Stability Analysis Of Systems Research Articles

The stability of present-day Antarctic grounding lines – Part 1: No indication of marine ice sheet instability in the current geometry

Abstract. Theoretical and numerical work has shown that under certain circumstances grounding lines of marine-type ice sheets can enter phases of irreversible advance and retreat driven by the marine ice sheet instability (MISI). Instances of such irreversible retreat have been found in several simulations of the Antarctic Ice Sheet. However, it has not been assessed whether the Antarctic grounding lines are already undergoing MISI in their current position. Here, we conduct a systematic numerical stability analysis using three state-of-the-art ice sheet models: Úa, Elmer/Ice, and the Parallel Ice Sheet Model (PISM). For the first two models, we construct steady-state initial configurations whereby the simulated grounding lines remain at the observed present-day positions through time. The third model, PISM, uses a spin-up procedure and historical forcing such that its transient state is close to the observed one. To assess the stability of these simulated states, we apply short-term perturbations to submarine melting. Our results show that the grounding lines around Antarctica migrate slightly away from their initial position while the perturbation is applied, and they revert once the perturbation is removed. This indicates that present-day retreat of Antarctic grounding lines is not yet irreversible or self-sustained. However, our accompanying paper (Part 2, Reese et al., 2023a) shows that if the grounding lines retreated further inland, under present-day climate forcing, it may lead to the eventual irreversible collapse of some marine regions of West Antarctica.

Quaternion version of the Itô’s formula

The classic Itô’s formulas in both real and complex fields are widely used to cope with the stability analysis of various stochastic systems. In this paper, the quaternion version of the Itô’s formula is established by resorting to the properties and the operation rules of quaternion, which covers the real and complex versions as special cases and can be applied to the stability analysis of stochastic quaternion-valued systems. Two examples are provided for demonstrating the validness of the proposed formula.

Safe Reinforcement Learning-Based Robust Approximate Optimal Control for Hypersonic Flight Vehicles

In this paper, a safe reinforcement learning-based robust approximate optimal controller (SRL-RAOC) is proposed with the framework of actor-critic for hypersonic flight vehicles. First, we develop a system transformation based on barrier function, which transforms the issue of full-state safety constraints into an unconstrained optimization problem. Next, the safe reinforcement learning algorithm is employed to design the approximate optimal controller under an online actor-critic framework. Further, a robustifying term is presented to compensate for the neural network approximation errors introduced by the actor-critic framework. Hereafter, the stability analysis of the closed-loop system is accomplished by utilizing the Lyapunov technique, which shows that SRL-RAOC can guarantee that the equilibrium point is asymptotically stable. Moreover, the control input obtained by SRL-RAOC is demonstrated to be close to the optimal control input within a small bound. Finally, a numerical example is provided to demonstrate the effectiveness of SRL-RAOC.

Stability Analysis of Time-Varying Neutral Stochastic Hybrid Delay System

Stability Analysis of Time-Varying Neutral Stochastic Hybrid Delay System

D-Q Impedance Modeling and Stability Analysis of a Three-Phase Four-Wire System With Single-Phase Loads

D-Q Impedance Modeling and Stability Analysis of a Three-Phase Four-Wire System With Single-Phase Loads

Effects of Nonlinear MPPT Control and PV Array on Stability Analysis for a Utility-Scale PV Energy System

Various studies have focused on the stability analysis of PV energy systems. However, the majority of these methods rely on a linearized model around an equilibrium point, which cannot exactly reveal the influence of the nonlinear power controller and PV array on the PV energy system at low frequencies. To conquer this gap, this article contributes to providing intuitive insight into stability analysis and establishing a complete system model including the PV panel, boost converter, DC line, central inverter and AC grid. The describing function (DF) of the nonlinear discontinuous element in PV and the transfer function of the linear elements in the system are derived to determine the system stability. To support the stability hypothesis based on the DF-based stability analysis method, a comparative study in contrast to existing stability analysis methods is provided. The impedance-based method may not be accurate when the division of the ‘source-load’ subsystem is different. The proposed DF method can offer further concluding remarks on MPPT control, the number of PV panels, DC/DC converter, etc. Based on a hardware-in-the-loop (HIL) operation, the proposed model is explicitly validated under different constraints, and the influence of control and circuit parameters on system stability are illustrated.

