Unknown Dynamics Research Articles

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.

Adaptive NN Controller of Nonlinear State-Dependent Constrained Systems With Unknown Control Direction.

Various constraints commonly exist in most physical systems; however, traditional constraint control methods consider the constraint boundaries only relying on constant or time variable, which greatly restricts applying constraint control to practical systems. To avoid such conservatism, this study develops a new adaptive neural controller for the nonlinear strict-feedback systems subject to state-dependent constraint boundaries. The nonlinear state-dependent mapping is employed in each step of backstepping procedure, and the prescribed transient performance on tracking error and the constraints on system states are ensured without repeatedly verifying the feasibility conditions on virtual controllers. The radial basis function neural network (NN) with less parameters approach is introduced as an identifier to estimate the unknown system dynamics and reduce computation burden. For removing the effect of unknown control direction, the Nussbaum gain technique is integrated into controller design. Based on the Lyapunov analysis, the developed control strategy can ensure that all the closed-loop signals are bounded, and the constraints on full system states and tracking error are achieved. The simulation examples are used to illustrate the effectiveness of the developed control strategy.

Data-Based Optimal Synchronization of Heterogeneous Multiagent Systems in Graphical Games via Reinforcement Learning.

This article studies the optimal synchronization of linear heterogeneous multiagent systems (MASs) with partial unknown knowledge of the system dynamics. The object is to realize system synchronization as well as minimize the performance index of each agent. A framework of heterogeneous multiagent graphical games is formulated first. In the graphical games, it is proved that the optimal control policy relying on the solution of the Hamilton-Jacobian-Bellmen (HJB) equation is not only in Nash equilibrium, but also the best response to fixed control policies of its neighbors. To solve the optimal control policy and the minimum value of the performance index, a model-based policy iteration (PI) algorithm is proposed. Then, according to the model-based algorithm, a data-based off-policy integral reinforcement learning (IRL) algorithm is put forward to handle the partially unknown system dynamics. Furthermore, a single-critic neural network (NN) structure is used to implement the data-based algorithm. Based on the data collected by the behavior policy of the data-based off-policy algorithm, the gradient descent method is used to train NNs to approach the ideal weights. In addition, it is proved that all the proposed algorithms are convergent, and the weight-tuning law of the single-critic NNs can promote optimal synchronization. Finally, a numerical example is proposed to show the effectiveness of the theoretical analysis.

Computationally Tractable Gaussian Process-based Stochastic Predictive Control Using Backoffs

Current stochastic nonlinear model predictive control (SNMPC) hinges on the lack of high-fidelity models that describe the system behavior and the lack of tractable solution methods that handle chance constraints. Motivated by this, a model-and data-driven predictive control approach using Gaussian processes (GP-MDPC) is synthesized in this paper. It exploits GPs to learn the unknown dynamics and apply Taylor expansion for uncertainty propagation through probabilistic modeling. A backoff approximation method is explored to reformulate the chance constraints into tractable expressions. Finally, a finite-horizon stochastic optimal control problem (FH-SOCP) is formulated.

Physics-Dominated Neural Network for Spatiotemporal Modeling of Battery Thermal Process

Modeling the temperature distribution of a battery is critical to its safe operation. Data-based modeling methods are computationally efficient, but require a large number of sensors; while physics-based modeling methods have better generalization, but the unknown dynamics of the actual scene are ignored. A physics-dominated neural network is presented to integrate electric-thermal mechanism of the battery and data information through a weight adaptive function. The electric-thermal coupling equation of the battery under complex conditions is taken as the prior knowledge to update parameters of the network; while the characteristic data obtained by the unique sensor is used to compensate the unknown disturbance in the actual scene. A well-trained model can predict the temperature distribution of the battery over entire space with a single sensor, and can also provide reasonable predictions for longer periods of time under extreme conditions. Experiments show that the proposed method outperforms traditional methods that rely only on pure data or pure physics.

