Unknown Nonlinear Dynamics Research Articles

Cooperative Maritime Search of Multi-Ship Based on Improved Robust Line-of-Sight Guidance

In this paper, an improved robust line-of-sight (RLOS) guidance-based fuzzy sliding mode controller is presented to control underactuated ships to conduct the cooperative maritime search operation under the presented improved creeping line search method. First, considering that the ship cannot perform turning with corners, an improved creeping line search method is presented by integrating the Bezier method into the traditional creeping line search method to smooth the transition points with corners and employing the cubic spline interpolation method to generate continuous reference paths. Second, an improved RLOS guidance method is presented for the first time by exploring the idea of robust adaptive control to mitigate the chattering effect of the RLOS guidance. Third, the fuzzy logic system with approximate ability is integrated into the design of sliding mode controller to handle unknown nonlinear model dynamics and environmental disturbances. Finally, an improved RLOS guidance-based fuzzy sliding mode controller is presented. The closed-loop stability is guaranteed by the Lyapunov theorem. Comparative simulations are conducted to illustrate the advantages and verify the effectiveness of the presented method.

An adaptive dynamic programming method for observer‐based sliding mode control of connected vehicles subject to deception attacks

AbstractThis article investigates the problem of optimal observer‐based sliding mode control (SMC) of connected vehicles subject to deception attacks and disturbances with adaptive dynamic programming (ADP) method. For a group of vehicles with unknown nonlinear dynamics term and disturbance, this article aims to give a control methodology to achieve secure tracking of the desired spacing, velocity and acceleration. A neural network (NN) and an observer are constructed to estimate the unknown nonlinear term and the states, respectively. Then, a SMC scheme incorporating NN approximation is developed and an off‐policy ADP method is used to implement the optimal control of sliding mode dynamics. The proposed method can ensure individual stability and string stability of the set of vehicles. Numerical simulations are conducted to demonstrate the validity of the proposed controller.

Path Following Control for Unmanned Surface Vehicles: A Reinforcement Learning-Based Method With Experimental Validation.

In this article, a reinforcement learning (RL)-based strategy for unmanned surface vehicle (USV) path following control is developed. The proposed method learns integrated guidance and heading control policy, which directly maps the USV's navigation states to motor control commands. By introducing a twin-critic design and an integral compensator to the conventional deep deterministic policy gradient (DDPG) algorithm, the tracking accuracy and robustness of the controller can be significantly improved. Moreover, a pretrained neural network-based USV model is built to help the learning algorithm efficiently deal with unknown nonlinear dynamics. The self-learning and path following capabilities of the proposed method were validated in both simulations and real sea experiments. The results show that our control policy can achieve better performance than a traditional cascade control policy and a DDPG-based control policy.

Reinforcement Learning-Based Predefined-Time Tracking Control for Nonlinear Systems Under Identifier-Critic-Actor Structure.

A novel reinforcement learning-based predefined-time tracking control scheme with prescribed performance is presented in this article for nonlinear systems in the presence of external disturbances. First, by employing the backstepping strategy, an adaptive optimized controller is developed under the identifier-critic-actor framework. Therein, the unknown nonlinear dynamics and the system control behavior can be learned effectively through neural networks. Moreover, aiming at obtaining the preset tracking performance, the prescribed performance control is integrated with the predefined-time control. In contrast to previous studies, the proposed scheme can not only constrain the tracking error rapidly to a prearranged vicinity of origin, but also ensure that the upper bound of convergence time can be adjusted in advance via a separate control parameter. In terms of the predefined-time stability theory, the boundedness of all system states can be proven within a predefined time. Finally, the availability and improved performances of the proposed control scheme are demonstrated by a numerical example and a single-link manipulator example.

Leader-Following Consensus of Multiple Uncertain Euler-Lagrange Systems via Fully Distributed Event-Triggered Adaptive Fuzzy Control.

This article deals with the leader-following consensus problem of multiple uncertain Euler-Lagrange systems with unknown nonlinear dynamics. By introducing a dynamic compensator for each agent, a fully distributed control strategy is developed based on the fuzzy approximation approach, which is independent of any priori global information associated with the communication topology. Meanwhile, a distributed event-triggering mechanism (ETM) is designed such that each agent broadcasts its states only when an event occurs. It is shown that with the proposed ETM, the leader-following consensus is achieved with aperiodic intermittent communication and Zeno behavior is excluded by contradiction. Moreover, the consensus tracking errors converge to small sets around the origin. Finally, an example is provided to illustrate the effectiveness of the obtained theoretical results.