Caputo−Wirtinger integral inequality and its application to stability analysis of fractional-order systems with mixed time-varying delays

Various techniques of integral inequality are widely used to establish the delay-dependent conditions for the dynamics of differential systems so that the conservatism of conditions can be reduced. In the integer-order systems, the integral term of ∫τωp˙T(s)Sp˙(s)ds often appears in the derivative of Lyapunov−Krasovskii functional, and how to scale down this term to obtain less conservative condition is a key problem. Similarly, the integral term of ∫τω(Dsα0Cp(s))TS0CDsαp(s)ds with fractional derivative may also be encountered in the analysis of dynamical behaviors for fractional-order systems. In view of this, the paper intends to construct several novel fractional Wirtinger integral inequalities under the sense of Caputo derivative, and to investigate the stability of fractional-order systems with mixed time-varying delays based on the constructed Caputo−Wirtinger integral inequalities. Meanwhile, in order to analyze the stability for our concerned models by the new inequalities, two new theorems of generalized fractional-order Lyapunov direct method are given. Finally, a numerical example is designed to validate the correctness and practicability of the obtained results.

Nonlinear control design and stability analysis of hybrid grid-connected photovoltaic-Battery energy storage system with ANN-MPPT method

The problem of controlling a grid-connected solar energy conversion system with battery energy storage is addressed in this work. The study’s target consists of a series and parallel combination of solar panel, DC/DC converter boost, DC/AC inverter, DC/DC converter buck-boost, Li-ion battery, and DC load. The main objectives of this work are: (i) PV voltage regulation: the PV panel voltage must track a given reference voltage corresponding to the maximum power point. The optimal reference voltage is generated by an optimizer based on the artificial neural network (ANN); (ii) DC link voltage regulation: The DC link voltage must track a reference voltage as closely as possible. (iii) PFC requirement: The grid currents must be sinusoidal with the same frequency and in phase with the voltage grid. The periodic nature of solar energy and the frequent fluctuations in load demand reduce battery life and charging performance. To deal with these limitations and ensure the battery’s safety, a battery energy management algorithm is developed with the following objectives: (iv) CC mode: When the battery’s state of charge is less than 100% (SOC<100%), it indicates that the battery is not fully charged, this aim has been adopted. The battery current should follow a constant reference as closely as possible to the permissible limits battery current; (v) CV mode: When the battery is completely charged, this mode is switched on. The voltage at the battery terminals then achieves its reference signal, which corresponds to the charge state’s of the battery SOC=100%. In addition, the energy management system which generates several energy flow scenarios, in this work, the focus is to balance the energy flows between the load and the different energy sources to minimize the system costs, to ensure the stability of the grid and to improve the power quality. To do this, a mathematical modeling of the overall system was performed. Subsequently, backstepping controllers are then synthesized in order to ensure the control objectives. The closed loop control convergence is formally analyzed using Lyapunov’s stability theory and its performances are illustrated by simulation. As a result, the simulation results indicate that the proposed controllers perform admirably in achieving their objectives.

Stability Analysis of Lane-Keeping Assistance System for Trucks under Crosswind Conditions

To enhance the control accuracy of lane-keeping assistance systems for trucks encountering crosswind-induced lateral deviations to improve the lateral stability of the vehicle, this study proposes a control strategy based on a linear quadratic regulator (LQR) using a path-tracking preview model. First, the lateral deviation is calculated using the path-tracking preview model. Then, an observer for the vehicle’s sideslip angle is designed using a vehicle lateral tracking deviation model and a Kalman filter controller, and this is used to solve the deviation of the sideslip angle. Finally, a feedforward controller is designed based on the LQR controller and a linear two-degrees-of-freedom vehicle model to eliminate steady-state errors arising from LQR optimization, thereby obtaining the steering angle of the vehicle when subjected to crosswind conditions. Comparing the test results of the sideslip angle, yaw rate, and lateral acceleration demonstrates that this strategy effectively improves the control accuracy of lane-keeping under crosswind conditions. The proposed method is validated through hardware-in-the-loop experiments on a test bench, yielding results consistent with simulations.

A theory on leading-edge vortex stabilization by spanwise flow

Natural flyers are capable of producing excessive lift via a stabilized leading-edge vortex (LEV), which appears to linger above the wing for a longer duration than it could in an equivalent two-dimensional flow. Previous studies found this stabilization behaviour closely related to a spanwise flow along the LEV axis; however, it is still debatable how the spanwise flow influences the LEV stability. In this work, potential flow theory is adopted to model an LEV attached to a flat-plate wing. To account for the spanwise flow effect, we propose a finite-area sink (FAS) model which allows the dynamical interaction between co-located LEV and spanwise flow. Through linear stability analysis of the dynamical system associated with the LEV movement, we arrive at a stable spiral-sink type of equilibrium, which is the first mathematical evidence supporting LEV stabilization by spanwise flow. It is further concluded that the LEV stability can be enhanced by either increasing the strength or decreasing the cross-section area of the spanwise flow.

