Error Dynamics Research Articles

Feasibility analysis and saturation control for underactuated spacecraft formation reconfiguration in elliptic orbits

This work proposes a saturation control scheme for underactuated spacecraft formation reconfiguration in elliptic orbits without radial or along-track thrust. Firstly, the rank criterion method is applied to analyze the controllability and feasibility of formation reconfiguration by linearizing the linear time-varying dynamics to linear time-invariant ones. Based on the inherent coupling of the linear time-varying system, the underactuated error dynamics are presented for either underactuated case. Subsequently, the developed underactuated saturation controller can ensure that the time-varying system trajectory asymptotically converges to the specified configuration. The Lyapunov-based analysis presents the constraint conditions of controller parameters and the stable reconfiguration accuracy of the system states. Finally, numerical simulations for both underactuated scenarios are performed in the environment with J2 perturbation to verify the validity of the proposed underactuated control scheme.

Inter-robot management via neighboring robot sensing and measurement using a zeroing neural dynamics approach

This paper proposes a complex number representation method for dynamically recording robot positions and develops an optimization strategy for measuring and minimizing inter-robot distances in real-time. Based on this, the optimization strategy is transformed into finding the theoretical solution of the complex time-varying matrix equation by combining the leader–follower frameworks, and a complex zeroing neural dynamics (CZND) model is proposed for this objective. Meanwhile, the effectiveness of the proposed CZND model and the ideal trajectories of the follower robots are ensured and given through rigorous theoretical analyses. Subsequently, these theoretical findings are validated by two numerical experiments (four cases). In addition, the superiority of the CZND model for inter-robot management tasks is comparatively analyzed from three perspectives: initial positions, number of follower robots, and design parameters. Compared to conventional gradient-based neural network (CGNN) methods, the proposed CZND model, based on a dynamic error function (which is not required to be non-negative as in CGNN), demonstrates improved handling of the dynamic behavior of the system by utilizing the first-order time derivatives of matrices, resulting in lower residual errors in the implementation of inter-robot management. Specifically, for the same inter-robot management task, the steady-state error implemented by CZND is on the order of 10−4, whereas for CGNN, it is on the order of 10−1, indicating a significantly larger lagging error.

Trajectory tracking control for underactuated autonomous vehicles via adaptive dynamic programming

In this paper, the trajectory tracking control problem for underactuated autonomous vehicles moving in 2-D space is studied. Firstly, the trajectory tracking error dynamics with the equivalent point being the origin are given. Since both model and input uncertainties of vehicles are considered, a robust control problem is formulated by giving the extended trajectory tracking error dynamics. Through showing that a robust control law is equivalent to an optimal control law for a nominal system under some conditions, the robust control problem is transformed into an equivalent optimal control problem and a cost function composed of uncertainty bounds and discount factor is constructed. In order to solve the optimal control problem, a policy iteration-based ADP algorithm is proposed, in which two neural networks, called critic and actor networks, are applied respectively to describe the unknown value function and control law. The weights of the two networks are tuned through the gradient descent method at each iteration and the optimality and convergence properties are provided in the sequel. At last, simulation results are given to illustrate the validity of the proposed algorithm.

Event-Triggered Path Following Robust Control of Underactuated Unmanned Surface Vehicles with Unknown Model Nonlinearity and Disturbances

An effective path-following controller is a guarantee for stable sailing of underactuated unmanned surface vehicles (USVs). This paper proposes an event-triggered robust control approach considering an unknown model nonlinearity, external disturbance, and event-triggered mechanism. The proposed method consists of guidance and dynamic control subsystems. Based on the tracking error dynamics equations, the guidance subsystem is designed to achieve the guidance law. For the dynamic control subsystem, the radial basis function neural networks (RBFNNs) are designed to approximate the unknown model nonlinearity and external disturbances to improve the robustness of the proposed method. In addition, an event-triggered mechanism is constructed to reduce the triggering times. The closed-loop system is proven to be stable, and the effectiveness of the proposed method is illustrated through simulation results.

