Interconnected Nonlinear Systems Research Articles

Distributed optimization for uncertain nonlinear interconnected multi-agent systems

Distributed optimization for uncertain nonlinear interconnected multi-agent systems is considered in this paper. The objective is to design distributed algorithms by using local information such that all the agents’ outputs converge to the global optimal output. The problem is challenging due to unknown modeling uncertainties and nonlinear interconnections. First, a distributed algorithm composed of a distributed state observer and a distributed optimal output observer is presented for heterogeneous outputs. Next, it is shown that the objective can be achieved by employing solely a distributed optimal output observer if the agents’ outputs are homogeneous. Finally, the algorithms’ effectiveness is validated by an electrical power system composed of four-machine subsystems.

Event-Based Distributed Fuzzy Load Frequency Control for Multiarea Nonlinear Power Systems With Switching Topology

This article investigates the event-based distributed fuzzy load frequency control approach for nonlinear interconnected power systems under a switching topology. Specifically, nonlinear factors and uncertain parameters existing in turbine and governor dynamics are modeled and analyzed under the interval type-2 fuzzy method. New memory-based adaptive event-triggered mechanisms, whose directions and threshold parameters are dynamically updated based on the output change trend and relative output error of multiple memories, are proposed to further save network energy. Aiming at communication topology changes in multiarea power systems, a novel switched control system is established by introducing a time-varying communication matrix. Then, the system’s asymptotic stability is ensured by the piecewise Lyapunov–Krasovskii method. Furthermore, to further relax stability conditions, slack matrices are considered with the boundary information of membership functions. Finally, three-area power systems are shown to demonstrate the effectiveness of proposed distributed load frequency control strategies.

Command filter-based adaptive fuzzy decentralized control for stochastic nonlinear large-scale systems with saturation constraints and unknown disturbance

In this article, the problem of decentralized fuzzy adaptive control is addressed for a class of stochastic interconnected nonlinear large-scale systems including saturation and unknown disturbance. Fuzzy logic systems (FLSs) are used to estimate packaged nonlinear uncertainties. The command filter technique is presented to eliminate the “explosion of complexity” obstacle associated with the backstepping procedures and the corresponding error compensation mechanism is constructed to alleviate the effect of the errors generated by command filters. The influence of input saturation is compensated by introducing an auxiliary system. Meanwhile, an improved adaptive fuzzy decentralized controller is developed and it is able to minimize calculation time since there is no need for repeated differentiation for the virtual control laws. The presented control scheme not only assures the semi-global boundedness of all the signals in the closed-loop system, but also makes the output tracking errors reach a small neighborhood around the origin. Finally, both numerical and practical examples are provided to illustrate the efficiency and effectiveness of our theoretic result.

Decentralised output tracking of interconnected systems with unknown interconnections using sliding mode control

In this paper, a class of nonlinear interconnected systems with matched and unmatched uncertainties is considered. The isolated subsystem dynamics are described by linear systems with nonlinear components. The matched uncertainties and unmatched unknown interconnection terms are assumed to be bounded by known nonlinear functions. Based on sliding mode techniques, a state feedback decentralised control scheme is proposed such that the outputs of the controlled interconnected system track given desired signals uniformly ultimately. The desired reference signals are allowed to be time-varying. Using appropriate transformations, the considered system is transformed into a new interconnected system with an appropriate structure to facilitate the sliding surface design and the decentralised control design. A set of conditions is proposed to guarantee that the designed controller drives the tracking errors onto the sliding surface. The sliding motion exhibited by the error dynamics is uniformly ultimately bounded. The developed results are applied to a river quality control problem. Simulation results show that the proposed decentralised control strategy is effective and feasible.

Diagonal Stability of Systems With Rank-1 Interconnections and Application to Automatic Generation Control in Power Systems

We study a class of matrices with a rank-1 interconnection structure, and derive a simple necessary and sufficient condition for diagonal stability. The underlying Lyapunov function is used to provide sufficient conditions for diagonal stability of approximately rank-1 interconnections. The main result is then leveraged as a key step in a larger stability analysis problem arising in power systems control. Specifically, we provide the first theoretical stability analysis of automatic generation control (AGC) in an interconnected nonlinear power system. Our analysis is based on singular perturbation theory, and provides theoretical justification for the conventional wisdom that AGC stabilizes under the typical time-scales of operation. We illustrate how our main analysis results can be leveraged to provide further insight into the tuning and dynamic performance of AGC.

