Uncertain Nonlinear Dynamics Research Articles

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.

Dynamic modeling and learning based path tracking control for ROV-based deep-sea mining vehicle

Track slippage and body sinking of the tracked mining vehicle in the traditional deep-sea mining system are the critical issues for operating stability. To solve this bottleneck problem, a novel ROV-based deep-sea mining system is proposed in this study, in which a remotely-operated vehicle (ROV) towering a sledge-shaped mining robot (MRT) named ROV-based Deep-sea Mining Vehicle (ROVDMV) is instead of the traditional tracked Deep-sea mining vehicle. The design of the ROVDMV can fundamentally overcome the bottleneck problem. However, the complex marine environment and multi-rigid-body design of the ROVDMV pose new challenges for its path-tracking control. Firstly, the dynamic model of the ROVDMV considering the ROV at a fixed depth is established based on the bicycle model, which is mainly used as the control object in the numerical simulation. Secondly, a learning-based path-tracking control strategy is proposed for the path-tracking control of the ROVDMV. In the control strategy, a novel nonparametric learning (NPL) method is introduced to learn the uncertain nonlinear dynamics considering the external disturbances and parametric uncertainty. The NPL method is proven to provide bounded estimated error. Besides, the enhanced NPL method can save approximately 33 % of the computation time, and the average computation time for its optimization control problem is only 12.47 ms. Finally, the numerical results show that the NPL method can learn nonlinear dynamics accurately, and the proposed strategy has proven to be effective

Robust Cooperative Control for Heterogeneous Uncertain Nonlinear High-Order Fully Actuated Multiagent Systems.

This research is intended to address a robust cooperative control problem of heterogeneous uncertain nonlinear high-order fully actuated multiagent systems (HUN-HOFAMASs). A nonlinear HOFA system model is used to describe the multiagent systems (MASs) with heterogeneous uncertain nonlinear dynamics, which is called the HUN-HOFAMASs. A predictive terminal sliding-mode control-based robust cooperative control scheme is presented to address this problem. In this scheme, heterogeneous nonlinear dynamics of original system are offset to establish a linear constant HOFA system with the help of full actuation feature. Then, a terminal sliding-mode variable for enhancing the system robustness is introduced to handle the uncertainties. Furthermore, a linear incremental prediction model is developed in a HOFA form by means of a Diophantine equation. According to this model, the multistep terminal sliding-mode predictions are yielded to optimize the robust cooperative control performance and compensate for the network-induced communication constraints in the feedback and forward channels. Based on a linear matrix inequality (LMI) method, a necessary and sufficient criterion is derived to discuss the simultaneous consensus and stability of closed-loop HUN-HOFAMASs. The simulation and comparison results of cooperative flying around of multiple spacecraft system are shown to illustrate the capability and advantage of the presented predictive terminal sliding-mode control for robust cooperative control.

Finite-time fuzzy adaptive consensus control for state-constrained MIMO nonlinear MASs with switched topologies

In this article, the adaptive fuzzy finite-time output feedback consensus control problem is investigated for multiple input and multiple output (MIMO) nonlinear multi-agent systems (MASs) with switched topologies and asymmetric state constraints. Fuzzy logic systems (FLSs) are utilised to approximate uncertain nonlinear dynamics, and a distributed observer and a state observer are established to estimate the unknown leader and system states, respectively. By constructing the barrier Lyapunov functions (BLFs), a finite-time output feedback consensus control scheme is presented via backstepping control technique. It is proved that the controlled MASs are stable, and the consensus errors converge in finite time. Moreover, the system states will not exceed the given bounds. Finally, the proposed finite-time consensus control approach is applied to control multiple unmanned surface vehicles (USVs), the simulation results check the feasibility of the developed finite-time consensus control methodology.

Command filtering‐based adaptive backstepping control for a class of discrete‐time uncertain nonlinear systems with mismatched disturbances

SummaryThis paper investigates the adaptive fuzzy backstepping control problem for uncertain discrete‐time nonlinear systems with mismatched disturbances. A novel adaptive fuzzy command filtered backstepping approach is proposed, which can overcome the noncausal problem by using the command filter. The filter errors generated by filter are removed by constructing error compensation mechanism. The fuzzy logic systems are used to approximate the uncertain nonlinear dynamics, and the unknown mismatched disturbances are actively attenuated by using adaptive control technique. Based on the proposed new weighed Lyapunov functions, all the signals in the close‐loop system are proved to be uniformly ultimately bounded. The viability of proposed method is demonstrated by simulation results.

Event-Triggered Adaptive Containment Control for Heterogeneous Stochastic Nonlinear Multiagent Systems.

