Interconnected Nonlinear Systems Research Articles

Finite-time boundedness and finite-time stabilization boundedness for nonlinear interconnected systems with Atangana–Baleanu–Caputo fractional derivative

In this paper, we consider the finite-time boundedness (FTB) and finite-time stabilization boundedness (FTSB) problems for a class of nonlinear interconnected systems with Atangana–Baleanu–Caputo (ABC) fractional derivative. By employing the FTB theory and some properties of ABC fractional derivative, and some basic mathematical transformations, we derive new conditions for the FTB and FTSB problems of ABC fractional-order nonlinear interconnected systems. These conditions are formed in linear matrix inequalities (LMIs), which can be effectively solved using the MATLAB LMI Control Toolbox. Finally, two numerical examples with simulations are provided to illustrate the efficiency of the proposed method.

Decentralized Event-Triggered Adaptive Control for Interconnected Nonlinear Systems With Actuator Failures

In this article, the problem of decentralized event-triggered fault-tolerant control (FTC) for a class of interconnected nonlinear systems with unknown strong coupling and actuator failures is considered. In order to enable each subsystem output to track the desired trajectory, a new decentralized adaptive control scheme is given. First, an event-triggering mechanism is introduced to reduce the signal transmission frequency between the controller and the actuator. Second, a fuzzy high-gain observer is designed for each subsystem to estimate unknown nonlinear functions and actuator efficiency factor. Third, a decentralized FTC strategy is proposed to compensate for the effects of actuator failures and achieve the desirable system tracking performance. With the aid of graph theory, it is shown that all the closed-loop signals are semiglobally uniformly ultimately bounded, and the tracking error of each subsystem can converge to an arbitrarily small residual set by adjusting a design parameter. The effectiveness of the proposed scheme is demonstrated by a practical interconnected system.

Decentralized sliding mode control for a class of nonlinear interconnected systems with unstable internal dynamic

Decentralized sliding mode control for a class of nonlinear interconnected systems with unstable internal dynamic

Adaptive decentralized stabilization of infinite networks of interconnected nonlinear systems with uncontrollable linearization

We solve the problem of decentralized adaptive stabilization for infinite networks of interconnected nonlinear systems in lower-triangular form with power integrators with uncontrollable linearization and with uncertainties in the last equation in which the control input appears. The feedback law is adaptive and continuous but not necessarily smooth, and the decentralized adaptive backstepping algorithm is based on small gain approach and on suitable gain assignment for each node of the infinite network.

Incremental-Dissipativity-Based Synchronization of Interconnected Systems with MIMO Nonlinear Operators

This paper considers a type of dynamical networks with incrementally dissipative multiple inputs and multiple outputs nonlinear operators that are interconnected both internal and external interconnections. A novel quadratic form of incremental dissipativity is used to investigate synchronization of such a network from an input-output approach point of view. It is shown that the synchronization problem is equivalent to a relative stability issue of a large-scale interconnected nonlinear system with dissipative subsystems. Therefore, traditional dissipativity theory is used for the synchronization analysis.

A Network Gain Theorem for Interconnected Systems

This paper provides general network gain conditions for the input-to-state (ISS) stability of an interconnected nonlinear system. The result generalizes the well-known small-gain theorem for a single-loop system to networked systems under very general assumptions on individual sub-systems. The work also generalizes the previously known matrix small-gain theorem and cyclic small-gain theorem for networked systems.

Reinforcement learning-based decentralized fault tolerant control for constrained interconnected nonlinear systems

This paper addresses the decentralized fault tolerant control problem for interconnected nonlinear systems under a reinforcement learning strategy. The system under consideration includes unknown actuator faults and asymmetric input constraints. By constructing an improved cost function related to the estimation of the actuator faults for each auxiliary subsystem, the original control issue is converted into finding an array of decentralized optimal control policies. Then, we prove that these optimal control policies can ensure the entire system to be stable in the sense of uniform ultimate boundedness. Moreover, a single critic network architecture is developed to acquire the solutions of Hamilton–Jacobi–Bellman equations, which simplifies the architecture of the reinforcement learning algorithm. All signals in the closed-loop auxiliary subsystems are uniformly ultimately bounded based on the Lyapunov theory, and numerical and practical simulation examples are conducted to validate the effectiveness of the designed method.

Distributed SDRE control design for a class of nonlinear interconnected dynamic systems

Distributed SDRE control design for a class of nonlinear interconnected dynamic systems

Finite‐time adaptive fault‐tolerant control for output‐constrained interconnected systems with unknown control coefficients

AbstractThis article studies the adaptive finite‐time tracking control problem for a class of output‐constrained nonlinear interconnected systems with unknown actuator faults and parametric uncertainties. By integrating the lower bounds of unknown virtual control coefficients into the Lyapunov functions design, an adaptive control strategy is proposed on the basis of adaptive estimations and some smooth functions, which make the controller effectively compensate the effects of unknown virtual control coefficients, unknown interconnected terms, and other uncertain nonlinear functions. Besides, the controller can also compensate the effect of actuator faults by fusing a two‐step design method into the backstepping design framework. Simultaneously, in view of the output constraint requirements, a barrier Lyapunov function is introduced, and it is a more general one that can reckon with time‐varying asymmetric output constraints. Furthermore, in light of the finite‐time stability criterion, all the signals of system are bounded and the tracking performance can be guaranteed in a finite time. Finally, the effectiveness of the proposed method is validated by some simulation results.

