Interconnected Nonlinear Systems Research Articles

Neural-network-based adaptive secure control for nonstrict-feedback nonlinear interconnected systems under DoS attacks

This paper investigates the problems of decentralized adaptive neural network (NN) secure control for a class of nonstrict-feedback nonlinear interconnected large-scale systems (NILSs) under denial-of-service (DoS) attacks. The considered systems contain not only unknown interconnected terms but also general nonlinear functions that are not required to be globally Lipschitz, in contrast to most of the existing results in the area. When the system subject to the DoS attack, the sampled data can neither be sent by the sensors nor received by the actuators due to the appearance of DoS in the sensor-to-controller (S-C) and the controller-to-actuator (C-A) communication channels. The data packets sent from the sensors are blocked and the traditional backstepping technology cannot be adopted. In order to solve this difficulty, a novel dynamic gain observer is constructed, which can obtain the desired states from the NILSs under DoS attacks. Considering the energy limitation of attackers, two reasonable Assumptions of DoS attack intensity are given. The stability is proven based on the Lyapunov stability theory (LST) and the improved average dwell time (ADT) method. The proposed controller guarantees that all signals in closed-loop systems are bounded, while the tracking error signals converge to a small residual set. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed control method.

On Topological Entropy of Interconnected Nonlinear Systems

We study topological entropy of a nonlinear system represented as an interconnection of smaller subsystems. Under suitable assumptions on the Jacobian matrices characterizing the interconnection, we obtain an explicit upper bound on the entropy of the overall system, and show that it can be related to upper bounds on the entropies of the subsystems. We also analyze in detail the special case of a cascade connection of two subsystems, establishing an upper bound on the entropy which is more tightly linked to individual entropy bounds for the subsystems.

Decentralized Fault Detection and Fault-Tolerant Control for Nonlinear Interconnected Systems

The nonlinear interconnected system is a complex and important system in daily production and life in general. Due to the interconnection influence between subsystems and external disturbance factors, the system is prone to failure. For this kind of system, a decentralized fault detection and fault tolerant control method is proposed here. Compared with the traditional control scheme, this paper designs a subsystem communication protocol to reduce the information exchange between subsystems. Based on this communication protocol, a fault detection scheme is then designed. Due to the existence of a fault detection threshold in this scheme, the system can detect the fault in time without missing it or having a false alarm. Under the assumed condition, the adaptive control rate is obtained by establishing the adaptive approximation model to approximate the upper bound of the fault, and the subsystem adaptively adjusts the control rate according to the fault condition, so that the system can quickly recover to stability. Finally, a simulation program is used to verify the proposed method.

Estimate of the domain of attraction for interconnected systems

In this paper, we estimate the domain of attraction of the origin of two interconnected nonlinear systems. For each subsystem we introduce an auxiliary system and assume that the origin is locally robustly asymptotically stable. Then an integral input-to state stable Lyapunov function for each subsystem on a bounded set is constructed via Zubov’s method and the introduced auxiliary system. A local version of small gain theorem is proposed. It is easier to check if the conditions of the proposed small gain theorem are satisfied. Moreover, an estimate for the domain of attraction for the whole system is obtained based on the proposed small gain theorem and the computed integral input-to state stable Lyapunov functions. We illustrate the effectiveness of the main results by an academic example.

Adaptive decentralized finite‐time tracking control for uncertain interconnected nonlinear systems with input quantization

AbstractCompared with the previous references, very few results are available to study control scheme directly for interconnected nonlinear systems (INSs) with strongly interconnected terms described by unknown state‐dependent‐nonlinear functions and input quantization in the finite‐time control literature. In this article, an adaptive decentralized finite‐time tracking control (ADFTTC) algorithm is developed to address the system output tracking problem for a class of INSs with input quantization and strongly interconnected terms. To reduce the computation complexity, the neural network technique is employed to reconstruct the derivative of virtual control laws in each step. By employing adding a power integrator technique, an adaptive decentralized finite‐time tracking controller is constructed, which guarantees all signals in the closed‐loop systems converge to a neighborhood of the origin. Moreover, the developed controller avoids the “singularity” and “explosion of complexity” problems in the recursive design scheme. An example of an inverted pendulum confirms the ADFTTC scheme.