This article investigates the event-triggered adaptive containment control problem for a class of stochastic nonlinear multiagent systems with unmeasurable states. A stochastic system with unknown heterogeneous dynamics is established to describe the agents in a random vibration environment. Besides, the uncertain nonlinear dynamics are approximated by radial basis function neural networks (NNs), and the unmeasured states are estimated by constructing the NN-based observer. In addition, the switching-threshold-based event-triggered control method is adopted with the hope of reducing communication consumption and balancing system performance and network constraints. Moreover, we develop the novel distributed containment controller by utilizing the adaptive backstepping control strategy and the dynamic surface control (DSC) approach such that the output of each follower converges to the convex hull spanned by multiple leaders, and all signals of the closed-loop system are cooperatively semi-globally uniformly ultimately bounded in mean square. Finally, we verify the efficiency of the proposed controller by the simulation examples.

Event-triggered adaptive tracking for constrained multi-agent systems with saturated inputs and actuator faults

An fault-tolerant tracking control of uncertain nonlinear multi-agent systems with state constraints and input saturation is investigated. A saturated controller is processed by converting the saturation function into a linear form of the control input. The uncertain nonlinear dynamics are approximated by fuzzy logic systems and the unknown parameters are estimated by adaptive laws. By utilizing the nonlinear state-dependent function, the constrained system is converted into the unconstrained one. An adaptive distributed event-triggered control mechanism for consensus tracking is developed utilizing the backstepping approach. By stability analysis, it is ensured that all system signals are bounded, consensus tracking can be achieved with bounded errors, and no Zeno behavior happens. Finally, simulation is done to validate the theoretical results.

Adaptive stabilization for a class of wave equations with uncertain nonlinear boundary actuator dynamics

This paper investigates the stabilization of a wave equation with uncertain boundary actuator dynamics. The remarkable characters of the system under investigation are revealed by the essential nonlinearities involved in the boundary actuator and the serious parametric unknowns coming from anti-damping coefficient at uncontrolled boundary and those in the actuator, which result into the incapability of the traditional control methods on this topic. For this, a novel adaptive control strategy is proposed in this paper. Specifically, a Riemann variables based state transformation is first introduced to change the original system into a new one whose stabilization implies that of the original system. Then, a state-feedback controller joint with some adaptive laws which are smartly chosen for the compensation of unknown parameters is explicitly designed by a finite-dimensional backstepping procedure. Owing to the compensation of boundary actuator dynamics, the performance analysis of the closed-loop system is more complicated than that of the related literature. For this, a rigorous recursive step is given to show the stability of the resulting closed-loop system. Finally, a numerical example is provided to verify the effectiveness of the proposed theoretical results.

Control of coupled nonaffine multiagent stochastic systems by classical PID

AbstractThe classical PID (proportional‐integral‐derivative) control is the most basic and widely used control algorithm in engineering systems by far. Whether PID control can effectively deal with coupled multiagent uncertain nonlinear dynamics is well worth investigating. In this article, a class of PID controlled multiagent stochastic systems with coupled uncertain dynamics is considered, where the control input is nonaffine. Each agent has its own regulation objective, and only has access to its own regulation error information for PID feedback. First, a PID parameter set will be constructed explicitly based on some prior knowledge about the nonlinear functions, such that the overall multiagent system can be stabilized globally in the mean square sense, as long as the PID parameters are chosen from the constructed set. Moreover, the regulation error will be proven to have an upper bound proportional to the noise intensity along the reference signal. Furthermore, it will be shown that the regulation error of each agent can be arbitrarily small by choosing the PID parameters suitably large. Finally, the theoretical results will be verified by simulations.

Time-Varying Optimal Formation Control for Second-Order Multiagent Systems Based on Neural Network Observer and Reinforcement Learning.

This article addresses a distributed time-varying optimal formation protocol for a class of second-order uncertain nonlinear dynamic multiagent systems (MASs) based on an adaptive neural network (NN) state observer through the backstepping method and simplified reinforcement learning (RL). Each follower agent is subjected to only local information and measurable partial states due to actual sensor limitations. In view of the distributed optimized formation strategic needs, the uncertain nonlinear dynamics and undetectable states may jointly affect the stability of the time-varying cooperative formation control. Furthermore, focusing on Hamilton-Jacobi-Bellman optimization, it is almost incapable of directly dealing with unknown equations. Above uncertainty and immeasurability processed by adaptive state observer and NN simplified RL are further designed to achieve desired second-order formation configuration at the least cost. The optimization protocol can not only solve the undetectable states and realize the prescribed time-varying formation performance on the premise that all the errors are SGUUB, but also prove the stability and update the critics and actors easily. Through the above-mentioned approaches offer an optimal control scheme to address time-varying formation control. Finally, the validity of the theoretical method is proven by the Lyapunov stability theory and digital simulation.

Data-Efficient Deep Reinforcement Learning for Attitude Control of Fixed-Wing UAVs: Field Experiments.