Robust Current Control for Grid-Connected VSC: Nonlinear Adaptive Control with Perturbation Estimation

This paper introduces a robust control strategy for grid-connected voltage source converters using Nonlinear Adaptive Control (NAC) enhanced by a perturbation observer (PO). This approach precisely regulates grid current and adapts to unknown dynamics, time-varying parameters, and disturbances impacting the system. By estimating and compensating for these perturbations, the strategy achieves adaptive feedback linearization, effectively managing the system’s inherent nonlinearity without requiring an exact model or extensive measurements. The NAC offers substantial improvements over traditional vector control and feedback linearization, particularly under conditions where grid voltage significantly deviates from normal levels. Simulation results confirm the superior performance of the proposed method.

Data-Driven Abstractions via Binary-Tree Gaussian Processes for Formal Verification

To advance formal verification of stochastic systems against temporal logic requirements for handling unknown dynamics, researchers have been designing data-driven approaches inspired by breakthroughs in the underlying machine learning techniques. As one promising research direction, abstraction-based solutions based on Gaussian process (GP) regression have become popular for their ability to learn a representation of the latent system from data with a quantified error. Results obtained based on this model are then translated to the true system via various methods. In a recent publication, GPs using a so-called binary-tree kernel have demonstrated a polynomial speedup w.r.t. the size of the data compared to their vanilla version, outcompeting all existing sparse GP approximations. Incidentally, the resulting binary-tree Gaussian process (BTGP) is characteristic for its piecewise-constant posterior mean and covariance functions, naturally abstracting the input space into discrete partitions. In this paper, we leverage this natural abstraction of the BTGP for formal verification, eliminating the need for cumbersome abstraction and error quantification procedures. We show that the BTGP allows us to construct an interval Markov chain model of the unknown system with a speedup that is polynomial w.r.t. the size of the abstraction compared to alternative approaches. We provide a delocalized error quantification via a unified formula even when the true dynamics do not live in the function space of the BTGP. This allows us to compute upper and lower bounds on the probability of satisfying reachability specifications that are robust to both aleatoric and epistemic uncertainties.

Robust Adaptive Leader-Following Formation Control of Nonlinear Multiagents Using Three-Layer Neural Networks.

This article studies a formation control problem for a group of heterogeneous, nonlinear, uncertain, input-affine, second-order agents modeled by a directed graph. A tunable neural network (NN) is presented, with three layers (input, two hidden, and output) that can approximate an unknown nonlinearity. Unlike one- or two-layer NNs, this design has the advantage of being able to set the number of neurons in each layer ahead of time rather than relying on trial and error. The NN weights tuning law is rigorously derived using the Lyapunov theory. The formation control problem is tackled using a robust integral of the sign of the error feedback and NNs-based control. The robust integral of the sign of the error feedback compensates for the unknown dynamics of the leader and disturbances in the agent errors, while the NN-based controller accounts for the unknown nonlinearity in the multiagent system. The stability and semi-global asymptotic tracking of the results are proven using the Lyapunov stability theory. The study compares its results with two others to assess the effectiveness and efficiency of the proposed method.

Data-Driven Optimal Tracking Control for Discrete-Time Nonlinear Systems With Unknown Dynamics Using Deterministic ADP.

This article aims to solve the optimal tracking problem (OTP) for a class of discrete-time (DT) nonlinear systems with completely unknown dynamics. A novel data-driven deterministic approximate dynamic programming (ADP) algorithm is proposed to solve this kind of problem with only input-output (I/O) data. The proposed algorithm has two advantages compared to existing data-driven deterministic ADP algorithms for the OTP. First, our algorithm can guarantee optimality while achieving better performance in the aspects of time-saving and robustness to data. Second, the near-optimal control policy learned by our algorithm can be implemented without considering expected control and enable the system states to track the user-specified reference signals. Therefore, the tracking performance is guaranteed while simplifying the algorithm implementation. Furthermore, the convergence and stability of the proposed algorithm are strictly proved through theoretical analysis, in which the errors caused by neural networks (NNs) are considered. At the end of this article, the developed algorithm is compared with two representative deterministic ADP algorithms through a numerical example and applied to solve the tracking problem for a two-link robotic manipulator. The simulation results demonstrate the effectiveness and advantages of the developed algorithm.