Finite‐horizon optimal tracking control for constrained‐input nonlinear interconnected system using aperiodic distributed nonzero‐sum games

This paper proposes a distributed adaptive dynamic programming scheme to investigate the optimal tracking control problem for finite-horizon non-linear interconnected systems with constraint inputs under aperiodic sampling. A N-player nonzero-sum differential game system is constructed with the presented non-linear interconnected system and the tracking error system by introducing the augment vectors. To address the problems of constrained-input and finite-horizon control, a non-quadratic utility function and a finite-horizon cost function are utilized which will arise in the time-varying Hamilton–Jacobi (HJ) equation. Then, a periodic event-triggered scheme is designed to realize aperiodic sampling, where the consumption of communication resources is reduced and the Zeno behavior is avoided. Under the designed periodic event-triggered scheme, the time-varying HJ equation is almost impossible to get an analytical solution due to its hybrid properties and non-linearity. Therefore, the critic neural networks are used to estimate the optimal solution of the HJ equation, and the weight update law is constructed to guarantee the uniformly ultimate bounded of approximated errors. Further, the hybrid nonzero-sum differential game is confirmed to be uniformly ultimate bounded by using the Lyapunov theory. Finally, the obtained distributed PET control strategy is successfully applied to dispose the missile-target intercepter problem.

Adaptive fuzzy decentralised control for fractional-order interconnected nonlinear systems with input saturation

This paper studies the fuzzy decentralised control issue for the fractional-order interconnected nonlinear systems with input saturation. The fuzzy logic systems (FLSs) and piecewise functions are used to approximate unknown nonlinear continuous functions and the input saturation of the considered systems. Under the frameworks of the backstepping control design technique and adaptive fuzzy decentralised control theory, an adaptive fuzzy decentralised control strategy is proposed. In view of fractional-order Lyapunov stability theory, it confirms the stability of the control plants and the convergence of the tracking errors. Finally, two simulation examples are applied to confirm the practicability and validity of the presented control strategy, in which, one is the two-order numerical fractional-order large-scale systems, the other one is the fractional-order permanent magnet synchronous motor (PMSM) model.

Event-triggered controllers based on the supremum norm of sampling-induced error

The paper proposes a novel event-triggered control scheme for nonlinear systems. Specifically, the closed-loop system is associated with a pair of auxiliary input and output. The auxiliary output is defined as the derivative of the continuous-time input function, while the auxiliary input is defined as the input disturbance caused by the sampling or equivalently the integral of the auxiliary output over the sampling period. As a result, it forms a cyclic mapping from the input to the output via the system dynamics and back from the output to the input via the integral. The event-triggered law is constructed to make the mapping contractive such that the stabilization is achieved and an easy-to-check Zeno-free condition is provided. Within this framework, we develop a theorem for the event-triggered control of interconnected nonlinear systems which is employed to solve the event-triggered control for lower-triangular systems with dynamic uncertainties.

Stability analysis of interconnected complex nonlinear systems using the Lyapunov and Finsler property

This study focuses on the question of the stability analysis of complex interconnected nonlinear systems using the property of Lyapunov and Finsler. The main idea is to minimize the effect of interconnections between the subsystems, for that, we use the Lyapunov function and the H∞ control, then applying Finsler’s lemma to release the conditions of stability, the independent matrices allow to obtain less conservative results. The proposed control approach is formulated in a minimization problem and derived in terms of linear matrix inequalities (LMIs) whose resolution yields the decentralized control gain matrices. All the developed results are tested on two representative examples and compared with some recent previous ones.

Decentralised state-feedback prescribed performance control for a class of interconnected nonlinear full-state time-delay systems with strong interconnection

This paper investigates the problem of the state-feedback control design for a class of interconnected nonlinear full-state time-delay systems with strong interconnection and prescribed performance. Based on the dynamic gain approach and Lyapunov-Krasovskii method, it overcomes the rigorous restriction that the interconnected time-delay functions should satisfy linear growth condition. Compared with the existing results, the main contribution is that the dynamic gain approach is extended to state-feedback control for interconnected time-delay systems, and it is strictly proved that the closed-loop system is globally bounded stable with the proposed decentralised control strategy. The problem of the strong interconnection terms is solved by combining the backstepping approach and graph theory. Furthermore, the expected transient and steady-state performance of the output can be guaranteed by considering prescribed performance control into such strongly interconnected systems. Finally, simulation is performed and the results show the effectiveness of the proposed method.

