Control Of Nonlinear Systems Research Articles

Mixed-Zero-Sum-Game-Based Memory Event-Triggered Cooperative Control of Heterogeneous MASs Against DoS Attacks.

This article studies the problem of memory event-triggered cooperative adaptive control of heterogeneous nonlinear multiagent systems (MASs) under denial-of-service (DoS) attacks based on the multiplayer mixed zero-sum (ZS) game strategy. First, a neural-network-based reinforcement learning scheme is structured to obtain the Nash equilibrium solution of the proposed multiplayer mixed ZS game scheme. Then, a memory-based event-triggered mechanism considering the historical data is proposed. This effectively avoids incorrect triggering information caused by unknown external factors. Moreover, thanks to the idea of switching topology, the mixed ZS game problem under the influence of node-based DoS attacks is solved efficiently. In accordance with the Lyapunov stability theory, it is proved that all signals of heterogeneous MASs are bounded, all heterogeneous followers can track the trajectory of the leader during the no-attack period, the attacked follower can achieve stabilization control during the attack period, and the remaining nonattacked followers can achieve cooperative control during the attack period. Finally, the effectiveness of the designed memory-event-triggered-based mixed ZS game cooperative control strategy is tested by the given simulation results.

Observer-based leader-centric time-varying formation tracking control for nonlinear multi-agent systems with collision avoidance

The article introduces a novel control design methodology to achieve leader-centric time-varying formation tracking (TVFT) with collision avoidance in Lipschitz nonlinear multi-agent systems (MASs) equipped with a leader-driven formation system. This methodology addresses challenges such as actuator bias faults and leader maneuvering within this MASs setup. It employs two control schemes: collision avoidance and a novel formation observer-based time-varying formation tracking (FO-based TVFT) control. These control schemes work in tandem. The collision avoidance scheme ensures safe operation by preventing inter-agent collisions, while the novel FO-based TVFT control scheme enables followers to achieve leader-driven formations while tracking the leader’s movements. To achieve this capability, each follower employs a formation observer (FO) that continuously estimates the leader’s dynamically driven formations throughout runtime, facilitating responsive formation tracking by the followers. Notably, this FO-based TVFT control scheme establishes a novel framework for integrated leader-driven formation switching and leader tracking (i.e., leader-centric TVFT) in MASs. Furthermore, this control methodology is specifically designed for Lipschitz nonlinear MASs susceptible to challenges like actuator bias faults and leader maneuvering. It guarantees that the followers’ collective formation tracking error is uniformly ultimately bounded (UUB), based on Lyapunov’s stability theory. Finally, an illustrative example validates the proposed approach’s effectiveness.

Vibration control of nonlinear viscoelastic systems with displacement delay feedback

In this study, the nonlinear vibration characteristics of a nonlinear Zener model under harmonic excitation, equipped with linear and nonlinear displacement delay feedback control, were investigated. The amplitude–frequency curve of the system’s main resonance was computed using the multi-scale method. Stability conditions for the system were then established based on the Lyapunov stability theory. The influence of several parameters on the system’s dynamic behavior was also analyzed, including time delay, displacement feedback gain coefficient, nonlinear term coefficient, damping coefficient, and external excitation. The findings revealed that the nonlinear displacement feedback gain coefficient was observed to exert a more substantial effect on the system’s amplitude than other factors. Further, the nonlinear displacement delay feedback gain coefficient and time-delay value diminish the amplitude of the vibration, leading all solutions to achieve a stable state. In instances with time-delay control, the impact of the main system parameters on system vibration was significantly diminished. The aim of this study is to provide a theoretical basis for the implementation of displacement delay controllers in nonlinear viscoelastic systems.