Assessing the effect of invasive organisms on forests under information uncertainty: The case of pine wood nematode in continental Europe

Forests worldwide are experiencing increasingly intense biotic disturbances; however, assessing impacts of these disturbances is challenging due to the diverse range of organisms involved and the complex interactions among them. This particularly applies to invasive species, which can greatly alter ecological processes in their invaded territories. Here we focus on the pine wood nematode (PWN, Bursaphelenchus xylophilus), an invasive pathogen that has caused extensive mortality of pines in East Asia and more recently has invaded southern Europe. It is expected to expand its range into continental Europe with heavy impacts possible.Given the unknown dynamics of PWN in continental Europe, we reviewed laboratory and field experiments conducted in Asia and southern Europe to parameterize the main components of PWN biology and host-pathogen interactions in the Biotic Disturbance Engine (BITE), a model designed to implement a variety of forest biotic agents, from fungi to large herbivores. To simulate dynamically changing host availability and conditions, BITE was coupled with the forest landscape model iLand. The potential impacts of introducing PWN were assessed in a Central European forest landscape (40,928 ​ha), likely within PWN’s reach in future decades.A parameter sensitivity analysis indicated a substantial influence of factors related to dispersal, colonization, and vegetation impact, whereas parameters related to population growth manifested a minor effect. Selection of different assumptions about biological processes resulted in differential timing and size of the main mortality wave, eliminating 40%–95% of pine trees within 100 years post-introduction, with a maximum annual carbon loss between 1.3% and 4.2%. PWN-induced tree mortality reduced the Gross Primary Productivity, increased heterotrophic respiration, and generated a distinct legacy sink effect in the recovery period. This assessment has corroborated the ecological plausibility of the simulated dynamics and highlighted the need for new strategies to navigate the substantial uncertainty in the agent’s biology and population dynamics.

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.

Data-Driven Model Predictive Control for Uncalibrated Visual Servoing

This paper addresses the image-based visual servoing (IBVS) control problem with an uncalibrated camera, unknown dynamics, and constraints. A novel data-driven uncalibrated IBVS (UIBVS) strategy is proposed, incorporated with the Koopman-based model predictive control (KMPC) algorithm and the adaptive robust Kalman filter (ARKF). First, to alleviate the need for calibration of the camera’s intrinsic and extrinsic parameters, the ARKF with an adaptive factor is utilized to estimate the image Jacobian matrix online, thereby eliminating the laborious camera calibration procedures and improving robustness against camera disturbances. Then, a data-driven MPC strategy is proposed, wherein the unknown nonlinear dynamic model is learned using the Koopman operator theory, resulting in a linear Koopman prediction model. Only input–output data are used to construct the prediction model, and hence, the proposed approach is robust against model uncertainties. Furthermore, with a symmetric quadratic cost function, the proposed approach solves the quadratic programming problem online, and visibility constraints as well as joint torque constraints are taken into account. As a result, the proposed KMPC scheme can be implemented in real time, and the UIBVS performance degradation which arises from the control torque constraints can be avoided. Simulations and comparisons for a 2-DOF robotic manipulator demonstrate the feasibility of the proposed approach. Simulation results further validate that the computation time of the proposed approach is comparable to the one of kinematic-based methods.

Fast finite‐time adaptive backstepping containment control for high‐order stochastic nonlinear multi‐agent systems

SummaryIn this paper, the fast finite‐time backstepping containment control strategy is considered for high‐order stochastic multi‐agent systems. The addition of the finite‐time command filter avoids calculating explosion which occurs in the differential process of virtual control signals for the high‐order system on the traditional backstepping and makes convergence speed of control system faster. The influence of filtering errors generated by filter for control systems is eliminated by establishing error compensation systems. The fuzzy logic systems approximate unknown dynamics of systems. It proves the closed‐loop systems are practically fast finite‐time stable in mean square. The given simulation results show the effectiveness of the proposed control strategy.