ПОРІВНЯЛЬНИЙ АНАЛІЗ ПОКАЗНИКІВ ЯКОСТІ ВІДПРАЦЮВАННЯ КУТОВОЇ ШВИДКОСТІ В ОДНОКОНТУРНІЙ СИСТЕМІ ПРОГНОЗНОГО КЕРУВАННЯ ДВИГУНОМ ПОСТІЙНОГО СТРУМУ

The results of a comparative study of two speed control systems for a DC motor with permanent magnets are presented: a cascaded system based on PI controllers, and a single-loop system developed on the basis of model predictive control methods. The research was carried out by the simulations for the case of speed trajectory tracking task. It is shown that, under the conditions of known parameters, the controller based on predictive control, designed as a system with one input and one output, unlike the system with PI controllers and compensations of derivatives of the reference signal, does not provide asymptotic speed trajectory tracking. The transients during constant load torque compensation are similar, both control schemes provide asymptotical speed regulation with similar performances. In the case of introduc-ing variations of DC motor moment of inertia, the levels of dynamic trajectory tracking errors become commensurate for both control systems. Unlike the system based on PI regulators, the controller based on model predictive control does not need to measure the armature current and provides improved dynamics in voltage limiting modes. Ref. 17, fig. 7. Keywords: model predictive control, DC motor, speed trajectory tracking, PI-controller.

Time Series Modeling and Forecasting of US Consumer Price Index Using WTI Crude Oil Price

This study aims to forecast U.S. inflation by using crude oil prices as a key variable. WTI crude oil price and Consumer Price Index Year-over-Year (CPI YoY) data from 2000 to 2022 are extracted to construct a time series model. The empirical analysis relies on Autoregressive Integrated Moving Average (ARIMA) model and regression to formulate forecasts based on historical patterns and error dynamics. The study finds out that compared to the automatically generated ARIMA model, using fitted values of the WTI time series model to predict CPI YoY through a multi-variable model is better. According to the prediction, the CPI YoY forecast for 2023 reveals a decreasing tendency in 2023, implying a slower rate of increase in U.S. inflation. The result provides insights into economic conditions, helps decision-making, and mitigates the potential risks associated with price fluctuations. Overall, the research contributes to a deeper understanding of the dynamics between energy markets and inflationary pressures in the United States.

Robust adaptive smooth variable structure Kalman filter for spacecraft attitude estimation

This paper proposes a novel robust adaptive filter that combines smooth variable structure filter and extended Kalman filter for the spacecraft attitude estimation with model uncertainty originating from gyro drift, parameter error, and installation error. The proposed filter employs the extended Kalman filter based on quaternion and fuses an adaptive factor and smooth variable structure filter to improve robustness to the model uncertainty and noise. To improve the robustness of the extended Kalman filter, an adaptive factor that tunes the predicted covariance matrix is utilized to design the attitude estimation strategy. Moreover, to further decrease the impact of the suddenly rapid maneuvering and improve its robust effect of model uncertainty induced by dynamic error, gyro drift, and so on, a smooth variable structure estimation strategy founded on sliding mode theory is derived and utilized for the satellite attitude estimation. Thereby, a novel filtering algorithm is proposed by incorporating an adaptive factor and a smooth variable structure estimation strategy. Simulation results indicate that our proposed algorithm delivers exceptional robustness and achieves high precision and accuracy in satellite attitude estimation compared with the traditional extended Kalman filter.

Outlier-Resistant Recursive Security Filtering for Multirate Networked Systems Under Fading Measurements and Round-Robin Protocol

This paper investigates the recursive filtering problem with fading measurements and cyber attacks for multisensor multirate networked systems (MRNSs) under Round-Robin protocol (RRP). By exploiting the lifting technique, the sampling periods for both sensors and the state of the system are uniformed. It is assumed that the phenomenon of fading measurements which better describes practical engineering arises stochastically, and the attenuation coefficients of which are described by a set of random variables with known statistical properties. In order to fully utilize the limited communication resources, RRP is introduced in the sensor-to-filter channel. Considering the measurement outliers, a saturation function is adopted in the filter structure to suppress the anomalous innovations, so as to reduce the negative impact of the outliers. By means of matrix difference equation, an upper bound is first obtained on the filtering error covariance, and the filter gain is designed to minimize the obtained upper bound by partial derivation. Moreover, the exponential boundedness of the filtering error dynamics is analyzed in the mean square sense. Finally, a numerical simulation example is given to demonstrate the validity of the proposed recursive security filtering scheme.