Admittance Criterion of Medium-Voltage DC Distribution Power System and Corresponding Small Signal Stability Analysis

Aiming at the stability of a medium-voltage DC network based on a modular multilevel converter (MMC), this paper proposes an admittance stability criterion considering the influence of current-limiting inductors at the medium voltage side, which prevents the complex products and matrix calculations of traditional criteria. The DC admittance model DC transformers (DCTs) under different working modes are then established based on Thevenin/Norton equivalent circuit methods to analyze the stability of the DC system based on the proposed admittance stability criterion, which proves that the voltage resonance problem at the medium voltage side can be improved by adding active damping control strategies on DCTs also proves the effectiveness of the proposed stability criterion. The time-domain simulation and the hardware-in-loop simulation are then built in PLECS and RT Box to further verify the correctness of the system stability analysis and the effectiveness of the proposed admittance criterion, which provides a theoretical basis and technical reserve for the stable operation of the DC distribution power system.

The Stability Analysis of Linear Systems with Cauchy—Polynomial-Vandermonde Matrices

The numerical approximation of both eigenvalues and singular values corresponding to a class of totally positive Bernstein–Vandermonde matrices, Bernstein–Bezoutian structured matrices, Cauchy—polynomial-Vandermonde structured matrices, and quasi-rational Bernstein–Vandermonde structured matrices are well studied and investigated in the literature. We aim to present some new results for the numerical approximation of the largest singular values corresponding to Bernstein–Vandermonde, Bernstein–Bezoutian, Cauchy—polynomial-Vandermonde and quasi-rational Bernstein–Vandermonde structured matrices. The numerical approximation for the reciprocal of the largest singular values returns the structured singular values. The new results for the numerical approximation of bounds from below for structured singular values are accomplished by computing the largest singular values of totally positive Bernstein–Vandermonde structured matrices, Bernstein–Bezoutian structured matrices, Cauchy—polynomial-Vandermonde structured matrices, and quasi-rational Bernstein–Vandermonde structured matrices. Furthermore, we present the spectral properties of totally positive Bernstein–Vandermonde structured matrices, Bernstein–Bezoutian structured matrices, Cauchy—polynomial-Vandermonde structured matrices, and structured quasi-rational Bernstein–Vandermonde matrices by computing the eigenvalues, singular values, structured singular values and its lower and upper bounds and condition numbers.

MATHEMATICAL MODELING OF DIRECT CURRENT MOTOR OPERATION WITH DIFFERENT EXCITATION TYPES FOR VIBRATIONAL MACHINES

This work is dedicated to the development and analysis of a mathematical model for a direct current motor with various types of excitation for vibrational machines. Vibrational machines play a crucial role in many industrial sectors, and their operational characteristics are determined by the efficiency and accuracy of motor performance. In this study, we investigate different types of excitation for direct current motors and develop corresponding mathematical models. Employing principles from control theory and quantitative electronics, we account for the influence of different excitation parameters on the motor's dynamic behavior. The obtained results could be valuable for the development of new hybrid excitation systems for vibrational machines, capable of operating in diverse modes depending on specific additional conditions. Additionally, the analysis and development of the mathematical model can serve as a foundation for further research in optimizing the operation of vibrational systems using direct current motors. Analyzing the results, we compare the efficiency of various excitation types and their impact on the operational characteristics of vibrational machines. Moreover, we explore possibilities for reducing power consumption and enhancing speed regulation accuracy. Special attention is devoted to analyzing system stability under different operating conditions and parameter variations. The findings of our research hold important practical applications in the design and improvement of vibrational machines for industrial, technical, and scientific purposes. They contribute to understanding the influence of different factors on the performance of direct current motors with various excitation types, which can aid engineers and designers in enhancing the efficiency and reliability of vibrational systems. In conclusion, this research is aimed at developing and analyzing a mathematical model for a direct current motor with various excitation types, considering their impact on the operational characteristics of vibrational machines. It makes a significant contribution to understanding and optimizing the processes of such systems, potentially exerting a substantial influence on the advancement of modern technology in the field of vibrational systems and their applications.

Robust stability analysis for uncertain neutral type descriptor systems with mixed delays

AbstractThe issue of robust stability here is carefully thought about for uncertain neutral type descriptor systems (NTDSs) with mixed delays. An augmented Lyapunov–Krasovskii functional considering the cross information of the singular matrix and state delay derivative is constructed. With the help of the zero‐value equation technique and an improved matrix inequality, a novel delay‐dependent admissible criterion is developed to make sure of the regularity, non‐impulsiveness, and stability of the NTDSs. On this basis, the robust stability of the uncertain NTDSs is further explored, and a novel robust stability criterion is developed. These criteria have less conservatism. Through three number‐based examples, some comparisons are provided to show the superiority and effectiveness of our method.