A Cyclic-Small-Gain-Based Adaptive Fuzzy Control of Interconnected Systems

This article investigates a novel adaptive fuzzy decentralized output-feedback control method for a class of uncertain large-scale interconnected nonlinear systems with unknown dynamics and immeasurable states. By employing fuzzy logic systems, the unknown nonlinear dynamics are estimated. Moreover, the immeasurable states are approximated by constructing a fuzzy decentralized state observer. Based on the Lyapunov stability theory and decentralized backstepping technique, the Lyapunov functions are constructed in a recursive way for each subsystem. In the last step of our process, an overall Lyapunov function is proposed to realize the control objective. Differing from other works, the interconnection influence of the large-scale system is compensated with a more relaxed assumption by introducing the cyclic-small-gain condition. Under the proposed control method, the closed-loop system is capable of being semiglobally uniformly ultimately bounded. Furthermore, the observer and stabilizing errors are able to be bounded by an arbitrarily small residual set around the origin. Finally, a simulation with comparison is provided to illustrate the viability of the presented control scheme.

Decentralized Adaptive Funnel Control of Uncertain Large-Scale Interconnected Nonlinear System

In this paper, a decentralized adaptive funnel control for a class of uncertain large-scale nonlinear systems is studied. By using a new funnel control method with a barrier Lyapunov function, a new adaptive decentralized funnel controller is recursively constructed to achieve output tracking of given transient behavior. To solve the interconnection terms issues in controller design, an auxiliary nonlinear function is introduced. Meanwhile, dynamic surface control is applied to the backstepping design in order to avoid the “explosion of complexity” problems in backstepping procedure. It is demonstrated that the proposed control scheme proves that all signals of the closed-loop system are bounded and that the tracking error always evolves in the funnel. Finally, the effectiveness of the scheme is verified by a numerical example and a third-order power network system model.

Event-triggered adaptive dynamic programming for decentralized tracking control of input constrained unknown nonlinear interconnected systems

This paper addresses decentralized tracking control (DTC) problems for input constrained unknown nonlinear interconnected systems via event-triggered adaptive dynamic programming. To reconstruct the system dynamics, a neural-network-based local observer is established by using local input–output data and the desired trajectories of all other subsystems. By employing a nonquadratic value function, the DTC problem of the input constrained nonlinear interconnected system is transformed into an optimal control problem. By using the observer-critic architecture, the DTC policy is obtained by solving the local Hamilton–Jacobi–Bellman equation through the local critic neural network, whose weights are tuned by the experience replay technique to relax the persistence of excitation condition. Under the event-triggering mechanism, the DTC policy is updated at the event-triggering instants only. Then, the computational resource and the communication bandwidth are saved. The stability of the closed-loop system is guaranteed by implementing event-triggered DTC policy via Lyapunov’s direct method. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed scheme.

Event-based decentralized adaptive finite-time tracking control of interconnected nonlinear time-varying systems

Event-based decentralized adaptive finite-time tracking control of interconnected nonlinear time-varying systems

System structure based decentralized sliding mode output tracking control for nonlinear interconnected systems

AbstractIn this article, a decentralized tracking control scheme is proposed for a class of nonlinear interconnected systems with uncertainties using sliding mode technique. Both matched nonlinear uncertainty and mismatched known nonlinear interconnections are considered. Under the condition that the nominal isolated subsystems have relative degrees, a geometric transformation is applied to transfer the interconnected system into a new nonlinear interconnected system with a special structure to facilitate the system analysis and design. Then, a composite sliding surface is designed in terms of tracking errors, and decentralized controllers are proposed to drive the system states to the designed sliding surface in finite time and maintain a sliding motion on it thereafter. A set of conditions are developed to guarantee that the output tracking errors converge to zero asymptotically while all system state variables are bounded. The considered interconnected systems are nonlinear and it is not required that either the isolated subsystems or the isolated nominal subsystems are linearizable. The desired output signals are allowed to be time‐varying. Finally, the developed results are applied to an inverted coupled‐pendulum system. Simulation demonstrates that the proposed control scheme is effective.

Small-Gain Approach to Fuzzy Adaptive Control for Interconnected Systems With Unmodeled Dynamics

This article presents a new stabilizing control scheme for a class of interconnected nonlinear systems subjected to unmodeled dynamics and immeasurable states. Fuzzy logic systems are applied to approximate the unknown functions, and a fuzzy-based state observer is constructed. The interconnection of the overall system is completely compensated via the cyclic-small-gain condition theorem, and the small-gain theorem is introduced to overcome the unmodeled dynamics in each subsystem. Furthermore, assumptions from prior literature are relaxed, and computing burden is reduced through the design of less adaptive laws. This article proves that under the designed control scheme, the closed-loop systems are controlled to be input-to-state practically stable and that all signals are guaranteed to be semiglobally uniformly ultimately bounded. Finally, this article’s simulation section illustrates the effectiveness of the proposed approach through an example derived from a practical system model.