Model-free scheme using time delay estimation with fixed-time FSMC for the nonlinear robot dynamics

<abstract><p>This paper presents a scheme of time-delay estimation (TDE) for unknown nonlinear robotic systems with uncertainty and external disturbances that utilizes fractional-order fixed-time sliding mode control (TDEFxFSMC). First, a detailed explanation and design concept of fractional-order fixed-time sliding mode control (FxFSMC) are provided. High performance tracking positions, non-chatter control inputs, and nonsingular fixed-time control are all realized with the FxSMC method. The proposed approach performs better and obtains superior performance when FxSMC is paired with fractional-order control. Furthermore, a TDE scheme is included in the suggested strategy to estimate the unknown nonlinear dynamics. Afterward, the suggested system's capacity to reach stability in fixed time is determined by using Lyapunov analyses. By showing the outcomes of the proposed technique applied to nonlinear robot dynamics, the efficacy of the recommended method is assessed, illustrated, and compared with the existing control scheme.</p></abstract>

Tracking control problem of nonlinear strict-feedback systems with input nonlinearity: An adaptive neural network dynamic surface control method.

In this work, the tracking control problem for a class of nonlinear strict-feedback systems with input nonlinearity is addressed. In response to the influence of input nonlinearity, an auxiliary control system is constructed to compensate for it. To process unknown nonlinear dynamics, radial basis function neural networks (RBFNNs) are introduced to approximate them, and some adaptive updating control laws are designed to estimate unknown parameters. Furthermore, during the dynamic surface control (DSC) design process, first-order low-pass filters are introduced to solve the complexity explosion problems caused by repeated differentiation. After that, an NN-based adaptive dynamic surface tracking controller is proposed to achieve the tracking control. By applying the proposed controller, it can be guaranteed that not only the output of the system can track the desired trajectory, but also that the tracking error can converge to a small neighborhood of zero, while all signals of the closed-loop system are bounded. Finally, the effectiveness of the proposed controller is verified through two examples.

Practical prescribed-time fuzzy tracking control for uncertain nonlinear systems with time-varying actuators faults

The paper investigates the practical prescribed-time fuzzy tracking control problem for a category of nonlinear system subject to time-varying actuator faults. The presence of unknown nonlinear dynamics and actuator faults makes achieving tracking control within a prescribed-time challenging. To tackle this issue, we propose a novel practical prescribed-time fuzzy tracking control strategy, which is independent of the initial state of the system and does not rely on precise modeling of the system and actuators. We apply the approximation capabilities of fuzzy logic systems to handle the unknown nonlinear functions and unidentified actuator faults in the system. The piecewise controller and adaptive law constructed based on piecewise prescribed time-varying function and backstepping technique method establish the theoretical framework of practical prescribed-time tracking control, and extend the range of prescribed-time tracking control to infinity. Regardless of the initial conditions, the proposed control strategy can guarantee that all signals remain uniformly bounded within the practical prescribed time in the presence of unknown nonlinear item and time-varying actuator faults. Simulation example is presented to demonstrate the effectiveness of the proposed control strategy.

Constrained docking control for shipborne UAV SideArm recovery

In this work, we sought to investigate constrained docking control during shipborne SideArm recovery of an Unmanned Aerial Vehicle (UAV) under preassigned safe docking constraints, rough ocean environments, and different initial positions. The aim was to solve the UAV tracking-lag problem that manifests when attempting to dock with a rapidly moving SideArm and to improve the accuracy and rapidity of docking. First, together with the formulations of the shipborne SideArm system and environmental airflows, the affine nonlinear dynamics of the hook was established to reduce tracking lag. Then, echo state network approximators with good approximation capacity and low computational consumption were designed to accurately approximate the UAV’s unknown nonlinear dynamics. With feedforward compensation provided by these approximators, a nonlinear-mapping-based constrained docking control law was developed for shipborne SideArm recovery of UAVs. This approach to controlling the docking trajectory and the forward docking speed of the UAV can achieve rapid and exact docking with a moving SideArm, without violating the preassigned safe docking-constraint envelopes. Simulations under different docking scenarios were used to validate the effectiveness and advantages of the proposed docking-control algorithm.

