Unknown System Dynamics Research Articles

Predictor-Based Neural Attitude Control of A Quadrotor With Disturbances

An attitude control issue is concerned for a quadrotor with external disturbances in this paper. For unknown system dynamics, predictor-based neural networks (NNs) are introduced, where prediction errors, angular velocities, are constructed, instead of tracking errors, for updating NNs' weights. This replacement reduces the occurrence of high-frequency oscillations in NNs' approximation. With this improved NNs, a predictorbased NN disturbance observer is then developed for compensation for external disturbances and NNs' approximation errors, and a normalization learning technique is employed for reduction of the number of learning parameters. A predictor-based neural attitude control strategy is proposed for a quadrotor with external disturbances. Furthermore, measurement noise are taken into account in our predictor-based neural attitude control strategy. The Lyapunov-based stability analysis shows that all closed-loop signals in the designed attitude system are semiglobally bounded. A numerical simulation and a hardware-in-loop experiment as well as outdoor flight verify the effectiveness of the proposed anti-disturbance attitude control strategy.

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 Tampered-Data Recovery Strategy With Encoding Against Stealthy Attack for Unknown Discrete-Time Systems.

This study addresses a tampered-data recovery problem for linear discrete-time systems with completely unknown system dynamics under stealthy attacks. The basic idea is to identify the stealthy attack, that lies in any of attack-stealthy subspaces, and compensate for it. Different from the existing sparse recovery methods which are applicable to nonstealthy sparse attacks, a novel encoding scheme, where a set of subdecoding matrices is designed specifically for each 1-D attack-stealthy subspace, is developed so that the parameters of the stealthy attack can be identified via a subspace projection technique. A necessary and sufficient condition of determining the targeted subspace by using n parallel attack identification filters is established for this encoding scheme. Especially, a composite encoding matrix characterizes the lower and upper boundaries of the recovery error covariance's trace. A simulation example of a flight vehicle illustrates the efficiency of the proposed approach.

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.

Online and Robust Intermittent Motion Planning in Dynamic and Changing Environments.

In this article, we propose RRT-Q X∞ , an online and intermittent kinodynamic motion planning framework for dynamic environments with unknown robot dynamics and unknown disturbances. We leverage RRT X for global path planning and rapid replanning to produce waypoints as a sequence of boundary-value problems (BVPs). For each BVP, we formulate a finite-horizon, continuous-time zero-sum game, where the control input is the minimizer, and the worst case disturbance is the maximizer. We propose a robust intermittent Q-learning controller for waypoint navigation with completely unknown system dynamics, external disturbances, and intermittent control updates. We execute a relaxed persistence of excitation technique to guarantee that the Q-learning controller converges to the optimal controller. We provide rigorous Lyapunov-based proofs to guarantee the closed-loop stability of the equilibrium point. The effectiveness of the proposed RRT-Q X∞ is illustrated with Monte Carlo numerical experiments in numerous dynamic and changing environments.

Learning Robust Predictive Control: A Spatial-Temporal Game Theoretic Approach.

This article investigates robust predictive control problem for unknown dynamical systems. Since the dynamics unavailability restricts feasibility of model-driven methods, learning robust predictive control (LRPC) framework is developed from the aspect of time consistency. Under feedback-like control causality, the robust predictive control is then reconstructed as spatialbKKtemporal games, and we guarantee stability through time-consistent Nash equilibrium. For gradation clarity, our framework is specified as four-follow contents. First, multistep feedback-like control causality is drawn from time series analysis, and Takens' theorem provides theoretical support from steady-state property. Second, control problem is reconstructed as games, while performance and robustness partition the game into temporal nonzero-sum subgames and spatial zero-sum ones, respectively. Next, multistep reinforcement learning (RL) is designed to solve robust predictive control without system model. Convergence is proven through bounds analysis of oscillatory value functions, and properties of receding horizon are derived from time consistency. Finally, data-driven implementation is given with function approximation, and neural networks are chosen to approximate value functions and feedback-like causality. Weights are estimated with least squares errors. Numerical results verify the effectiveness.