Practical prescribed time control based on high-order fully actuated system approach for strong interconnected nonlinear systems

Practical prescribed time control based on high-order fully actuated system approach for strong interconnected nonlinear systems

Robust NN-based decentralized optimal tracking control for interconnected nonlinear systems via adaptive dynamic programming

Robust NN-based decentralized optimal tracking control for interconnected nonlinear systems via adaptive dynamic programming

Decentralized adaptive neural asymptotic control of switched nonlinear interconnected systems with predefined tracking performance

This article aims at the problem of decentralized adaptive neural asymptotic tracking for switched nonlinear interconnected systems with unknown strong interconnections and predefined transient performance. Technically, unknown strong interconnection terms are handled by intrinsic properties of the basis function vector. In addition, unlike prescribed performance bound control, a new error-dependent transformation with a time-varying function is proposed, which completely circumvents the initial condition-dependence problem. With such transformation and a class of integral bounded-based tuning functions, a decentralized adaptive neural asymptotic control strategy is established so that closed-loop stability can be preserved, and the output tracking error not only asymptotically converges to zero but also evolves within the prescribed boundary. Finally, illustrative examples validate the obtained results.

Adaptive-Critic Design for Decentralized Event-Triggered Control of Constrained Nonlinear Interconnected Systems Within an Identifier-Critic Framework.

This article studies the decentralized event-triggered control problem for a class of constrained nonlinear interconnected systems. By assigning a specific cost function for each constrained auxiliary subsystem, the original control problem is equivalently transformed into finding a series of optimal control policies updating in an aperiodic manner, and these optimal event-triggered control laws together constitute the desired decentralized controller. It is strictly proven that the system under consideration is stable in the sense of uniformly ultimate boundedness provided by the solutions of event-triggered Hamilton-Jacobi-Bellman equations. Different from the traditional adaptive critic design methods, we present an identifier-critic network architecture to relax the restrictions posed on the system dynamics, and the actor network commonly used to approximate the optimal control law is circumvented. The weights in the critic network are tuned on the basis of the gradient descent approach as well as the historical data, such that the persistence of excitation condition is no longer needed. The validity of our control scheme is demonstrated through a simulation example.

Decentralized sampled-data [formula omitted] fuzzy filtering with exponential time-varying gains for nonlinear interconnected systems

This study proposes a technique to design a decentralized sampled-data H∞ fuzzy filter for nonlinear interconnected systems. Unlike previous studies, a novel sampled-data fuzzy filter design includes exponential time-varying gains, which leads to enlargement of the sampling period and improvement in the decay rate performance of the filter. The filter design technique includes both measurable and immeasurable premise variable cases. In the latter case, the H∞ performance criterion is newly defined to minimize the effect of immeasurability on filtering performance. This study also focuses on deriving less conservative design conditions of the filter. First, a novel two-sided looped Lyapunov–Krasovskii functional (LKF) is constructed to make full use of the actual sampling pattern. Then, by utilizing an extended reciprocally convex matrix inequality along with Writinger-based integral inequality, less conservative design conditions are derived as linear matrix inequalities (LMIs)-based optimal problem. Finally, the effectiveness and superior performance of the proposed filtering design techniques are demonstrated through two simulation examples.

Frequency Regulation of Nonlinear Power Systems using Neural Network Observer-Based Optimized Resilient Controller

This study introduces a resilient frequency controller for nonlinear interconnected power systems to counteract endogenous/exogenous system disturbances. A neural network-based observer (NNO) is intended to estimate lumped system disturbances, such as unmodelled dynamics and unknown disturbances. The estimated NNO’s output is incorporated with a second-order sliding mode controller (SOSMC) to minimize chattering in the control effort and improve the nominal performance of the undertaken plant. The design parameters of SOSMC have been optimally identified by applying Harris hawk optimization (HHO), exercising integral error-based objective function. HHO has demonstrated superior tuning capabilities than other well-known optimization methodologies in terms of convergence rate and transient measurements of system outputs. The asymptotic convergence of estimated error and overall stability of the system has been established employing the Lyapunov argument. System outputs are compared with the results reported in the literature to validate the efficacy of the proposed resilient frequency controller. Presented results showcase the mastery of the applied NNO-based SOSMC over its counterparts in weaker chattering, fast disturbance rejection, and a high degree of robustness against endogenous/exogenous disturbances.

Fixed Time Event-triggered Tracking Control for Interconnected Nonlinear Uncertain Systems: An Observer-based Approach

Fixed Time Event-triggered Tracking Control for Interconnected Nonlinear Uncertain Systems: An Observer-based Approach

Distributed control reconfiguration of nonlinear interconnected systems in the presence of actuator faults

AbstractThis article proposes a new method of distributed fault‐tolerant control for a class of nonlinear interconnected systems with actuator faults. This method is based on fault‐hiding idea as a reconfiguration control scheme and tries to redesign the control signal according to the dynamics of the faulty subsystem. Based on fault‐hiding principle, after diagnosing actuator faults, control signals are modified by a predesigned dynamic block which is implemented in the closed‐loop control structure with the same nominal controller. Subsystems are considered as nonlinear Lipschitz systems which interact with each other through nonlinear interconnection dynamics. Because of interactions, occurring a fault in one subsystem causes instability in the overall large‐scale system. A distributed control scheme based on solving a new linear matrix inequality is presented to obtain the control inputs so that it can recover stability and performance of the overall system. Simulation results illustrate and verify the effectiveness of the proposed control approach.