Command Filtered-Based Adaptive Predefined-Time Control for Uncertain Nonlinear Systems With Applications to RLC Circuit

Command Filtered-Based Adaptive Predefined-Time Control for Uncertain Nonlinear Systems With Applications to RLC Circuit

Robust adaptive prescribed performance control for nonlinear systems with arbitrary initial states

The initial state of nonlinear MIMO strict feedback systems is often unpredictable and random, and existing prescribed performance control (PPC) techniques can only guarantee system output constraints within a fixed initial value performance boundary. In this paper, an adaptive PPC method tailored for nonlinear systems was introduced, enabling the system stable tracking regardless of the arbitrary initial states. To guarantee that the tracking error consistently meets the prescribed performance boundary(PPB) envelope, we introduce a nonlinear mapping between the initial value of the prescribed performance functions(PPFs) and the system tracking errors, resulting in an asymmetric time-varying performance boundary. Building upon this foundation, an adaptive PPC scheme is proposed under the backstepping framework, integrated with a nonlinear disturbance observer (NDO). This method ensures that the tracking error remains within the desired PPB, regardless of external disturbances or system initial states. To prevent ‘complexity explosion’, a dynamic surface control (DSC) technology is employed to filter the virtual control signals of each subsystem. Furthermore, the ultimate uniform boundedness of the closed-loop signal has been demonstrated, and a practical flight vehicles roll control case was introduced to validate the efficacy of the proposed method.

Adaptive SOSM Control for Nonlinear Systems With Parametric Uncertainties and Time-Varying Asymmetric Output Constraints

Adaptive SOSM Control for Nonlinear Systems With Parametric Uncertainties and Time-Varying Asymmetric Output Constraints

Fixed-time Disturbance Observer-based Fixed-time Prescribed Performance Control for Nonlinear Systems With Disturbances and Full-state Constraints

Fixed-time Disturbance Observer-based Fixed-time Prescribed Performance Control for Nonlinear Systems With Disturbances and Full-state Constraints

Adaptive Prescribed-Time Neural Control of Nonlinear Systems via Dynamic Surface Technique

Adaptive Prescribed-Time Neural Control of Nonlinear Systems via Dynamic Surface Technique

Double-Layered Iterative Learning Control for Nonlinear Systems

Double-Layered Iterative Learning Control for Nonlinear Systems

On-line data-driven control for uncertain systems based on greedy algorithm

Considering a result that persistently exciting data can be used to replace the linear system model, this paper is devoted to applying this result in the field of data-driven control of nonlinear systems. An on-line iteration based on greedy algorithm to stabilize uncertain discrete-time systems is proposed. The method tends to obtain approximate optimal control through solving a series of programming problems. Every programming problem is linear for the convenience of solving. Besides, in particular, the method requires few prior conditions, as long as the system is controllable and observable and the equilibrium state of the system is known. First, we prove that under certain circumstances, the solution to our linear matrix inequality can stabilize the system. Next, a multi-objective programming problem is proposed to deal with situations where the required conditions are unknown. Finally, an on-line iteration is used to enhance robustness as well as real-time evaluation. The method is illustrated to be effective through a simulation under repeated experiments.

Controllability and Optimal Fast Operation of Nonlinear Systems

A new method for solving the problem of controllability and optimal transient behavior of nonlinear systems subject to boundary conditions and constraints on control values was proposed. Unlike existing methods, this new approach is based on constructing a general solution of the integral equation for a linear controlled system, followed by transforming the original problem into a special initial optimal control problem. We propose a new method for studying the global asymptotic stability of dynamical systems with a cylindrical phase space with a countable equilibrium position based on a non-singular transformation of the equation of motion and estimation of improper integrals along the solution of the system. Conditions for global asymptotic stability were obtained without involving any periodic Lyapunov function, as well as the frequency theorem. The effectiveness of the proposed method is shown with an example.