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.

Adaptive neural network fixed‐time control for an uncertain robot with input nonlinearity

AbstractThe article introduces an innovative adaptive fixed‐time control strategy designed for a robot system grappling with challenges like actuator saturation and model uncertainty. Two strategies are explored: model‐based control and neural networks control. In instances of model uncertainty, neural networks are leveraged to contend with the unknown dynamics of the robot system. These networks undergo training to approximate the elusive model parameters. Through this neural network approach, we establish adaptive laws grounded in fixed‐time convergence, ensuring that system tracking errors converge to a confined range near zero within a predetermined time frame. To tackle the issue of actuator saturation, an enhanced auxiliary system is introduced. This auxiliary system is tailored to counterbalance the adverse impacts of actuator saturation, thereby augmenting the tracking performance of the robot system. The proposed control policy is rigorously analyzed using Lyapunov theory, demonstrating that the system's tracking errors converge within a fixed time frame. To validate the efficacy of the proposed methodology, both numerical simulations and practical experiments are conducted, affirming the effectiveness of the approach.

Neural Network-Based Adaptive Sigmoid Circular Path-Following Control for Underactuated Unmanned Surface Vessels under Ocean Disturbances

This study describes a circular curve path-following controller for an underactuated unmanned surface vessel (USV) experiencing unmodeled dynamics and external disturbances. Initially, a three degrees of freedom kinematic model of the USV is proposed for marine environmental disturbances and internal model parameter deterrence. Then, the circular path guidance law and controller are designed to ensure that the USV can move along the desired path. During the design process, a proportional derivative (PD)-based sigmoid fuzzy function is applied to adjust the guidance law. To accommodate unknown system dynamics and perturbations, a radial basis function neural network and adaptive updating laws are adopted to design the surge motion and yaw motion controllers, estimating the unmodeled hydrodynamic coefficients and external disturbances. Theoretical analysis shows that tracking errors are uniformly ultimately bounded (UUB), and the closed-loop system is asymptotically stable. Finally, the simulation results show that the proposed controller can achieve good control effects while ensuring tracking accuracy and demonstrating satisfactory disturbance rejection capability.

Adaptive neural identification and non-singular control of pure-feedback nonlinear systems

This paper proposes a new constructive identification and adaptive control method for nonlinear pure-feedback systems, which remedies the ’explosion of complexity’ and potential control singularity encountered in the traditional adaptive backstepping controllers. First, to avoid using the backstepping recursive design, alternative state variables and the corresponding coordinate transformation are introduced to reformulate the pure-feedback system into an equivalent canonical model. Then, a high-order sliding mode (HOSM) observer is used to reconstruct the unknown states for this canonical model. To remedy the potential singularity in the control, the unknown system dynamics are lumped to derive an alternative identification structure and one-step control synthesis, where two radial basis function neural networks (RBFNN) are adopted to online estimate these lumped dynamics. In this framework, the online estimation of control gain is not in the denominator of controller, and thus the division by zero in the controllers is avoided. Finally, a new online learning algorithm is constructed to obtain the RBFNNs’ weights, ensuring the convergence to the neighborhood of true values and allowing accurate identification of unknown dynamics. Theoretical analysis elaborates that the convergence of both the tracking error and the estimation error is obtained simultaneously. Simulations and practical experiments on a hydraulic servo test-rig verify the effectiveness and utility of the suggested methods.

Research and analysis of manipulator control method based on deep learning

Aiming at the stability and accuracy of grasping objects, this paper studies the adaptive neural network control and learning of manipulator control system with unknown system dynamics. First, a stable adaptive neural network (NN) controller is designed, and the unknown closed-loop system dynamics of the manipulator is approximated by using radial basis function (RBF) neural network. The LSTM long and short memory algorithm is introduced, and the RBF based hybrid neural network model is constructed. The LSTM algorithm is used to design the input gate, forgetting gate and output gate structures to suppress the gradient expansion problem during coordinate data training, and accurate trajectory correction instructions are given. Lyapunov stability theorem is used to analyze stability. Partial persistent excitation (PE) conditions of some internal signals in the closed-loop system are satisfied in the control process of tracking the circular reference trajectory. Under the PE condition, the proposed adaptive NN controller can accurately identify the dynamic uncertainties of the manipulator in the stability control process. Then, a new NN learning control method is proposed, which effectively uses the knowledge learned without re adapting to the unknown manipulator control system dynamics to achieve closed-loop stability and improve control performance. The effectiveness of the proposed method is studied through simulation.Keyboard