Distributed model predictive control for nonlinear large-scale systems based on reduced-order cooperative optimisation

In this paper, a novel cooperative constrained distributed model predictive control algorithm is proposed to control the nonlinear interconnected constrained large-scale systems. In this algorithm, a novel reduced-order cooperative optimisation approach is proposed which is its main contribution that reconstructs and improves the global cost function of any local controller. In proposed algorithm, each local controller computes its optimal control by minimising the corresponding global cost function which is a combination of its own and its neighbouring subsystems’ cost functions. The sufficient conditions are derived to guarantee the recursive feasibility and closed-loop stability specifications to ensure the convergence of the overall states into the positive region which is the neighbourhood of origin. The performance of the proposed algorithm is illustrated via simulation results of a nonlinear large-scale cart-spring-damper system.

Decentralized event-triggered adaptive control of a class of uncertain interconnected nonlinear systems using local state feedback corrupted by unknown injection data

This paper investigates a decentralized event-triggered adaptive control problem of uncertain interconnected lower-triangular nonlinear systems using corrupted local state feedback. The unknown injection data such as sensor faults or cyber attacks are assumed to be added to full state feedback measurements of each subsystem with unknown nonlinearities. Under this assumption, exactly measured local state variables are unknown during Lyapunov-stability-based recursive control design steps. The primary contributions of this study are (i) to develop a recursive adaptive control design strategy for achieving decentralization of unmatched interconnected nonlinearities using corrupted local state feedback information and (ii) to design a decentralized asynchronous event-triggering mechanism using the corrupted local state variables. To this end, local injection data compensators using neural networks and adaptive tuning laws are designed to compensate for unknown injection data and nonlinear interaction effects. It is shown that the proposed decentralized control system via the corrupted local state feedback ensures the practical stability of the total closed-loop system and the exclusion of Zeno behavior.

Decentralized Adaptive Neuro-Output Feedback Saturated Control for INS and Its Application to AUV.

This article investigates the problem of the decentralized adaptive output feedback saturated control problem for interconnected nonlinear systems with strong interconnections. A decentralized linear observer is first established to estimate the unknown states. Then, an auxiliary system is constructed to offset the effect of input saturation. With the aid of graph theory and neural network technique, a decentralized adaptive neuro-output feedback saturated controller is designed in a nonrecursive manner. A sufficient criterion is established to achieve the uniform ultimate boundedness (UUB) of the closed-loop system. An application example of autonomous underwater vehicle (AUV) is provided to verify the effectiveness of the developed algorithm.

Cooperative optimization-based distributed model predictive control for constrained nonlinear large-scale systems with stability and feasibility guarantees

This paper proposes a cooperative distributed model predictive control (DMPC) to control the constrained interconnected nonlinear large-scale systems. The main contribution of this approach is its proposed novel cooperative optimization that improves the global cost function of any subsystem. Each subsystem calculates its optimal control by solving the corresponding global cost function. For each subsystem, the global cost function is defined based on a combination of cost functions of all subsystems. If the sampling time is selected appropriately, then the feasibility of the proposed approach will be guaranteed. Furthermore, the sufficient conditions for stability and consequently, for the convergence of the whole system states towards the neighborhood of the origin’s positive region are provided. The effectiveness and performance of the proposed approach are demonstrated via applying it to a nonlinear quadruple-tank system for both minimum-phase and nonminimum-phase models.

Stability analysis of interconnected nonlinear mixed passive and negative-imaginary systems

This paper presents an analytical framework to establish finite gain stability for nonlinear interconnected mixed passive and negative imaginary systems. The stability analysis is presented using the notation of dissipitivity. The proposed stability framework enables us to extend the number of existing results from the linear mixed systems to the wide range of nonlinear mixed systems. Accordingly, the stability analysis of this paper extends the work of Das et al. (in: 2013 Australian control conference. IEEE, pp 445–449, 2013) to nonlinear cases. A numerical example is presented in the paper to test the results of the proposed analytical framework.