Attitude control of fixed-wing unmanned aerial vehicles (UAVs) is a difficult control problem in part due to uncertain nonlinear dynamics, actuator constraints, and coupled longitudinal and lateral motions. Current state-of-the-art autopilots are based on linear control and are thus limited in their effectiveness and performance. Gls drl is a machine learning method to automatically discover optimal control laws through interaction with the controlled system that can handle complex nonlinear dynamics. We show in this article that deep reinforcement learning (DRL) can successfully learn to perform attitude control of a fixed-wing UAV operating directly on the original nonlinear dynamics, requiring as little as 3 min of flight data. We initially train our model in a simulation environment and then deploy the learned controller on the UAV in flight tests, demonstrating comparable performance to the state-of-the-art ArduPlane proportional-integral-derivative (PID) attitude controller with no further online learning required. Learning with significant actuation delay and diversified simulated dynamics were found to be crucial for successful transfer to control of the real UAV. In addition to a qualitative comparison with the ArduPlane autopilot, we present a quantitative assessment based on linear analysis to better understand the learning controller's behavior.

Direct Adaptive Fuzzy Control with Prescribed Tracking Accuracy for Orbit Adjustment of Satellites

In this paper, we investigate the orbit-adjustment problem of satellite systems in the presence of nonlinear uncertainties in kinematics and dynamics. We propose a novel direct adaptive fuzzy control scheme with prescribed tracking accuracy to address uncertain nonlinear dynamics by employing advanced fuzzy logic systems and integrating a class of sophisticated smooth functions, thereby ensuring convergence of the tracking error within a precisely defined interval. The ingeniously designed control scheme guarantees negative semi-definiteness of the Lyapunov function, ensuring boundedness for all variables. Moreover, our groundbreaking control approach requires only one adaptive law, completely eliminating any direct correlation with the number of nonlinear functions. Simulation results unequivocally validate the remarkable effectiveness and superiority of our innovative control approach.

Fuzzy adaptive time‐varying formation control of USVs with actuator faults

SummaryThis paper investigates the fuzzy adaptive time‐varying formation control problem for fully‐actuated unmanned surface vehicles (USVs) systems. The studied USVs systems include uncertain dynamics and actuator faults. Fuzzy logic systems (FLSs) and disturbance observer are employed to estimate uncertain nonlinear dynamics in system model and external time‐varying disturbances, respectively. Meanwhile, the prescribed performance control (PPC) technique is applied to construct the constraint requirements of collision avoidance and connectivity preservation in time‐varying formation control. Additionally, a new robust adaptive fault‐tolerant control (FTC) algorithm is presented. Hence, by the aid of adaptive backstepping technique with performance functions, a robust fuzzy adaptive time‐varying formation FTC scheme of time‐varying formation is developed. The proposed formation control scheme not only has the advantages of avoiding collision and preserving connectivity, but also ensures all the signals are uniformly ultimately bounded (UUB). Finally, the simulation results are provided to demonstrate the effectiveness of the proposed approach.

Event-Based Finite-Time Neural Control for Human-in-the-Loop UAV Attitude Systems.

This article focuses on the event-based finite-time neural attitude consensus control problem for the six-rotor unmanned aerial vehicle (UAV) systems with unknown disturbances. It is assumed that the six-rotor UAV systems are controlled by a human operator sending command signals to the leader. A disturbance observer and radial basis function neural networks (RBF NNs) are applied to address the problems regarding external disturbances and uncertain nonlinear dynamics, respectively. In addition, the proposed finite-time command filtered (FTCF) backstepping method effectively manages the issue of "explosion of complexity," where filtering errors are eliminated by the error compensation mechanism. In addition, an event-triggered mechanism is considered to alleviate the communication burden between the controller and the actuator in practice. It is shown that all signals of the six-rotor UAV systems are bounded and the consensus errors converge to a small neighborhood of the origin in finite time. Finally, the simulation results demonstrate the effectiveness of the proposed control scheme.

Opposition-based differential evolution for synchronized control of multi-agent systems with uncertain nonlinear dynamics

Multi-agent systems (MAS) have gained increasing research attention in recent years due to their wide applications in cooperative control of autonomous vehicles, sensor networks, robotics, etc. However, designing effective distributed control strategies for MAS with complex dynamics remains challenging. This paper proposes an improved differential evolution (DE) based cooperative control strategy to stabilize and synchronize MAS with uncertain nonlinear dynamics. Specifically, we develop a new mutation strategy inspired by opposition-based learning to enhance the exploration ability and adopt an adaptive parameter mechanism to balance exploration and exploitation. Moreover, a distributed sliding mode term is incorporated in the control input to counteract uncertainties and external disturbances. Rigorous stability analysis shows that the closed-loop MAS can achieve synchronization under the proposed control strategy. Extensive simulations demonstrate that compared to other state-of-the-art DE algorithms and cooperative control methods, the proposed strategy achieves lower synchronization error, control cost, higher convergence speed, and higher accuracy for MAS with different scales, dynamics, and uncertainties.