Chaotic signal denoising based on energy selection TQWT and adaptive SVD.

Aiming at the problem of denoising chaotic signals with low signal-to-noise ratio and unknown dynamic system parameters, a new chaotic signal denoising algorithm is proposed, which combines adjustable Q-factor wavelet transform (TQWT) and adaptive singular value decomposition (ASVD). This method uses TQWT to decompose the noisy chaotic signal. According to the maximum wavelet entropy theory and energy threshold rule, the subband of TQWT is accurately divided into signal subband and noise subband. For noise subbands, adaptive SVD is used to denoise them, to achieve preliminary denoising. In ASVD, the standard deviation of the singular value subset is used to determine the effective reconstruction order to improve the noise suppression effect. To further remove noise in the signal subband, TQWT reconstruction is performed on the preliminarily denoised signal, and ASVD is used to denoise the reconstructed signal again to obtain the chaotic signal after secondary denoising. Chua's simulated signal and four kinds of underwater radiated noise measured by TQWT-ASVD were denoised, and compared with the SVD denoising method, TQWT denoising method, complete ensemble empirical mode decomposition with adaptive noise and threshold denoising method (CEEMDAN-WT) and modified ensemble empirical mode decomposition combined with least squares denoising method (MEEMD-LMS), The experimental results show that the TQWT-ASVD method can reduce the noise of chaotic signals more effectively. Compared with SVD, TQWT, CEEMDAN-WT, MEEMD-LMS, and Chua's signal denoising method, the signal-to-noise ratio (SNR) of this method increased by 23.22%, 26.46%, 18.79%, 16.11% the root mean square error (RMSE) decreased by 32.53%,39.48%, 30.96%, 27.94%, and the row entropy (PE) decreased by 40.44%, 41.96%, 22.78%, 20.59%; After reducing the radiation noise of cargo ships, the PE value of this method is reduced by 13.91%, 10.18%, 10.88%, 8.68% respectively, and the FE value is reduced by 33.66%, 31.42%, 26.98%, 21.32% respectively.

Optimal tracking control for unknown nonlinear systems with uncertain input saturation: A dynamic event-triggered ADP algorithm

This paper is devoted to proposing a novel dynamic event-triggered adaptive dynamic programming (ADP) algorithm to tackle the tracking control problem of unknown nonlinear systems with uncertain input saturation. Initially, an augmented system is established to address the investigated optimal tracking control issue with a discounted cost function. An online identifier based on neural networks (NNs) is designed to recover the unknown system dynamics. Furthermore, the controller design consists of two parts, including the optimal control policy for the nominal system and the NN-based feedforward compensator. In particular, the latter leverages adaptive NN techniques to cope with uncertain input constraints which can be deemed as uncertain saturation nonlinearities. A critic NN is constructed to obtain the approximate optimal control policy for the nominal system. Moreover, rather than traditional time-triggered and static event-triggered control schemes, an adaptive dynamic event-triggering condition is designed to determine the system sampling as well as the controller execution to further reduce transmission and computation burden. The introduction of an internal dynamic variable in possession of a positive constant lower bound can realize the dynamic adjustment of triggering threshold and effectively exclude Zeno behavior. Notice that the weights of identifier NN and critic NN are updated simultaneously, only at the event-triggering instants. Subsequently, the Lyapunov-based theoretical analysis is conducted to confirm the uniform ultimate boundedness of the tracking error and all the NN weight estimation errors. Eventually, the feasibility and effectiveness of the developed algorithm are validated by means of two simulation examples.