Event‐triggered consensus secure control for nonlinear MASs under mixed sensor attacks and actuator faults

SummaryThis article investigates the adaptive neural network (NN) output‐feedback event‐triggered consensus secure control problem for a class of nonlinear multi‐agent systems (MASs) under mixed sensor attacks and actuator faults. Since the considered nonlinear MASs contain unknown nonlinear dynamics, the NNs are first adopted to model unknown agents. Then, a nove NN learning secure state observer is proposed to estimate the sensor attacks and unmeasured states. To reduce unnecessary updating times of the actuator, an event‐triggered mechanism is constructed. By using the backstepping control design technique and the design NN state observer, a NN adaptive output‐feedback event‐triggered consensus secure control scheme is formulated. It is proved that the developed consensus secure control scheme can guarantee the controlled nonlinear MASs are stable and consensus tracking errors converge even under mixed sensor attacks and actuator faults. Simulation and comparative results illustrate the effectiveness of the proposed scheme.

Event-Triggered Predefined-Time Output Feedback Control for Fractional-Order Nonlinear Systems With Input Saturation

The event-triggered predefined-time output feed- back control problem is considered for fractional-order nonlinear systems (FONSs) with input saturation. The controlled plant contains unknown nonlinear dynamics and unmeasured states. The unknown nonlinear dynamics are handled by using fuzzy approximation technique, a fuzzy state observer is established to estimate unmeasured states and an event-triggered mechanism is given to improve the efficiency of communication resource utilization. The predefined-time stable criterion of fractional- order nonlinear systems is first developed. Then, an event- triggered predefined-time output feedback control is proposed by using the dynamic surface control (DSC) technique. Based on the proposed predefined-time stable criterion and Lyapunov function, it is proved that the controlled system is semi-global practically predefined-time stable (SGPPTS) and all the signals are bounded in predefined-time interval. Finally, the simulation results are given to confirm the effectiveness of the presented predefined-time control method.

Prescribed-Time Formation Control for a Class of Multiagent Systems via Fuzzy Reinforcement Learning

This paper concerns optimal prescribed-time forma- tion control for a class of nonlinear multi-agent systems (MASs). Optimal control depends on the solution of the Hamilton-Jacobi- Bellman equation, which is hard to be calculated directly due to its inherent nonlinearity. To overcome this difficulty, the rein- forcement learning strategy with fuzzy logic systems is proposed, in which identifier, actor, and critic are used to estimate unknown nonlinear dynamics, implement control behavior, and evaluate system performance, respectively. Different from the existing optimal control algorithms, a new performance index function considering formation error cost and control input energy cost is constructed to achieve optimal formation control of MASs within a prescribed time. The presented control strategy can ensure that the formation error converges to the desired accuracy within a prescribed time. Finally, the validity of the presented strategy is verified via a simulation example.

An adaptive bearing rigid formation control of multi-agent systems with nonlinear dead-zone inputs

In this paper, an adaptive bearing rigid formation control strategy for a class of nonlinear system with unknown dead-zone inputs and external disturbance is proposed. Firstly, the I-Type fuzzy system is used to approximate the unknown nonlinear dynamics of the formation model, and the approximation errors and unknown external disturbance are eliminated by the parameter adaptive estimation. Furthermore, the adaptive dynamic estimation algorithm is utilized to estimate and compensate the unknown dead-zone parameters, effectively suppressing the impact of dead-zone on formation system performance. Finally, the stability of the formation system is proved based on LaSalle’s invariance principle, and the effectiveness of the algorithm is verified by simulation results.

Continuous action iterated dilemma under double-layer network with unknown nonlinear dynamics and its convergence analysis

Continuous action iterated dilemma under double-layer network with unknown nonlinear dynamics and its convergence analysis

Interval-valued fuzzy estimation and its application to adaptive control of quadrotor

In this paper, a combination of fuzzy clustering estimation and sliding mode control is used to control a quadrotor system, whose mathematical model is complex and contains unknown elements, including structure and parameters. Additionally, the system may be susceptible to external environmental disturbances. Initially, the nonlinear unknown components of the system are estimated using a fuzzy model. We introduce a novel approach for constructing a Takagi–Sugeno (TS) interval-valued fuzzy model (IVFM) based on input–output data obtained from the identified system. Following the construction of the fuzzy model that estimates the unknown aspects of the quadrotor system, we implement a control strategy with online adjustments for the fuzzy-modeled dynamics. In this phase, the system’s model is estimated in an adaptive manner, allowing the dynamic equations to be utilized in sliding mode control. Finally, we apply the proposed technique to a quadrotor, presenting simulation results to demonstrate the effectiveness of this approach in controlling a system characterized by unknown nonlinear dynamics.