Fuzzy Adaptive Fixed-Time Tracking Control for State-Constrained Nonlinear Systems with Application to Induction Motors

Fuzzy Adaptive Fixed-Time Tracking Control for State-Constrained Nonlinear Systems with Application to Induction Motors

Adaptive neural self-triggered bipartite consensus control for nonlinear fractional-order multi-agent systems with actuator fault

Adaptive neural self-triggered bipartite consensus control for nonlinear fractional-order multi-agent systems with actuator fault

Distributed Adaptive Fuzzy Output Consensus Control of Nonlinear Multi-agent Systems with Different Measurement Sensitivities

Distributed Adaptive Fuzzy Output Consensus Control of Nonlinear Multi-agent Systems with Different Measurement Sensitivities

Nonlinear hysteresis system control based on sliding mode neural network and observer

In this paper, a sliding mode neural network controller with observer is presented and employed in a nonlinear hysteresis system to eliminate the system’s unknown hysteresis and uncertainties. First, a sliding mode controller is proposed for trajectory tracking, which simplifies the computational complexity and ensures robustness. Second, radial basis function neural network is applied for approximating unknown nonlinear function in the control system. Then, an observer is utilized to estimate and observe the hysteresis nonlinearity and cancel the effect of the hysteresis phenomenon. Based on the proposed control scheme, the influence of hysteresis is suppressed, and the system has robust stability and achieves high output tracking performance. Finally, theoretical analysis and numerical simulations confirm the effectiveness of the designed control law.

Interval Type-2 Fuzzy Sampled-Date Control for Nonlinear Systems with Packet Dropouts via a Switched System Approach

Interval Type-2 Fuzzy Sampled-Date Control for Nonlinear Systems with Packet Dropouts via a Switched System Approach

Adaptive neural network terminal sliding mode tracking control for uncertain nonlinear systems with time-varying state constraints

Exploring a novel adaptive asymmetric sliding mode control methodology with time-varying state constraints (TVSCs), we address trajectory tracking issues in uncertain nonlinear systems. The asymmetric barrier Lyapunov functions (ABLFs) and neural networks is employed within each subsystem’s virtual control design process using back-stepping control (BSC) method. This ensures the imposition of TVSCs and effectively addresses challenges posed by system uncertainties. Additionally, to enhance the convergence of tracking deviations within small zero neighborhoods, a nonsingular integral terminal sliding mode control (NITSMC) method is incorporated into the actual control algorithm design. This method illustrates that, the system states consistently stay within the specified boundaries, tracking errors rapidly converge to a confined range. All signals within the system remain bounded. Simulation findings affirm the efficacy of the suggested control strategy.

Adaptive tracking control of high-order nonlinear systems with unknown time-varying input delay and unmodeled dynamics

Adaptive tracking control of high-order nonlinear systems with unknown time-varying input delay and unmodeled dynamics

Dual-channel event-triggered prescribed performance adaptive fuzzy time-varying formation tracking control for nonlinear multi-agent systems

This paper is concerned with the problem of dual-channel event-triggered prescribed performance adaptive fuzzy time-varying formation tracking control for multi-agent systems subject to actuator saturation, in which state variables are unmeasurable and nonlinear functions are totally unknown. A fuzzy state observer is constructed to estimate unmeasurable states. Meanwhile, fuzzy logic systems are used to approximate unknown nonlinear functions. To effectively save the usage of communication resources, this paper designs both sensor output signal and control signal triggering mechanisms, respectively. Unfortunately, the output triggering can lead to a problem that virtual control laws are non-differentiable. To solve this problem, we first utilize observer output signals to construct virtual control laws to ensure the first-order differentiation of virtual control laws. Then, a dynamic filtering technology is introduced to avoid the repeated differentiation of virtual control laws. Furthermore, an improved first-order auxiliary system is designed to compensate for the impact of actuator saturation. It is shown that the designed controller can guarantee tracking errors steer to a preset accuracy within a prescribed settling time, and all signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, simulation results verify the effectiveness of the developed control scheme.

Event-triggered adaptive fault estimation and fault-tolerant control for strict-feedback nonlinear systems with full state constraints

Event-triggered adaptive fault estimation and fault-tolerant control for strict-feedback nonlinear systems with full state constraints