of the error system. Based on the relationship between the interconnection matrices and the input matrices, a distributed controller using not only the local state vector information but also the interconnection term information is designed for the error systems. Under this controller, the closed‐loop error system is decoupled. With the help of Lyapunov‐Krasovskii functional, the sufficient conditions, the asymptotic stability of the closed‐loop error system with disturbance attenuation level, are established. The distributed preview tracking controller, which is composed of state feedback, integrator, and preview feedforward, is acquired by integrating the controller of the error system. The proposed preview controller is applied to the chemical reactor recycles system and double‐parallel inverted pendulum system. The simulation verify that this controller is very effective in improving the tracking performance.

Distributed extended state observer design and output feedback anti‐disturbance control for nonlinear interconnected systems: A dynamic memory event‐triggered mechanism

AbstractThis paper investigates a distributed extended state observer design and output feedback anti‐disturbance control for nonlinear interconnected systems (ISs) with multiple disturbances. First, a distributed extended state observer with a sparse observer communication network is established to estimate the system states and external disturbances. Then, an output feedback controller with a disturbance compensation (DC) item is designed, where a novel dynamic memory event‐triggered mechanism (DMETM) is proposed to save communication resources. Third, under the proposed controller, the closed‐loop signals are bounded and the system states and the estimation errors converge to zero. Additionally, the system outputs satisfy performance. Finally, the simulation examples demonstrate the effectiveness of the DMETM in reducing the number of data transmissions compared to the dynamic event‐triggered mechanism (ETM).

Reinforcement Learning-Based Decentralized Safety Control for Constrained Interconnected Nonlinear Safety-Critical Systems.

This paper addresses the problem of decentralized safety control (DSC) of constrained interconnected nonlinear safety-critical systems under reinforcement learning strategies, where asymmetric input constraints and security constraints are considered. To begin with, improved performance functions associated with the actuator estimates for each auxiliary subsystem are constructed. Then, the decentralized control problem with security constraints and asymmetric input constraints is transformed into an equivalent decentralized control problem with asymmetric input constraints using the barrier function. This approach ensures that safety-critical systems operate and learn optimal DSC policies within their safe global domains. Then, the optimal control strategy is shown to ensure that the entire system is uniformly ultimately bounded (UUB). In addition, all signals in the closed-loop auxiliary subsystem, based on Lyapunov theory, are uniformly ultimately bounded, and the effectiveness of the designed method is verified by practical simulation.

Joint Estimation of State and Unknown Input for Nonlinear Interconnected Systems Based on Multiple Intermediate Estimator

This brief investigates the issue of state estimation and unbounded unknown input reconstruction for a class of one-sided Lipschitz nonlinear interconnected systems with uncertain output and mismatched unknown input distribution matrix. Based on descriptor augmentation strategy and coordinate transformation, the effect of measurement noise and matched unknown input parts are firstly decoupled. Then, a novel multi-intermediate estimator-assisted unknown input observer is constructed to estimate state and mismatched unknown input. In addition, sufficient conditions in linear matrix inequality (LMI) form is derived to guarantee the stability of the observer and to facilitate observer parameter tuning. Finally, a simulation example is provided to illustrate the effectiveness and merits of the proposed methods.

A Decentralized Learning Control Scheme for Constrained Nonlinear Interconnected Systems Based on Dynamic Event-Triggered Mechanism

This article presents a decentralized learning control method for a class of partially unknown nonlinear systems with asymmetric control input constraints and mismatched interconnections via a novel dynamic event-triggering condition. By employing an integral reinforcement learning strategy, the system drift dynamics can be avoided in the learning process. Meanwhile, a critic neural network is designed to obtain the approximated value function and tuned by using the gradient descent approach. Furthermore, a novel dynamic event-triggering condition is designed to determine the occurrence of an event by introducing a dynamic variable. By using the Lyapunov theory, all signals in the closed-loop system are proved to be uniformly ultimately bounded. Finally, we present a nonlinear interconnected system and an interconnected power system to verify the effectiveness of the proposed method.