Multilayer neurocontrol of servo electromechanical systems with disturbance compensation

For servo electromechanical systems, the existing modeling uncertainties, signal measurement noises and so on always make it difficult to design high-performance closed-loop controllers. In this paper, a novel intelligent controller will be designed to deal with these uncertainties. Specifically, two multilayer neuroadaptive disturbance observers will be proposed to estimate the uncertain nonlinear dynamics and exogenous disturbances simultaneously. And these uncertainties will be compensated feedforwardly. Moreover, in order to reduce the influence of signal measurement noises, the desired-command compensation technique will be incorporated. Additionally, different validation examples will be proposed to demonstrate the advantages of the designed controller.

Active Human-Following Control of an Exoskeleton Robot With Body Weight Support.

This article presents an active human-following control of the lower limb exoskeleton for gait training. First, to improve safety, considering the human balance, the OpenPose-based visual feedback is used to estimate the individual's pose, then, the active human-following algorithm is proposed for the exoskeleton robot to achieve the body weight support and active human-following. Second, taking the human's intention and voluntary efforts into account, we develop a long short-term memory (LSTM) network to extract surface electromyography (sEMG) to build the estimation model of joints' angles, that is, the multichannel sEMG signals can be correlated with flexion/extension (FE) joints' angles of the human lower limb. Finally, to make the robot motion adapt to the locomotion of subjects under uncertain nonlinear dynamics, an adaptive control strategy is designed to drive the exoskeleton robot to track the desired locomotion trajectories stably. To verify the effectiveness of the proposed control framework, several recruited subjects participated in the experiments. Experimental results show that the proposed joints' angles estimation model based on the LSTM network has a higher estimation accuracy and predicted performance compared with the existing deep neural network, and good simultaneous locomotion tracking performance is achieved by the designed control strategy, which indicates that the proposed control can assist subjects to perform gait training effectively.

Tracking Control of Uncertain Neural Network Systems with Preisach Hysteresis Inputs: A New Iteration-Based Adaptive Inversion Approach

To describe the hysteresis nonlinearities in smart actuators, numerous models have been presented in the literature, among which the Preisach operator is the most effective due to its capability to capture multi-loop or sophisticated hysteresis curves. When such an operator is coupled with uncertain nonlinear dynamics, especially in noncanonical form, it is a challenging problem to develop techniques to cancel out the hysteresis effects and, at the same time, achieve asymptotic tracking performance. To address this problem, in this paper, we investigate the problem of iterative inverse-based adaptive control for uncertain noncanonical nonlinear systems with unknown input Preisach hysteresis, and a new adaptive version of the closest-match algorithm is proposed to compensate for the Preisach hysteresis. With our scheme, the stability and convergence of the closed-loop system can be established. The effectiveness of the proposed control scheme is illustrated through simulation and experimental results.

Finite-Time Adaptive Dynamic Surface Asymptotic Tracking Control of Uncertain Multi-Agent Systems with Unknown Control Gains

In this work, the finite-time asymptotic tracking control problem of uncertain multi-agent systems with unknown control gains is studied. For the unknown control gain of each subsystem in multi-agent systems, we consider using the Nussbaum gain function techniques to handle them. To deal with the unknown uncertain nonlinear dynamics, the radial basis function neural network is introduced in each step of the dynamic surface control design. In addition, a nonlinear compensating term with the estimation of an unknown bounded parameter is designed to avoid repeated differentiation of each virtual control law. Then, based on the neural network control method, dynamic surface control technique, and finite-time control theory, an adaptive neural network finite-time dynamic surface control law is finally designed. Using stability analysis, it is proven that the presented adaptive control law can guarantee all signals of the closed-loop system semi-global practical finite-time stable, and the tracking error of each follower agent can converge to a small neighborhood of zero in finite time. Finally, a class of single-link robot systems is provided to illustrate the effectiveness of the designed control law.

Fixed-Time System Identification Using Concurrent Learning.

This article presents a fixed-time (FxT) system identifier for continuous-time nonlinear systems. A novel adaptive update law with discontinuous gradient flows of the identification errors is presented, which leverages concurrent learning (CL) to guarantee the learning of uncertain nonlinear dynamics in a fixed time, as opposed to asymptotic or exponential time. More specifically, the CL approach retrieves a batch of samples stored in a memory, and the update law simultaneously minimizes the identification error for the current stream of samples and past memory samples. Rigorous analyses are provided based on FxT Lyapunov stability to certify FxT convergence to the stable equilibria of the gradient descent flow of the system identification error under easy-to-verify rank conditions. The performance of the proposed method in comparison with the existing methods is illustrated in the simulation results.