Guaranteed Set-Membership Estimation for Local Nonlinear Uncertain Fuzzy Systems Subject to Partially Decouplable Unknown Inputs

Local nonlinear fuzzy systems are useful for control solutions due to their ability to handle unmeasurable/inexact premise variables and reduce computational complexity. However, their estimation problems still require further development. This paper addresses this issue by investigating set-membership estimation for a class of discrete-time local nonlinear uncertain Takagi–Sugeno fuzzy systems with guaranteed performance. We propose a new observer architecture that solves partially decouplable unknown inputs and converts nonlinear error dynamics into a linear parameter-varying type. Using the systematic <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _\infty$</tex-math></inline-formula> -technique, the design conditions in the form of linear matrix inequalities ensure stability and output performance of the state estimation. We also derive a straightforward and effective zonotopic analysis method, considering the fuzzy and local nonlinear context, for less conservative results without using any specific interval set computation. Furthermore, a fast fault detection logic is proposed as an application of the set-membership estimation. Finally, we demonstrate the feasibility and advantages of our approach through three compelling examples, showcasing its efficacy in different scenarios.

Analysis and Chaos Control and Synchronization of the Nonlinear Newton–Leipnik System Via Feedback Adaptive Control Techniques

This paper presents the system analysis and chaos control synchronization of the Newton–Leipnik system. Uniqueness and existence solutions (equilibrium points or fixed points) of Newton–Leipnik system have been discussed and local analysis of the system at each equilibrium points is studied. Lyapunov exponents and Kaplan–Yorke dimensions, bifurcation diagrams and poincare sections are analyzed and plotted to establish the presence of chaos in the system. Control feedback techniques are simulated in the nonlinear Newton–Leipnik system. Controlling chaos of systems to find the desired result are established. Synchronization methodologies of two identical integer-order Newton–Leipnik systems are yielded applying adaptive control technologies which have been verified through plotting the graphs of tracking the trajectories of master to slave systems, parameter identification results and synchronization of error dynamics diagrams of Newton–Leipnik systems. These findings offer valuable insights and tools applicable to various scientific and technological domains. These results highlight the originality of our study and deepen our understanding of chaos in Newton–Leipnik systems, offering practical applications and enhanced insights for researchers and scientists in chaos analysis.

A Sampling Control Framework and Its Applications to Robust and Adaptive Control

In this paper, we propose a novel sampling control framework based on the emulation technique where the sampling error is regarded as an auxiliary input to the emulated system. Utilizing the supremum norm of sampling error, the design of periodic sampling and event-triggered control law renders the error dynamics bounded-input-bounded-state (BIBS), and when it is coupled with system dynamics, achieves global or semi-global stabilization. The proposed framework is then extended to tackle the stabilization problem for a system where the state of dynamic uncertainty is not available for feedback and the dynamics is subject to parameter uncertainties. The proposed framework is further extended to solve two classes of event-triggered adaptive control problems where the emulated closed-loop system does not admit an input-to-state stability (ISS) Lyapunov function. For the first class of systems with linear parameterized uncertainties, even-triggered global adaptive stabilization is achieved without the global Lipschitz condition on nonlinearities as often required in the literature. For the second class of systems with uncertainties whose bound is unknown, the event-triggered adaptive (dynamic) gain controller is designed for the first time. Finally, theoretical results are verified by three numerical examples.

Implementation of a Robust PMAE Algorithm to Limit Large Gain Variation in a Fuel-Cell Integrated EV Charging Architecture

This paper proposes an adaptive error convergence technique to improve the charging dynamics of an electric vehicle (EV) charging system in a grid-integrated proton-exchange membrane fuel cell (PEMFC) architecture. The fuel cell is most often characterized by its slow dynamics during multiple load transients and preferably operated as an auxiliary energy source in EV charging architecture. The delayed response affects the overall charging dynamics with further controller phase lag and non-linear system parameters to induce a significant convergence error during reference command tracking. To effectively control multi-source integrated charging dynamics in an EV charging architecture, a projection-modified adaptive estimation (PMAE) algorithm is proposed in this paper. The control algorithm establishes a variable gain adaptation within a bounded error contour and updates the controller gains based on the tracking error dynamics gradient. The fuel cell, supporting other energy resources, provides a stronger charging resiliency with a duty-modified control technique at the EV charging station. To validate the effectiveness of the controller implementation, a grid-integrated multi-objective EV charging prototype is designed and developed for grid-to-vehicle (G2V) and vehicle-to-grid (V2G) at variable operating conditions.