Adaptive ELM-Based Security Control for a Class of Nonlinear-Interconnected Systems With DoS Attacks

This article is concerned with the output feedback security control of a class of high-order nonlinear-interconnected systems with denial-of-service (DoS) attacks, nonlinear dynamics, and exogenous disturbances. First, extreme learning machine (ELM) and adaptive techniques are adopted to approximate the unknown nonlinearities. Then, novel adaptive ELM-based nonlinear state observers with adaptive compensation functions are developed to estimate the unmeasurable states during DoS attacks under the influence of the disturbances. Further, by combining with the backstepping control and filtering techniques, adaptive ELM-based controllers are proposed to achieve uniformly ultimately bounded results based on the observation and adaption control signals under the influence of DoS attacks, nonlinear dynamics, and exogenous disturbances. Comparative studies are carried out to validate the effectiveness of the developed ELM-based adaptive observation and control strategies for two interconnected power systems.

Adaptive Fuzzy Decentralized Control for Stochastic Nonlinear Interconnected System With Nontriangular Structural Dynamic Uncertainties

This paper constructs an adaptive fuzzy decentralized fault tolerant control strategy for stochastic nonlinear interconnected system with non-triangular structural uncertainties, unmodeled dynamics and actuator faults. During the controller design process, the difficultly of system controller design caused by non-triangular structural uncertainties that mixed unmodeled dynamics are handled by utilizing the variable separation technique and fuzzy logic system (FLS). Then, based on the adaptive compensation technique, a fault tolerant controller is designed to solve the influence of actuator faults for system stability. Finally, the stability of stochastic nonlinear interconnected system can be ensured by stochastic Lyapunov stability theory. In addition, numerical and practical simulations also illustrate the effectiveness of the proposed control strategy.

Decentralized adaptive fault-tolerant control of interconnected systems with sensor faults

The paper considers a class of interconnected nonlinear systems with unknown sensor faults and uncertain interactions. Each subsystem is subject not only to the local sensor faults but also to the possible effects of faults from other subsystems through uncertain interactions. Both multiplicative and time-varying additive sensor faults are taken into consideration, which are allowed to be unknown. A decentralized adaptive fault-tolerant control (FTC) scheme has been established. To eliminate the effects of faults in the control loop, several auxiliary quantities are constructed wisely and estimated by the designed adaptive mechanism. A smooth function is proposed, by which the uncertain interactions can be compensated even if they are coupled with sensor faults. It is proved that, by using only the corrupted states, all the closed-loop signals are globally uniformly bounded, and the output tracking error converges into an adjustable residual set. Finally, simulation and comparison studies are presented to illustrate the effectiveness of the proposed scheme.

Quantized-state-based decentralized neural network control of a class of uncertain interconnected nonlinear systems with input and interaction time delays

This paper presents a quantized-state-based decentralized control strategy for uncertain interconnected nonlinear systems with time-varying delays under a networked control environment. Full state variables quantized via a uniform-hysteretic quantizer are available only for a decentralized adaptive control design. Unlike the existing decentralized adaptive recursive control designs, this study is focused on establishing a quantized-state-based decentralized learning mechanism for neural networks using discontinuously quantized states. Moreover, the stability of a decentralized neural network tracking system in the presence of time delays is analyzed. For each subsystem, a neural-network-based local adaptive tracker using a delay compensator is designed based on the local quantized state feedback. Technical lemmas pertaining to quantization errors and adaptive laws are presented to ensure the boundedness of all closed-loop signals and the convergence of local tracking errors to an adjustable neighborhood of the origin. Finally, illustrative simulations clarify and verify the decentralization strategy of the developed state-quantized adaptive tracking system. The control performance is evaluated using the root mean square control errors, where the values are 0.0293 and 0.0134 for each subsystem in Example 1 and 0.0467 and 0.0384 for each subsystem in Example 2.

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.

Fast fault detection for nonlinear interconnected systems via deterministic learning

In this paper, a fast fault detection scheme is developed for a class of nonlinear interconnected systems with output measurements. First, through combining an adaptive high gain observer with the deterministic learning theory, the system states and unknown dynamics are estimated simultaneously. However, large value of gain may let the estimator becomes noise sensitive. Thus, the observer structure is modified to avoid this issue. Second, by reusing the estimated knowledge which is stored in the constant radial basis function (RBF) neural networks, a bank of dynamic estimators are constructed. Then, the average [Formula: see text] norms of residuals are generated. The smallest residual principle is considered for decision-making in the detection phase. Third, the fault detection conditions and detection time are analyzed under the influence of observer gain. A simulation example is utilized to illustrate the effectiveness of this scheme.

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.

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.