Deterministic learning-based neural identification and knowledge fusion

Recent deterministic learning methods have achieved locally-accurate identification of unknown system dynamics. However, the locally-accurate identification means that the neural networks can only capture the local dynamics knowledge along the system trajectory. In order to capture a broader knowledge region, this article investigates the knowledge fusion problem of deterministic learning, that is, the integration of different knowledge regions along different individual trajectories. Specifically, two kinds of knowledge fusion schemes are systematically introduced: an online fusion scheme and an offline fusion scheme. The online scheme can be viewed as an extension of distributed cooperative learning control to cooperative neural identification for sampled-data systems. By designing an auxiliary information transmission strategy to enable the neural network to receive information learned from other tasks while learning its own task, it is proven that the weights of all localized RBF networks exponentially converge to their common true/ideal values. The offline scheme can be regarded as a knowledge distillation strategy, in which the fused network is obtained by offline training through the knowledge learned from all individual system trajectories via deterministic learning. A novel weight fusion algorithm with low computational complexity is proposed based on the least squares solution under subspace constraints. Simulation studies show that the proposed fusion schemes can successfully integrate the knowledge regions of different individual trajectories while maintaining the learning performance, thereby greatly expanding the knowledge region learned from deterministic learning.

Robust Adaptive Learning Control of Space Robot for Target Capturing Using Neural Network.

This article investigates the robust adaptive learning control for space robots with target capturing. Based on the momentum conservation theory, the impact dynamics is constructed to derive the relationship of generalized velocity in the pre-impact and post-impact phase. Considering the nonlinear dynamics with contact impact, the robust control using nonsingular terminal sliding mode (NTSM) and fast NTSM is designed to achieve the fast realization of the desired states. Furthermore, for the unknown dynamics of the combination system after capturing a target, the adaptive learning control is developed based on neural network and disturbance observer. Through the serial-parallel estimation model, the prediction error is constructed for the update of adaptive law. The system signals involved in the Lyapunov function are proved to be bounded and the sliding mode surface converges in finite time. Simulation studies present the desired tracking and learning performance.

Model-Free Adaptive Sliding Mode Control Method for Unmanned Surface Vehicle Course Control

A novel data-driven-based adaptive sliding-mode control scheme is proposed for unmanned surface vehicle course control in the presence of disturbances. The proposed method utilizes the model-free adaptive control (MFAC) theory. On account of the unknown dynamics of the USV course system, the control scheme is only established by online input and output information of the system. Based on a model-free adaptive control scheme, the system disturbance estimation technique is applied to compensate for the disturbances in the established compact form dynamic linearization data model. The controller is designed and combined with the sliding mode method, and a second-order switching surface with a fast terminal sliding function is employed to achieve finite-time convergence. Furthermore, an analysis of the stability of the control system is provided. Finally, MATLAB simulations are implemented to verify the validity and robustness of the proposed control scheme by comparing it with PID and typical model-free adaptive sliding mode control.

Learning-based sliding mode synchronization for fractional-order Hindmarsh-Rose neuronal models with deterministic learning.

In recent years, extensive research has been conducted on the synchronous behavior of neural networks. It is found that the synchronization ability of neurons is related to the performance of signal reception and transmission between neurons, which in turn affects the function of the organism. However, most of the existing synchronization methods are faced with two difficulties, one is the structural parameter dependency, which limits the promotion and application of synchronous methods in practical problems. The other is the limited adaptability, that is, even when faced with the same control tasks, for most of the existing control methods, the control parameters still need to be retrained. To this end, the present study investigates the synchronization problem of the fractional-order HindmarshRose (FOHR) neuronal models in unknown dynamic environment. Inspired by the human experience of knowledge acquiring, memorizing, and application, a learning-based sliding mode control algorithm is proposed by using the deterministic learning (DL) mechanism. Firstly, the unknown dynamics of the FOHR system under unknown dynamic environment is locally accurately identified and stored in the form of constant weight neural networks through deterministic learning without dependency of the system parameters. Then, based on the identified and stored system dynamics, the model-based and relearning-based sliding mode controller are designed for similar as well as new synchronization tasks, respectively. The synchronization process can be started quickly by recalling the empirical dynamics of neurons. Therefore, fast synchronization effect is achieved by reducing the online computing time. In addition, because of the convergence of the identification and synchronization process, the control experience can be constantly replenished and stored for reutilization, so as to improve the synchronization speed and accuracy continuously. The thought of this article will also bring inspiration to the related research in other fields.

