Control Of Nonlinear Systems Research Articles

Variable impulsive bipartite coordination control of nonlinear systems with DoS attacks

Variable impulsive bipartite coordination control of nonlinear systems with DoS attacks

Predictor-based sampled-data output-feedback control for feedforward nonlinear time-delay systems

Predictor-based sampled-data output-feedback control for feedforward nonlinear time-delay systems

Asymptotic tracking control for state-constrained nonlinear systems with disturbances: theory and experiment

Asymptotic tracking control for state-constrained nonlinear systems with disturbances: theory and experiment

Control of Nonlinear Systems with Input Delay

An algorithm for control of nonlinear systems with sector nonlinearity and a constant known time-delay in the control channel is proposed. To design the control law, a predictor of the controlled variable by the time-delay value is used. Unlike the predictor of O. Smith, the predictor under consideration can be applied to unstable systems, and differently from the predictor of A. Manitius and A. Olbrot, the proposed predictor does not contain an integral component, which requires accurate implementation to predict the regulated signal. Next, based on the proposed predictors, subpredictors are built, which are a sequential connection of a series of similar predictors, but with a shorter time-delay. As a result, the use of a subpredictor allows one to control plants with a larger time-delay, which is reflected in the closed-loop system, where the time-delay is as many times less than the original one as the number of predictors used in the prediction scheme of the controlled variable. Using the method of Lyapunov-Krasovsky functionals and the S-procedure, sufficient conditions for the stability of the closed-loop system are obtained in the form of solvability of linear matrix inequalities. The asymptotic convergence to zero of the state vector and the uniformly boundedness of all signals in the closed-loop system are proven. It is shown that the resulting linear matrix inequalities depend on the parameters of the plant, sector boundaries for nonlinearity and time-delay, which makes it possible to calculate their upper values when the closed-loop system remains stable. These problems may be relevant when calculating the upper value of the sector of the nonlinearity under consideration or the upper value of the time-delay during remote control. The results of computer modeling are presented, which illustrate the efficiency of the proposed approaches and demonstrate an increase in the possible time-delay in the system when using a subpredictor scheme. The example shows that when using a serial connection of two subpredictors instead of one, the maximum time-delay in the control channel can be doubled. Moreover, in contrast to the predictor of A. Manitius and A. Olbrot, the subpredictor scheme is simple due to the lack of implementation of the integral component.

Model-free event-triggered resilient control for discrete-time nonlinear systems under sparse actuator attacks via GrHDP

Model-free event-triggered resilient control for discrete-time nonlinear systems under sparse actuator attacks via GrHDP

Fast finite‐time stabilization of stochastic nonlinear systems with output constraints and an application to single‐link robot

AbstractThis article studies the fast finite‐time stabilization problem for stochastic nonlinear systems with asymmetric output constraints. To address the issue of slow convergence encountered in previous finite‐time control designs of stochastic nonlinear constrained systems, this paper extends the fast finite‐time stabilization mechanism to such systems. First, a novel asymmetric barrier Lyapunov function is employed to tackle the output constraint. Then, by adding a power integrator technique and the barrier Lyapunov function, a state‐feedback controller for stochastic nonlinear systems is explicitly designed using the backstepping method. The designed controller achieves fast finite‐time stability in probability of the stochastic nonlinear system while ensuring no violation of the output constraints. Finally, two examples are presented to demonstrate the effectiveness of the controller scheme.

Consensus tracking control of heterogeneous nonlinear multi-agent systems with random switching and uncertain targets

Consensus tracking control of heterogeneous nonlinear multi-agent systems with random switching and uncertain targets

Adaptive RISE-based tracking control of uncertain nonlinear systems: A FAS approach

