Complete Stability Analysis Research Articles

Research on stability for blended-wing-body aircraft

The primary goal of this research is to research the stability properties of a blended-wing-body (BWB) aircraft. This section examines the assessment and selection of aircraft design parameters, planform design, and reflex wing and conducts a complete aircraft stability analysis. A BWB aircraft conceptual design has been completed and the design. To attain static stability, it was examined and refined. The BWB aircraft's study was performed at three distinct values. The analytical findings were used to calculate the angle-of-attack (AOA) and the stall AOA. We determined the estimated initial departure angle of attack and departure region by assessing the results of the trials and a set of stability criteria.

Two Adaptive Sliding Mode Control Algorithms for Vehicle Stability Enhancement

This paper discusses two adaptive sliding mode control (ASMC) algorithms for enhancing vehicle stability through direct yaw moment control (DYC). DYC is based on a logic process derived from the understeering and oversteering behavior of a cornering vehicle. Furthermore, to achieve DYC in a four-wheeled passenger vehicle, the reference yaw moment computed by the proposed algorihms is converted into a braking pressure that is to be applied to the four wheels. The objective is to minimize the yaw rate error and constrain the sideslip angle to an acceptable range. According to Lyapunov theory, complete stability analysis guarantees the closed-loop stability and robustness of a control system. Simulation results were used to compare the two ASMC algorithms, and both algorithms showed high performance even under critical operating conditions.

Complete stability analysis of iterative adaptive critic designs with discounted cost

Complete stability analysis of iterative adaptive critic designs with discounted cost

Spatiotemporal dynamics of prey-predator model incorporating Holling-type II functional response with fear and its carryover effects.

The recent focus in the fields of biology and ecology has centered on the significant attention given to the mathematical modeling and analyzing the spatiotemporal population distribution among species engaged in interactions. This paper explores the dynamics of the temporal and spatiotemporal delayed Bazykin-type prey-predator model, incorporating fear and its carryover effect. In our model, we incorporated a functional response of the Holling-type II. In the temporal model, a detailed dynamic analysis was carried out, investigating the positivity and boundedness of solutions, establishing the uniqueness and existence of positive interior equilibria, and examining both local and global stability. Additionally, we explored the presence of saddle-node, transcritical, and Hopf bifurcations varying attack rate parameter. The delayed system shows highly periodic behavior. Additionally, for the spatiotemporal model, we provide a complete analysis of local and global stability, and we derive the conditions for the existence of Turing instability for both self-diffusion and cross-diffusion, respectively. The two-dimensional diffusive model is further discussed, highlighting various Turing patterns, including holes, stripes, and hot and cold spots, along with their biological significance. Numerical simulations are executed to validate the analytical findings in both temporal and spatiotemporal models.

A Resilient Control for Distributed Energy Storage Units in an Islanded AC Microgrid

A high number of charge/discharge cycles results in premature aging of Distributed Energy Storage Units (DESUs). Since classical droop control does not consider this issue and leads to MG voltage and frequency fluctuations in steady state, controls such as State of Charge (SoC) synchronization control are used to minimize DESUs number of charge/discharge cycles. However, few methods in the literature investigate frequency and voltage (f & V) restoration while ensuring a functional SoC equalization control in both charge and discharge modes. In this paper, an Adaptive Frequency Droop based on Virtual Power (AFDVP) method is proposed to achieve DESUs SoC equalization to prolong their lifespan while ensuring MG voltage and frequency regulation. In addition, AFDVP strategy ensures optimal use of second life batteries, since they are naturally less solicited due to the decrease in their capacity. DESUs SoC equalization is achieved thanks to virtual active powers using a PI controller. A complete stability analysis is provided to choose optimal parameters for the proposed distributed control. Experimental tests are performed to check the performance of the AFDVP technique in several study cases. A comparison is also performed with a SoC equalization strategy from the literature.

Goldilocks Fluctuations: Dynamic Constraints on Loop Formation in Scale-Free Transport Networks.

Adaptive transport networks are known to contain loops when subject to hydrodynamic fluctuations. However, fluctuations are no guarantee that a loop will form, as shown by loop-free networks driven by oscillating flows. We provide a complete stability analysis of the dynamical behavior of any loop formed by fluctuating flows. We find a threshold for loop stability that involves an interplay of geometric constraints and hydrodynamic forcing mapped to constant and fluctuating components. Loops require fluctuation in the relative size of the flux between nodes, not just a temporal variation in the flux at a given node. Hence, there is both a minimum and a maximum amount of fluctuation relative to the constant-flux component where loops are supported.