Learning-based model predictive control for two-point incremental sheet forming

Two-point incremental sheet forming (TPIF) is known to provide higher geometric accuracy compared to single point incremental sheet forming (SPIF). However, it may not always ensure that the maximum allowable absolute geometric error for complex industrial parts is below 0.75 mm. To overcome this challenge, we propose an on-line learning-based model predictive control (MPC) approach to enhance accuracy in TPIF. In this proposed design, the controller parameters can be updated adaptively and effectively on-line, based on historical data, current state, and system inputs, even with unknown system dynamics in future steps. The developed controller is experimentally validated using three benchmark shapes, namely a dog-bone shape, a hemispherical shape, and a water-drop shape, each with different geometric features, in TPIF. The experimental findings demonstrated that the percentage of errors below 0.75 mm can be significantly increased from less than 42 % without control to over 92 % with control for all the tested shapes, while maintaining the safety of the manufacturing process. This highlights the effectiveness and robustness of the developed MPC controller in achieving higher precision for complex parts. This will unlock TPIF capability to form custom high-accuracy parts, thereby enabling ISF as a commercially viable process with increased robustness and accuracy in the future.

Adaptive-Neuro-Learning Tracking Control for the Permanent Magnet Synchronous Motor with Full-State Prescribed Performances and Time Delays

High-performance tracking control is essential for permanent magnet synchronous motors in the perturbed environment. Given this, a new hybrid controller is proposed in this study for a permanent magnet synchronous motor with load disturbances as well as time delays. First, a new prescribed performance method is proposed to achieve the full-state performance constraints with load disturbances. Second, a time-varying filter is proposed for the first time to avoid the “complexity explosion” problem of the backstepping method while guaranteeing the convergence of the filtering error. Third, by combining Lyapunov–Krasovskii functionals with adaptive neural networks, the time-delay disturbance and unknown nonlinear dynamics of the control system have been solved. The stability analysis proves that all signals in the closed-loop system are bounded. To show the effectiveness of the intelligent controller, the comparison simulations are given to confirm the advantages of the proposed adaptive neural control scheme.

Robust prescribed performance trajectory tracking control with improved fast nonsingular terminal sliding surface of robot manipulators

This paper investigates the high-precision model-free control of robot manipulators. To this end, a model-free robust prescribed performance controller with an improved fast nonsingular terminal sliding mode surface (IFNTSM) and unknown system dynamics estimator (USDE) has been designed. An USDE method is employed to estimate model informations and further to achieve model-free control, which can avoid complex mathematical model calculation. Compared with some other model-free control methods like time-delay control (TDC) and neural-networks control (NNC), the USED does not require acceleration signal and is easy to implement. Then the prescribed performance control (PPC) has been used to limit error trajectory, which means the error can be pre-limit in a constraint band. A new transform function (TF) is designed for PPC, it has unlimited domain and can still maintain stability although tracking error will exceed PPC boundary sometimes, but the PPC with traditional TF will crash in this case. This is a great improvement for the stability of system compared with traditional TF. An improved fast nonsingular terminal sliding mode surface (IFNTSM) with a new adaptive law is proposed to accelerate convergence rate and improve steady-state accuracy on the sliding manifold. Finally, a practical finite-time controller (PFTC) has been constructed to drive sliding variable to a set centered on zero within a finite time, which means the convergence time can be calculated depending on the initial state. The transient response time can be shorten compared with traditional asymptotic stable. Abundant simulations and experimental results also verified the effectiveness of the proposed scheme.