A fully actuated system (FAS) approach integrated with adaptive robust integral of the sign of the error (ARISE) feedback control strategy is proposed for multi-input multi-output nonlinear systems in the presence of both external disturbances and parametric uncertainties. Owing to an inability to eliminate unmeasured disturbances and model inaccuracies simultaneously, the existing results based on the FAS approaches are typically limited to the uniformly ultimate boundedness of the tracking errors. To achieve the asymptotic tracking performance confronted with parametric uncertainties and time-varying disturbances, an ARISE feedback controller with desired compensation is synthesized to suppress the adverse effects arising from nonlinearity and uncertainty of the system. The improvements compared to the traditional RISE feedback control are attributed to two aspects: (i) the feedback gains in the RISE term are adjustable-online without having to know the prior bounds of disturbances and their time derivatives; (ii) a desired compensation-based adaptive feedforward term, primarily employing the desired trajectories in place of the measured states, could weaken the underlying interaction between the adaptive compensation and robustness part. A rigorous stability analysis is provided to demonstrate that the system state can asymptotically track a bounded desired trajectory in spite of bounded disturbances and parametric uncertainties. Comparative simulations on an under-actuated planar manipulator, possessing an equivalent multi-order FAS model, have been conducted to verify the effectiveness and merits of the developed controller. Experimental validation on a two-wheeled self-balancing robot is also provided to show the feasibility of the proposed approach.

Output Feedback Consensus Control of Nonlinear Multi-agent System Under Communication Faults and Actuator Faults

Output Feedback Consensus Control of Nonlinear Multi-agent System Under Communication Faults and Actuator Faults

Fixed-time prescribed performance control for nonlinear multi-agent systems with novel uncertainties

This paper addresses an approach to fixed-time prescribed performance control design for multi-agent systems with novel uncertainties, i.e., the uncertainties from system input powers, and a new neural backstepping control design is proposed such that the prescribed performance can be guaranteed within a fixed-time. Unlike existing adaptive results, the upper boundary of stability time is decided only by the design parameters and also is independent of the initial states of the system. By leveraging Lyapunov stability theory and graph theory, it is demonstrated that every follower agent can synchronize to the leader agent, and tracking errors converge to the origin’s neighborhood. Finally, the simulation results verify the effectiveness of the control strategy.

Nonlinear Control System for Flat Plate Structures Considering Interference Based on Operator Theory and Optimization Method

In recent years, vibration control utilizing smart materials has garnered considerable attention. In this paper, we aim to achieve vibration suppression of a plate structure with a tail-fin shape by employing piezoelectric actuators—one of the smart materials. The plate structure is rigorously modeled based on the Kirchhoff–Love plate theory, while the piezoelectric actuators are formulated in accordance with the Prandtl–Ishlinskii model. This research proposed a control system that addresses the interference effects arising during vibration control by dividing multiple piezoelectric elements into two groups and implementing MIMO control. The efficacy of the proposed control method was validated through simulations and experiments.

Approximation-based adaptive two-bit-triggered bipartite tracking control for nonlinear networked MASs subject to periodic disturbances

Purpose This paper aims to investigate the problem of adaptive bipartite tracking control in nonlinear networked multi-agent systems (MASs) under the influence of periodic disturbances. It considers both cooperative and competitive relationships among agents within the MASs. Design/methodology/approach In response to the inherent limitations of practical systems regarding transmission resources, this paper introduces a novel approach. It addresses both control signal transmission and triggering conditions, presenting a two-bit-triggered control method aimed at conserving system transmission resources. Additionally, a command filter is incorporated to address the problem of complexity explosion. Furthermore, to model the uncertain nonlinear dynamics affected by time-varying periodic disturbances, this paper combines Fourier series expansion and radial basis function neural networks. Finally, the effectiveness of the proposed methodology is demonstrated through simulation results. Findings Based on neural networks and command filter control method, an adaptive two-bit-triggered bipartite control strategy for nonlinear networked MASs is proposed. Originality/value The proposed control strategy effectively addresses the challenges of limited transmission resources, nonlinear dynamics and periodic disturbances in networked MASs. It guarantees the boundedness of all signals within the closed-loop system while also ensuring effective bipartite tracking performance.