High-Order Fully Actuated Control Approaches of Flexible Servo Systems Based on Singular Perturbation Theory

This work presents a high-order fully actuated (HOFA) control approach for flexible servo (FS) systems via singular perturbation (SP) method. The HOFA approach has the advantages of simplicity and intuition on the control design of FS systems due to its full-actuation feature, but suffers the high-order derivative problem of signals. To overcome this difficulty, this article separates the original system via the SP approach with two time-scale properties. By using the slow model, the state feedback control with dynamical compensator is designed via HOFA approach to obtain the desired tracking error dynamics. It not only avoids the high-order derivatives of signals but also improves the disturbance rejection. Based on the fast model, a simple active damping control is applied for the resonance suppression, aiming at obtaining larger control gains to further increase the control accuracy. SP theory is employed for stability analysis of the full system in the presence of uncertainties. Simulations and experiments are carried out to verify the effectiveness of the proposed approach.

Stable approximate Q-learning under discounted cost for data-based adaptive tracking control

In this paper, the stability of tracking error dynamics under the data-based discounted iterative Q-learning is investigated. First, a novel performance index with a discount factor is introduced into the iterative Q-learning-based tracking control. Then, considering the approximation errors caused by the Q-function approximator, the finite error bound between the iterative and optimal Q-functions is established. Moreover, based on the new stability analysis, the selection rule of the discount factor is developed, which ensures that the corresponding optimal control policy is admissible. Next, to ensure the stability of the tracking error dynamics under iterative control policies, the stability condition about the approximate Q-function is established. It is guaranteed that iterative control policies derived from the critic network drive the tracking error to zero. Additionally, considering the adopted policy function approximator, the upper bound function of the approximation errors is developed. It is ensured that the trained action network stabilizes the tracking error dynamics. Finally, a simulation example is utilized to implement the data-based discounted iterative Q-learning and verify the present theoretical results.

Accuracy Assessment of Charge-Mode Accelerometers Using Multivariate Regression of the Upper Bound of the Dynamic Error

This paper presents the mathematical basis and related procedures for the regression of the upper bound of the dynamic error produced by charge-mode accelerometers. The integral-square error obtained in response to simulation signals with one constraint appearing at the input of the accelerometer is considered. Physical models of accelerometers are presented with related equations and mathematical formulae that make it possible to obtain the error and the corresponding constrained signal. Examples of the regression for predefined values of the accelerometer parameters are also discussed. The solutions presented in this paper may contribute to increasing the accuracy of the charge-mode accelerometers commonly used in energy systems. Development of the functions approximating the integral-square error for the given ranges of accelerometer parameters constitutes the original contribution of this paper.

Dynamic matching error of stress sensors in concrete structures

The matching error between the sensors and media is an important factor in determining the reliability of measurement results. To investigate the dynamic matching error between the sensors and the media, the causes of static and dynamic matching errors and their influence trend are theoretically analyzed in this study; and the dynamic matching error between the sensor and the concrete structure under explosion load through test and numerical simulation are quantitatively analyzed. Our results show that the difference between the wave impedance of the sensor and the medium is the main factor affecting the dynamic matching error; the static matching error is usually constant, while the dynamic matching error is a variable related to the stress wavelength. A larger ratio of the stress wavelength to the thickness of the sensor correlates to a lower dynamic matching error. The dynamic matching error with the stress signal rise time increases and decreases.

Smooth Sliding Mode Control for Path Following of Underactuated Surface Vehicles Based on LOS Guidance

In this paper, a solution to the problem of following a curved path for underactuated unmanned surface vehicles (USVs) with unknown sideslip angle and model uncertainties is studied. A novel smooth sliding mode control (SSMC) based on a finite-time extended state observer (FTESO) for heading control is proposed. Firstly, the model of a USV with rudderless double thrusters is established. Secondly, the path-following error dynamics of a USV is established in a path-tangential reference frame. Thirdly, a finite-time observer is introduced to estimate the unidentified sideslip angle, and the line-of-sight (LOS) guidance law is applied to produce the desired heading angle. Finally, an SSMC controller is proposed to force USV tracking at the desired heading angle and surge speed, in which FTESO is used to estimate and compensate the unknown disturbance in sliding mode dynamics. The theoretical analysis for FTESO-SSMC verifies that the controller can provide finite-time convergence to and stability on the sliding surface. Simulation studies and contrast test are conducted to demonstrate the robustness and rapidity of the proposed FTESO-SSMC controller.