Relaxed Stabilization Conditions for Interconnected Nonlinear Systems

This paper deals with the conservatism reduction of stability and stabilization conditions for nonlinear continuous-time interconnected systems. Based on Takagi–Sugeno modeling, the interconnected system is described by a convex combination of interconnected linear systems. Line integral fuzzy Lyapunov functions are considered to develop stability and stabilizability criteria for the considered class of interconnected nonlinear systems. All analysis and design conditions are formulated in LMI terms. The effect of the coupling due to interconnection terms is also investigated and taken into account to obtain less conservative conditions. Examples are given to illustrate the merit of the obtained results.

A near-optimal decentralized control approach for polynomial nonlinear interconnected systems

This article tackles the decentralized near-optimal control problem for the class of nonlinear polynomial interconnected system based on a shifted Legendre polynomials direct approach. The proposed method converts the interconnected optimal control problems into a nonlinear programming one with multiple constraints. In light of the formulated NLP optimization, state and control coefficients are used to design a nonlinear decentralized state feedback controller. Overall closed-loop system stability sufficient conditions are investigated with the help of Grönwall lemma. The triple inverted pendulum case is considered for simulation. Satisfactory results are obtained in both open-loop and closed-loop schemes with comparison to collocation and state-dependent Riccati equation techniques.

Event-triggered distributed self-learning robust tracking control for uncertain nonlinear interconnected systems

In this paper, a novel event-triggered self-learning robust tracking control scheme for a class of nonlinear interconnected systems with uncertain interconnections is developed based on adaptive dynamic programming (ADP). Initially, the robust tracking control problem of interconnected systems is transformed to the robust stabilization one of augmented interconnected systems. To address the uncertain interconnections as well as optimize the sample intervals, a group of auxiliary subsystems, each with a novel discounted cost function, are introduced, which enables the robust stabilization problem to be further converted to a group of two-player zero-sum differential games. Next, an event-triggered ADP algorithm is proposed to obtain the saddle point solutions, based on which the distributed event-triggered robust tracking control policies for the overall system are established. Specifically, the proposed event-triggered mechanism is asynchronous and distributed where the sample intervals are optimized to further reduce the computational burden and save the communication resources. Moreover, the tracking errors and the approximation errors of critic network weights are demonstrated to be uniformly ultimately bounded by using the Lyapunov approach. Finally, two simulation examples are provided to verify the effectiveness of the proposed method.

Adaptive finite‐time fault‐tolerant control for interconnected nonlinear systems

AbstractThis paper addresses the adaptive finite‐time output tracking control problem for nonlinear large‐scale systems whose power‐exponentials are positive odd rational numbers. The considered systems contain actuator loss‐of‐effectiveness and bias fault, which can be addressed by fault‐tolerant control technique. The intelligent approximator is presented to approximate the unknown nonlinear function. Meanwhile, the technique named adding a power integrator is used, which validly overcomes the problem of the system with power‐exponentials. A finite‐time fault‐tolerant controller is proposed based on the finite‐time Lyapunov stability theory and backstepping algorithm. Moreover, the tracking errors can converge to a small neighborhood of the origin in finite time. Finally, a simulation example is given to illustrate the effectiveness of the proposed adaptive finite‐time control strategies.

$$H_{\infty }$$ Optimization-Based Stabilization for Nonlinear Disturbed Time Delay Systems

This paper contemplates designing a $$H_{\infty }$$ dynamic output-feedback decentralized control for nonlinear interconnected disturbed time delay systems. Pursuant to Lyapunov–Krasovskii functional techniques and linear matrix inequality methods, asymptotic stability conditions for the robust stability and stabilization of the studied system are conducted in an optimization problem subject to linear matrix inequalities. The resolution of such a problem enables computing jointly the robust observation and control gain matrices, maximizing the bounds of nonlinear interconnections tolerated by the system without being unstable, improving the performance of the proposed control strategy by minimizing a $$H_{\infty }$$ criterion and ensuring the stability of the closed-loop system despite exogenous disturbances applied to the subsystems. Simulation results are provided by a prominent application example of a 3-interconnected machine power system with time delay to demonstrate the efficacy of the designed delay-independent control approach.