Attack-Dependent Adaptive Event-Triggered Security Fuzzy Control for Nonlinear Networked Cascade Control Systems Under Deception Attacks

This article investigates the issue of H∞ security output feedback control for a nonlinear networked cascade control system with deception attacks. First, to further reduce the amount of communication data, reasonably schedule network resources, and alleviate the impact of multi-channel deception attacks, an attack-dependent adaptive event-triggered mechanism is introduced into the primary network channel, and its adaptive triggered threshold can be adjusted according to the random attack probability. Secondly, the output dynamic quantization of the secondary network channel is considered. Then, a novel security cascade output feedback controller design framework based on the Takagi–Sugeno (T-S) fuzzy networked cascade control system under deception attacks is established. In addition, by introducing the Lyapunov–Krasovskii stability theory, the design conditions of the controller are given. Finally, the effectiveness and superiority of the proposed design strategies are verified by two simulation examples of power plant boiler–turbine system and power plant boiler power generation control system.

Signed-network-based consensus control for nonlinear multi-agent systems: a dynamic encryption–decryption approach

Abstract This paper is concerned with the bipartite secure control issue for a class of discrete-time nonlinear multi-agent systems under a dynamic encryption–decryption approach. First, the coupling relationships between agents are portrayed through a signed graph topology containing the edges of positive and negative connection weights. Next, the information transmissions between agents and their neighbors are executed via a shared communication network. The dynamic encryption–decryption approach is implemented to transform original signals into ciphertexts. Under the assumption that the signed graph is structurally balanced, a signed-network-based bipartite secure controller is designed to achieve the desired state control for the nonlinear multi-agent system and sufficient conditions are obtained for the existence of the desired signed-network-based state controller. Furthermore, a precise definition of the minimum channel capacity is proposed to understand the factors affecting the minimum channel capacity. Finally, the effectiveness of the proposed approach is illustrated by two simulation examples.

NMPC‐Based Control of Underactuated Spacecraft: A Neighboring Extremal Approach Extended to SE(3)

ABSTRACTThe present work revolves around employing the benefits of neighboring extremal approach in the nonlinear model predictive control of mechanical systems evolving on SE(3). In the NMPC process, necessary conditions of optimality are extracted based on some discrete‐time version of the equations of motion referred as LGVI and the obtained TPBVP equations are solved using simplified sensitivity derivatives by means of an indirect shooting method. Taking into consideration that the repetitive optimization process of the NMPC is time consuming, making its implementation challenging, a method of neighboring extremal is proposed here for recalculating the responses of the systems in scenarios that face some unexpected changes in their parameters or are encountering some last‐minute re‐planning schemes. Based on the existing responses of the system to the first set of initial conditions, the reaction of the system to the altered set of initial conditions can be reconstructed without the need to solve the whole optimization process from scratch by utilizing the features of the NE method. A spacecraft model evolving on SE(3) with actuation constraints confirms the efficiency of the whole process in term of accuracy versus computation burden. Forasmuch as actuator failure is a probable yet important event in aerial/spatial missions, the performance of the control system in dealing with such situations is examined. The algorithm robustness and its capability to compensate the effects of the actuator loss is checked.

Fault-tolerant control of nonlinear networked control systems based on a dynamic event-triggered mechanism under dual cyber attacks

In this paper, the fault-tolerant control problem of actuator failures for nonlinear networked control systems under deception attacks and denial-of-service attacks is investigated based on a dynamic event-triggered mechanism. Firstly, denial-of-service attacks and deception attacks are modeled as two independent variables that conform to the Bernoulli probability distribution, and the fault-tolerant control problem of nonlinear networked control systems is considered under the possible actuator failures. Then, an appropriate Lyapunov-Krasovskii functional is constructed, and sufficient conditions for ensuring asymptotic stability of the closed-loop systems are obtained using Jensen inequality. Meanwhile, the designed fault-tolerant controller can handle possible actuator failures. Finally, the effectiveness of the proposed method is proved through an example.