Event-Based Finite-Time Control for High-Order Interconnected Nonlinear Systems With Asymmetric Output Constraints

This article aims to solve the problem of decentralized event-based finite-time control for a class of high-order interconnected nonlinear systems with an asymmetric output constraint. In order to achieve finite-time stability and reduce the update frequency of the controller, a novel controller and its event-trigger mechanism is proposed by adding a power integral technique and utilizing sign function. To fulfill the requirement of asymmetric output constraints, an asymmetric barrier Lyapunov function (BLF) is constructed, which is different from tan-type and log-type BLFs. Based on the contradictory idea and finite-time stability theory, it is proved that there is no Zeno phenomenon under this event-trigger mechanism and all state variables of the closed-loop system attenuate to the origin in the finite-time while the output signals never violate the constraint. Furthermore, the result in this article is expanded to fixed-time control. Finally, a simulation example is given to demonstrate the effectiveness of the presented strategy.

Decentralized Neurocontroller Design With Critic Learning for Nonlinear-Interconnected Systems.

We consider the decentralized control problem of a class of continuous-time nonlinear systems with mismatched interconnections. Initially, with the discounted cost functions being introduced to auxiliary subsystems, we have the decentralized control problem converted into a set of optimal control problems. To derive solutions to these optimal control problems, we first present the related Hamilton-Jacobi-Bellman equations (HJBEs). Then, we develop a novel critic learning method to solve these HJBEs. To implement the newly developed critic learning approach, we only use critic neural networks (NNs) and tune their weight vectors via the combination of a modified gradient descent method and concurrent learning. By using the present critic learning method, we not only remove the restriction of initial admissible control but also relax the persistence-of-excitation condition. After that, we employ Lyapunov's direct method to demonstrate that the critic NNs' weight estimation error and the states of closed-loop auxiliary systems are stable in the sense of uniform ultimate boundedness. Finally, we separately provide a nonlinear-interconnected plant and an unstable interconnected power system to validate the present critic learning approach.

Decentralized event-triggered adaptive neural network control for nonstrict-feedback nonlinear interconnected systems with external disturbances against intermittent DoS attacks

This paper discusses the issue of decentralized event-triggered adaptive neural network (NN) control for nonstrict-feedback nonlinear interconnected systems with external disturbances and intermittent denial-of-service (DoS) attacks. In the presence of DoS attack, all state variables are not used to design a feedback controller via the standard backstepping method. To solve this problem, a novel switching-type adaptive state observer with a disturbance compensation is constructed, where the disturbance compensation is obtained via constructing a disturbance observer. A decentralized event-triggered adaptive controller is designed by using the backstepping method to weaken the influences of DoS attack and the waste of communication resources, where a first-order sliding mode differentiator is introduced to prevent the “calculation explosion”. By using linear matrix inequality techniques, some solvable sufficient conditions are attained to derive the observer gain. The closed-loop system is proved to be stable via the improved average dell time method and the piecewise Lyapunov stability theories. This control scheme ensures that all closed-loop signals remain bounded. Finally, simulation results are utilized to demonstrate the effectiveness of the proposed method.

Decentralized adaptive neural fixed‐time tracking control of constrained interconnected nonlinear systems with partially unmeasurable states

AbstractThis article devises a new adaptive fixed‐time tracking control strategy for interconnected nonlinear systems containing partially unmeasurable states and time‐varying output constraints. Radial basis function neural networks, as function approximators, are utilized to model the unknown functions, and the partially unmeasurable states of the systems are estimated by a reduced‐order observer. By constructing a transferred function, system outputs are directly constrained in a time‐varying constraint bound. Meanwhile, the first‐order sliding mode differentiators are utilized to reduce the computational burden caused by the repeated differentiations of virtual controllers. Under the Lyapunov function and the fixed‐time theory, the decentralized adaptive fixed‐time controllers are constructed. It is proved that the closed‐loop systems are fixed‐time stable and the output signals are restricted in the bounded compact set. Finally, two simulation examples demonstrate the validity of the proposed control scheme.

Event-triggered control of interconnected nonlinear systems subjected to cyber-attacks and time-varying coupling

This paper addresses the problem of efficient control of nonlinear distributed networked control systems in the presence of stochastic deception attacks and time-varying coupling strength. A strategy combining model-based and event-triggered control to reduce the number of transmissions over a network thereby, saving network resources is proposed. In this strategy, a plant model at the controller end is used to estimate the state of each subsystem. Further, the control law between the two adjacent triggering instants changes in accordance with dynamics of the plant model. The nonlinearities present in each subsystem are approximated via neural network. The neural network weights and feedback signal are updated only when the event-triggering condition at the sensor end is violated. Also, a lower bound on the inter-event time is computed to avoid the occurrence of Zeno phenomena. Finally, the efficacy of the proposed methodology are verified through simulation examples.