Asymptotical Neuro-Adaptive Consensus of Multi-Agent Systems With a High Dimensional Leader and Directed Switching Topology.

We study the asymptotical consensus problem for multi-agent systems (MASs) consisting of a high-dimensional leader and multiple followers with unknown nonlinear dynamics under directed switching topology by using a neural network (NN) adaptive control approach. First, we design an observer for each follower to reconstruct the states of the leader. Second, by using the idea of discontinuous control, we design a discontinuous consensus controller together with an NN adaptive law. Finally, by using the average dwell time (ADT) method and the Barbǎlat's lemma, we show that asymptotical neuroadaptive consensus can be achieved in the considered MAS if the ADT is larger than a positive threshold. Moreover, we study the asymptotical neuroadaptive consensus problem for MASs with intermittent topology. Finally, we perform two simulation examples to validate the obtained theoretical results. In contrast to the existing works, the asymptotical neuroadaptive consensus problem for MASs is firstly solved under directed switching topology.

Adaptive Neural Network Event-Triggered Output-Feedback Containment Control for Nonlinear MASs With Input Quantization.

This article investigates the adaptive neural network (NN) event-triggered containment control problem for a class of nonlinear multiagent systems (MASs). Since the considered nonlinear MASs contain unknown nonlinear dynamics, immeasurable states, and quantized input signals, the NNs are adopted to model unknown agents, and an NN state observer is established by using the intermittent output signal. Subsequently, a novel event-triggered mechanism consisting of both the sensor-to-controller and controller-to-actuator channels are established. By decomposing quantized input signals into the sum of two bounded nonlinear functions and based on the adaptive backstepping control and first-order filter design theories, an adaptive NN event-triggered output-feedback containment control scheme is formulated. It is proved that the controlled system is semi-globally uniformly ultimately bounded (SGUUB) and the followers are within a convex hull formed by the leaders. Finally, a simulation example is given to validate the effectiveness of the presented NN containment control scheme.

Finite-Time Command Filtered Adaptive Control for Robot Manipulators in Random Vibration Environment

This paper introduces a finite-time tracking control algorithm for robot manipulator systems in a random vibration environment, which addresses the challenges of parameter uncertainty and input saturation. The algorithm combines command filtered adaptive backstepping with neural networks to approximate unknown nonlinear dynamics and avoid the singularity problem of traditional finite-time backstepping methods. An error compensation mechanism based on the fractional power function is also introduced to improve trajectory tracking accuracy, and the algorithm is shown to ensure practical finite-time stability in mean square. Numerical simulations demonstrate that the effectiveness of proposed method.

Optimization‐based adaptive control for MIMO nonlinear systems: A data‐driven method

AbstractThis article concentrates on the challenging adaptive tracking problem of multi‐input and multi‐output (MIMO) nonlinear systems with unknown nonlinear dynamics, for which a novel optimization‐based data‐driven adaptive control (ODDAC) equipped with an extended dynamic linearization method is developed. Through considering MIMO nonlinear systems in the fully‐actuated case and over‐actuated case separately, the ODDAC is proposed consisting of a parameter updating algorithm and an adaptive control law. A new design of parameter updating algorithm is presented such that the estimation can be guaranteed to be bounded by a strict contraction process. By leveraging properties of the nonnegative matrix, a grouping‐based contraction mapping (GCM) analysis method is proposed for the convergence of tracking error. Notably, the GCM does not require the contraction mapping condition to hold at all time instants. The proposed ODDAC is data‐based, avoiding reliance on model information, and its validity is verified through simulations.

Predefined-time fuzzy adaptive decentralised control for fractional-order nonlinear large-scale systems by a cyclic-small-gain-based approach

The predefined-time fuzzy adaptive output feedback decentralised control problem is considered for fractional-order nonlinear large-scale (FONLS) systems. Firstly, by using fuzzy logic systems (FLSs) to model unknown nonlinear dynamics, a fuzzy decentralised state observer is designed to solve the immeasurable state problem. Secondly, the predefined-time stability criterion of fractional-order nonlinear systems is proposed, and then, based on the established predefined-time stability criterion of the fractional-order nonlinear systems, a predefined-time fuzzy adaptive output feedback decentralised control method is developed by combining the backstepping design technique with the cyclic-small-gain approach, and the semi-global practically predefined-time stable (SGPPTS) of the control system is proved. Finally, the numerical simulation is given and shows the effectiveness of the presented predefined-time control method.