Fuzzy adaptive asynchronous sampled-data consensus control for nonlinear multi-agent systems under DoS attacks

This article investigates the problem of fuzzy adaptive resilient asynchronous sampled-data consensus control (SDCC) for a class of uncertain nonlinear strict-feedback multi-agent systems (MASs) under denial-of-service (DoS) attacks and with a directed graph. Firstly, the upper bounds on the sampling intervals and a distributed sampled-data observer are proposed to estimate the leader's output and its high-order derivatives under DoS attacks. Then, the sufficient conditions to ensure the asymptotic convergence of the designed distributed sampled-data observer are established. Based on the distributed sampled-data observer and backstepping control design technique, a distributed fuzzy adaptive resilient control algorithm is developed. It is proved that the proposed control scheme can guarantee that the controlled MASs are stable, and the consensus errors converge to a small neighbourhood of zero. Finally, a simulation example on heterogeneous vehicular platoons verifies the feasibility of the proposed control scheme.

Existence of a mild solution and approximate controllability for fractional random integro-differential inclusions with non-instantaneous impulses

This paper investigates the existence and approximate controllability (ACA) of fractional neutral-type stochastic differential inclusions (NTSDIs) characterized by non-instantaneous impulses within a separable Hilbert space (HS) framework. Employing the Atangana–Baleanu–Caputo (ABC) derivative, we transform the system into an equivalent fixed-point (FP) problem through an integral operator. Subsequently, the Bohnenblust–Karlin FP theorem is leveraged to establish existence results. By assuming ACA of the corresponding linear system, we derive sufficient conditions for the ACA of the nonlinear stochastic impulsive control system. Our analysis relies on concepts from stochastic analysis, fractional calculus, FP theory, semigroup theory, and the theory of multivalued maps (MVMs). The theoretical findings are illustrated through a concrete example.

Event-Triggered Fuzzy Adaptive Predefined-Time Control for Fractional-Order Nonlinear Systems with Time-Varying Deferred Constraints and Its Application

This paper focuses on the fuzzy adaptive predefined-time control for fractional-order nonlinear systems with time-varying deferred constraints. First, a modified dynamic surface control technique is introduced to address the problem of computational complexity exposed in the backstepping framework, and the interval type-2 fuzzy logic systems are applied to model the unknown nonlinearities of the systems. Next, a shifting function and the barrier Lyapunov function with variational barrier bounds are formulated to deal with the constraints issue. Particularly, the constraint conditions can be satisfied within a predetermined time, even if they are transgressed initially. Furthermore, a switching threshold event-triggered controller is devised to balance the control energy and communication resources. With the help of the predefined-time stability criterion, it is proven that the presented predefined-time event-triggered controller can ensure that all the signals involved in the closed-loop system are bounded and the tracking error fluctuates to a small neighborhood of the origin in a predefined-time interval. Finally, two simulation examples are provided to confirm the effectiveness of the put-forward control algorithm.

Adaptive Event-Triggered Consensus Control of Nonlinear Multi-Agent Systems via Output Feedback Methodology: An Application to Energy Efficient Consensus of AUVs

For dealing with the energy consumption in multi-agent systems (MASs), an event-triggered (ET) methodology is promising, which relies on the activation of communication devices only when communication of data is needed. This paper explores the leaderless consensus for nonlinear MASs using an adaptive ET approach via an output feedback methodology. This adaptive ET scheme is preferred as it can adapt to the environment through setting a communication threshold. The proposed approach renders the observed states of agents by use of nonlinear observers in an output feedback control dilemma, making it more practical. Simple Luenberger observers are developed to avoid the problem of always measuring agents’ states. The strategy of adaptive ET-based control is employed to minimize resource use and information transmission. Design conditions for the observer-based adaptive ET consensus control of nonlinear MASs have been derived via a Lyapunov function, containing state estimation error, consensus error, adaptation term, and nonlinearity bounds. In contrast to the existing methods, the present approach applies a more practical output feedback schema, uses adaptive ET proficiency, and deals with nonlinear agents. An example of a formation of autonomous underwater vehicles achieving the basic consensus realization between displacement and velocity is included to illustrate the viability of the resultant approach.