Dynamic performance analysis of a gear transmission system due to cavitation in gerotor pump

In this work, a dynamic model considering time-varying mesh stiffness and backlash was proposed and a test rig was built to investigate the vibration behavior of the idle gear set in a gerotor pump. The effects of input shaft speed, torque fluctuation, and gear tooth backlash on the dynamic performance of gerotor pump were analyzed according to the numerical and experimental results. Results demonstrate that when the torque fluctuation is neglected, the dynamic transmission error of drive gear is dominated by the first three mesh harmonic components; however, the RMS values of vibration acceleration have high frequency characteristics. When the torque fluctuation is considered, the dynamic responses of gerotor pump are modulated by the torque fluctuation. The effect of tooth backlash on the dynamic performance of gerotor pump is limited and mostly depended on the torque fluctuation condition. The gerotor pump noise is dominated by the low frequency component around the mesh frequency. The vibration energy can be divided into two parts in the frequency domain. In the low frequency band, the vibration energy is caused by the mechanical vibration. However, in the high frequency band, the cavitation phenomena may cause the concentration of the vibration energy and resonant of pump structure.

Observer-based event-triggered recursive optimal tracking control for a class of strict-feedback nonlinear systems

In this paper, an innovative event-triggered optimal tracking control algorithm is proposed for input saturated strict-feedback nonlinear systems with unknown dynamics. In order to reduce the requirement of configuring a complete suit of sensors and enhance the reliability of the controlled system, a neural networks (NNs) based adaptive state observer is developed firstly to reconstruct the system states. Subsequently, based on the state estimation information, a hybrid-triggered feedforward controller is designed to transform the original tracking control problem into an equivalent regulation issue, which is then solved by developing an event-triggered optimal controller. Therefore, the final controller consists of a hybrid-triggered feedforward controller and an event-triggered optimal controller. In order to make the actual input signals of the two controllers be updated simultaneously, a synchronization-oriented triggering rule is established by using multiple triggering errors. By virtue of this unique framework, the proposed control scheme can not only minimize the predefined cost function, but also greatly reduce the data transmission. What is more, the convergence properties of the proposed control strategy are achieved by using Lyapunov theory. It is important to note that unlike the widely adopted observer-controller framework, where the separation principle holds for the design of the state observer, there is a considerable coupling relationship between the error dynamics of the state observer and the event-triggered optimal controller in this paper. The distinguishing feature of the proposed method is its ability to ensure a satisfactory level of precision in both state estimation and tracking control, even in the presence of control saturation issues. At last, the proposed control strategy is applied to the tracking control problem of a high-order robot system and marine surface vehicle to demonstrate its effectiveness.

Extended Calibration of Charge Mode Accelerometers to Improve the Accuracy of Energy Systems

This paper presents an extended calibration procedure for mode accelerometers, which makes it possible to compare the accuracy of sensors of this type from different manufacturers. This comparison involves determining the upper bound on dynamic error for a given quality criterion, i.e., the integral square error and absolute error. Therefore, this article extends the standard calibration implemented in engineering practice using tests, providing a value for the upper bound on dynamic error as an additional parameter describing the accelerometer under consideration. This paper presents the theoretical basis for this type of solution, which is partly based on measurement data obtained from a standard calibration process and on the results of parametric identification. The charge mode accelerometer is considered here because this type of sensor is commonly used in the energy industry, as it can operate over a wide range of temperatures. The calculation results presented in this paper were obtained using MathCad 5.0 software, and the tests were carried out using an accelerometer of type 357B21. In the experimental part of this article (Results of Extended Calibration section), values for the upper bound of the dynamic error were determined for two error criteria and constrained simulation signals related to these errors. The impact of interference on the results of accelerometer tests was omitted in this paper.