Neural Network-Based Region Tracking Control for a Flexible-Joint Robot Manipulator

Abstract The present paper proposes a neural network-based adaptive region-tracking control strategy for a flexible-joint robot manipulator subjected to region constraints. The developed neural network-based control strategy can globally stabilize the robot manipulator and cope with model uncertainties and the external unknown bounded disturbances. Different from the existing literature, by using the sliding mode technology and the singular perturbation theory, the developed control strategy does not require the high-order derivatives of the link states such as jerk and acceleration since the high-order derivative information is not always available in practical applications. By using Lyapunov stability theory, it is proved that the proposed neural network-based control strategy can guarantee that all the parameter variables in the closed-loop system are bounded, and the flexible-joint robot manipulator with unknown dynamics can reach inside the dynamic region and also maintain the velocity matching with the desired moving region. Since the assumption of linearization of the unknown dynamic parameters is removed, the proposed control strategy does not require the calculation of the complex regression matrix. Therefore, the proposed method has great robustness and the ability of model generalization. Simulations are given to demonstrate the validity 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.

Actor–critic learning based PID control for robotic manipulators

In this paper, we propose a reinforcement learning structure for auto-tuning PID gains by solving an optimal tracking control problem for robot manipulators. Capitalizing on the actor–critic framework implemented by neural networks, we achieve optimal tracking performance, estimating unknown system dynamics simultaneously. The critic network is used to approximate the cost function, which serves as an indicator of control performance. With feedback from the critic, the actor network learns time-varying PID gains over time to optimize control input, thereby steering the system toward optimal performance. Furthermore, we utilize Lyapunov’s direct method to demonstrate the stability of the closed-loop system. This approach provides an analytical procedure for a stable robot manipulator system to systematically adjust PID gains, bypassing the ad-hoc and painstaking process. The resultant actor–critic PID-like control exhibits stable adaptive and learning capabilities while maintaining a simple structure and inexpensive online computational demands. Numerical simulations underscore the effectiveness and advantages of the proposed actor–critic neural network PID control.

Interval strategy-based regularization approach for force reconstruction with multi-source uncertainties

A force reconstruction method for uncertain structures instead of direct measurement is proposed in this paper. Considering the multi-source uncertainties as unknown-but-bounded (UBB) parameters including unknown structural dynamics and measurement errors, this study proposed a novel force reconstruction method using an interval strategy-based regularization approach with truncated singular value decomposition (TSVD). To overcome the drawbacks of incompleted models and limited information, the overall modelling and inversion of the interval force are reconstructed based on the non-probabilistic uncertainty theory. First, The interval uncertainty-based kernel function for force inversion is deduced using the second-order interval perturbation method, in which the uncertainties of the reconstructed force originate from the uncertain singular values and measurement errors. Based on the regularization of the TSVD, the interval bounds of the singular values can be accurately obtained. Combining the two typical regularization approaches, a novel interval strategy-based regularization approach is proposed to optimize the best regularization parameter based on the uncertain interval distribution of singular values. This novel strategy can not only balance the two typical regularization approaches but also reduce the burden of force inversion. Two numerical examples including a truss and space capsule are applied to access the proposed method, and the estimated accurate force can prove the effectiveness.

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.

Adaptive neural tracking control for upper limb rehabilitation robot with output constraints

AbstractThe authors investigate the trajectory tracking control problem of an upper limb rehabilitation robot system with unknown dynamics. To address the system's uncertainties and improve the tracking accuracy of the rehabilitation robot, an adaptive neural full‐state feedback control is proposed. The neural network is utilised to approximate the dynamics that are not fully modelled and adapt to the interaction between the upper limb rehabilitation robot and the patient. By incorporating a high‐gain observer, unmeasurable state information is integrated into the output feedback control. Taking into consideration the issue of joint position constraints during the actual rehabilitation training process, an adaptive neural full‐state and output feedback control scheme with output constraint is further designed. From the perspective of safety in human–robot interaction during rehabilitation training, log‐type barrier Lyapunov function is introduced in the output constraint controller to ensure that the output remains within the predefined constraint region. The stability of the closed‐loop system is proved by Lyapunov stability theory. The effectiveness of the proposed control scheme is validated by applying it to an upper limb rehabilitation robot through simulations.