Finite-Time Distributed Identification for Nonlinear Interconnected Systems

In this paper, a novel finite-time distributed identification method is introduced for nonlinear interconnected systems. A distributed concurrent learning-based discontinuous gradient descent update law is presented to learn uncertain interconnected subsystems' dynamics. The concurrent learning approach continually minimizes the identification error for a batch of previously recorded data collected from each subsystem as well as its neighboring subsystems. The state information of neighboring interconnected subsystems is acquired through direct communication. The overall update laws for all subsystems form coupled continuous-time gradient flow dynamics for which finite-time Lyapunov stability analysis is performed. As a byproduct of this Lyapunov analysis, easy-to-check rank conditions on data stored in the distributed memories of subsystems are obtained, under which finite-time stability of the distributed identifier is guaranteed. These rank conditions replace the restrictive persistence of excitation (PE) conditions which are hard and even impossible to achieve and verify for interconnected subsystems. Finally, simulation results verify the effectiveness of the presented distributed method in comparison with the other methods.

Adaptive Critics for Decentralized Stabilization of Constrained-Input Nonlinear Interconnected Systems

This article considers the decentralized stabilization problem of continuous-time nonlinear systems subject to unmatched interconnections and asymmetric input constraints. Initially, with the nonquadratic value functions being introduced to constrained auxiliary subsystems, the decentralized stabilization problem is converted into an array of nonlinear optimal control problems. It is proved that all solutions of these nonlinear optimal control problems together assure asymptotic stability of the entire system. Then, in the framework of adaptive critics, the critic-only architecture is built to solve the Hamilton–Jacobi–Bellman equations associated with these solutions. The critic-only architecture is implemented via critic neural networks (NNs) with their weight vectors being tuned through an improved gradient descent method. A remarkable feature of the present gradient descent approach is that it simultaneously utilizes previously stored and instantaneous state data, which makes the persistence of excitation conditions relaxed. After that, with Lyapunov’s techniques being employed, asymptotic stability of the closed-loop auxiliary subsystems and uniform ultimate boundedness of the critic NNs’ weight estimation errors are demonstrated. Finally, simulations of an unmatched interconnected nonlinear plant are provided to validate the present decentralized control method.

NN‐based decentralized adaptive event‐triggered control for nonlinear interconnected systems under intermittent DoS and injection attacks

SummaryThis article investigates the problem of decentralized adaptive neural network event‐triggered control of strict feedback nonlinear interconnected systems suffering injection attacks and intermittent denial‐of‐service (DoS) attacks. When DoS attacks occur, the sensor‐controller communication channel is jammed. This may result in system states and traditional backstepping methods are unavailable. A novel switching‐type state observer is constructed to overcome the aforementioned challenges. When the injection attacks occur, the input signals of the controller‐actuator communication channel are changed. A decentralized adaptive event‐triggered controller is designed by using the backstepping method, where a first‐order sliding mode differentiator is introduced to avoid “computational explosion.” The observer gain is derived via the linear matrix inequality technique simultaneously. By using an improved average dwell time method and Lyapunov function theory, all closed‐loop signals are bounded. Finally, a numerical example is used to verify the effectiveness of the proposed control scheme.

Active event-driven reliable defense control for interconnected nonlinear systems under actuator faults and denial-of-service attacks

Active event-driven reliable defense control for interconnected nonlinear systems under actuator faults and denial-of-service attacks

Decentralized Fuzzy Fixed-Time Fault-Tolerant Tracking Control of Nonlinear Interconnected Systems with Dual Performance

Decentralized Fuzzy Fixed-Time Fault-Tolerant Tracking Control of Nonlinear Interconnected Systems with Dual Performance

An Overview on Modelling of Complex Interconnected Nonlinear Systems

This paper proposes new mathematical models of representation, which can describe the dynamic behavior of large-scale nonlinear systems, such as an extended mathematical model of Volterra series, interconnected Hammerstein structures, and interconnected Wiener structures. In this research, we focus on the class of large-scale nonlinear systems, which are composed of several interconnected nonlinear subsystems. In this context, a discrete nonlinear mathematical model with unknown time-varying parameters, mono-variable, characterizes each interconnected subsystem operating in a deterministic or stochastic environment. An illustrative numerical simulation example of two interconnected nonlinear processes is provided to prove the validity and the performance of the developed theoretical results.

Decentralized robust control for T-S fuzzy bi-linear interconnected system

This paper presents decentralized fuzzy robust control for a class of nonlinear interconnected large-scale systems which is composed of a number of Takagi-Sugeno (T-S) fuzzy bilinear subsystems with interconnections. Based on the Lyapunov stability analysis theory and the parallel distribute compensation scheme, some robust stabilization sufficient conditions are derived for the whole close-loop fuzzy interconnected systems. The corresponding decentralized fuzzy controller design is converted into a convex optimization problem with linear matrix inequality (LMI) constraints.