Stability Analysis of the Immune System Induced by Chemotaxis

Stability Analysis of the Immune System Induced by Chemotaxis

The state of the art of electronic power system under different disturbance conditions

As a new generation of electric power system, the electronic power system has advantages such as flexibility and large capacity that the traditional power system does not have, but the high performance is accompanied by the increased difficulty in operation. The characteristics such as multi-coupling and nonlinear make the situation to be considered by the electronic power system more complicated, and the application and analysis will be hindered. In this paper, the stability analysis of electronic power system will be discussed from the large disturbance, small disturbance and power imbalance.

A Dynamic Cross-Collaborative Interception Algorithm Based on GTSMC and Virtual Geometry

In the model (m:n), to improve the autonomous collaborative interception capability for air vehicle, a new autonomous cross-collaborative interception algorithm based on GTSMC (Global Terminal Sliding Mode Control) and real-time virtual geometry is proposed in this paper. Firstly, the conception of an autonomous cross-collaboration is defined and the multi-air vehicle for the multi- object interception problem is formulated. Then, this paper presents the dynamic situation assessment function, which considers the real-time flight status and cooperative status of the air vehicle during the interception of the object. At the same time, this paper states the condition of whether the air vehicle is in a cooperative state and proves it. After completing the dynamic situation assessment, and considering the dynamic of the air vehicles, a new controller is designed by using GTSMC and the idea of backstepping method. Simultaneously, this paper gives a stability analysis of the closed-loop system by using Lyapunov theory. Finally, to demonstrate the effectiveness of the proposed algorithm, several simulation cases which consider different interception scenarios are given. The simulation results show that the new collaborative interception algorithm can provide better autonomous cross-collaborative interception capability and higher accuracy.

Synergetic Theory of Information Entropy Based on Failure Approach Index for Stability Analysis of Surrounding Rock System.

It is generally acknowledged that the stability evaluation of surrounding rock denotes nonlinear complex system engineering. In order to accurately and quantitatively assess the safety states of surrounding rock and provide a scientific basis for the prevention and control of surrounding rock stability, the analysis method of the synergetic theory of information entropy using the failure approach index has been proposed. By means of deriving the general relationship between the total two-dimensional plastic shear strain and the total three-dimensional plastic shear strain and obtaining the numerical limit analysis step of the plastic shear strain, the threshold value of the ultimate plastic shear strain can be determined, which has provided the key criterion for the calculation of the information entropy based on the failure approach index. In addition, combining with the synergetic theory of the principle of maximum information entropy, the evolution equation of the excavation step and information entropy based on the failure approach index of the surrounding rock system in underground mining space are established, and the equations of the general solution and particular solution as well as the expression of the destabilizing excavation step are given. To account for this, the method is applied to analyze the failure states of the floor surrounding rock after the mining of the 71 coal seam in Xutuan Coal Mine and involve the disturbance effect and stability control method of the underlying 72 coal seam roof from the macroscopic and microscopic aspects. Consequently, the validity of the analysis method of synergetic theory of information entropy based on the failure approach index has been verified, which presents an updated approach for the stability evaluation of surrounding rock systems that is of satisfactory capability and value in engineering applications.

Cooperation of robot manipulators with motion constraint by real-time RNN-based finite-time fault-tolerant control

The nonlinear cooperative dynamics of m robots with motion constraint and faulty input saturation is addressed. To the best of our knowledge, the motion constraint for the cooperative control of multiple robots is first discussed as one of the designed concepts such that the proposed cooperative control system is more practical and its performance is also improved. Together with a finite-time concept, a real-time recurrent-neural-network-based finite-time fault-tolerant cooperation constraint control (RT-RNN-FTFTCCC) is designed to tackle the aggregately dynamic uncertainties brought about by motion constraint error, cooperation uncertain dynamics, disturbance torque, faulty input saturation, unsatisfying skew-symmetric matrix condition, and others. Moreover, the stabilized learning law includes two terms to cover all the range of filtering cooperation errors such that learning weights converge even in uncertain circumstances. Finally, the stability analysis of the overall cooperation control system is achieved by Lyapunov stability theory. In comparison to adaptive compensation control, recurrent-neural-network-based control without the motion constraint compensation, and different stabilized learning laws, the cooperative control of bi-robotic arms of 3-link in-plane with new constraint validates the improvement and robustness of the proposed control.

Stability analysis of sampled-data control systems with input saturation: A hybrid system approach

This work addresses the stability analysis of sampled-data control systems subject to variable sampling intervals and input saturation. From a hybrid system representation, stability conditions based on quadratic timer-dependent Lyapunov functions are proposed. Considering affine and generic polynomial timer-dependence, these conditions are cast in semidefinite and sum-of-squares optimization problems to provide maximized estimates of the region of attraction or to provide a lower bound for the maximum allowable intersampling time considering a given set of admissible initial conditions.