Practical Finite-Time Event-Triggered Control of Underactuated Surface Vessels in Presence of False Data Injection Attacks

Abstract The results of studies on a trajectory-tracking problem affected by false data injection attacks (FDIAs) and internal and external uncertainties are presented in this paper. In view of the FDIAs experienced by the system, we compensate for the serious navigation deviation caused by malicious attacks by designing an online approximator. Next, we study the internal and external uncertainties introduced by environmental factors, system parameter fluctuations, or sensor errors, and we design adaptive laws for these uncertainties to approximate their upper bounds. To further enhance the response velocity and stability of the system, we introduce finite-time technology to ensure that the unmanned underactuated surface vessels (USVs) reach the predetermined trajectory-tracking target within finite time. To further reduce the update frequency of the controller, we introduced event-triggered control (ETC) technology. This saves the system’s communication resources and optimizes the system. Through Lyapunov stability theory, a strict and complete stability analysis is provided for the control scheme. Finally, the effectiveness of the control scheme is verified using two sets of simulations.

A simple model of nutrient recycling and dormancy in a chemostat: Mathematical analysis and a second-order nonstandard finite difference method

A chemostat is an apparatus that sustains a homogeneous environment through continuous inflow and outflow. Presented is a chemostat model that characterizes the dynamics of dormancy-capable microorganisms. This model of coupled systems of nonlinear ordinary differential equations (ODEs) can apply to various types of organisms, such as different species of bacteria, archaea, algae, fungi, viruses, and protozoa. However, these species reside in different environments and rely on different sets of nutrients. Thus, the model adapts to each species’ limiting nutrient through nutrient recycling. This paper includes a complete stability analysis, supporting phase plane portraits, and accompanying bifurcation diagrams. The paper also proposes an advanced second-order, positivity-preserving, and elementary stable nonstandard finite difference method for solving the mathematical model. Series of numerical simulations are presented that support the theoretical results and explore different biological scenarios. The stability analysis reveals that (1) if the overall dilution, death, and conversion are less than the overall growth, both the dormant and active populations persist when introduced to a chemostat; and (2) if the overall dilution, death, and conversion are more than the overall growth, the microorganism population in its entirety will die off when introduced to a chemostat. Furthermore, the model study suggests that neither dormancy nor nutrient recycling provides substantial survival advantages in a basic chemostat when no threat to the active microorganism is present.

Proportional-retarded control of a quasi-zero-stiffness vibration isolator

This paper explores the control design and performance analysis of an active quasi-zero-stiffness vibration isolator utilizing the proportional-retarded (PR) control architecture. The PR architecture replaces the conventional “derivative” term in the proportional-derivative (or displacement-velocity) controller with the novel “retarded (time-delayed)” term, which is a new and effective way of active vibration suppression. Comprehensive gain-delay conjoint regulation strategies are developed for the strengthened isolation performance. For impact excitations, a complete stability analysis is conducted near the equilibrium position. Furthermore, a parameterized dominant pole placement algorithm is proposed to optimize the transient response of the PR-actuated isolator. Focusing on the rectangular pulse and long-duration step impacts, the algorithm adjusts the dominant poles to optimize the transient performance metrics, including the maximum displacement overshoot, steady-state displacement overshoot, and settling time. Regarding harmonic excitations, the delay-coupled effect is scrutinized for better low-frequency isolation performance, including the resonance frequency, nonlinear steady-state amplitude, multiple steady-state bands and nonlinearity elimination, equivalent active damping and stiffness, and absolute displacement transmissibility. In the case of random excitations, we demonstrate the superiority of the PR structure over the passive system.

Comprehensive Analysis of Aircraft Dynamics Stability with SCSim: Integration and Assessment

This research presents a comprehensive analysis of the dynamic stability of aircraft using modules of the software named SCSim (Stability and Control Simulation Tool), which is dedicated to the analysis of aircraft stability and control. The stability of an aircraft can be examined in two directions: longitudinal and lateral. The ability to determine an aircraft's limits and handling qualities depends on its stability. This study report demonstrates a complete dynamic stability analysis using SCSim with aerodynamic input data from the commercial software Advanced Aircraft Analysis (AAA). SCSim is implemented within a common framework in MATLAB, adapted from a MATHCAD script, providing an easier way to enter user-defined input data, and introducing a set of new features. The study is divided into three main parts, each based on an analysis of stability. First, static stability is examined to understand how the system behaves when it is in equilibrium. Then, dynamic stability is assessed to understand how the system reacts to perturbations and disturbances. Finally, handling qualities systematically assess the dynamic modes of the aircraft's behavior and establish the levels of handling qualities. In this paper, a generic model of a propeller-driven aircraft is used for the study due to the availability of flight parameters, geometric, and aerodynamic data. The obtained results demonstrate the capabilities of the Stability and Control Simulation Tool (SCSim) in designing and analysing an aircraft's stability under various flight conditions and configurations, with validation using AAA.

Fuzzy Adaptive Finite-Time Tracking Control for a Class of Nonlinear Systems: An Event-Triggered Quantized Control Scheme

This brief proposes a fuzzy adaptive event-triggered quantized finite-time control (ETQFTC) scheme for uncertain strict-feedback nonlinear systems with full-state constraints. By means of state transformation, filtered backstepping technique and fuzzy adaptive control with the idea of minimum learning parameter (MLP), a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C^{1}$</tex-math></inline-formula> ETQFTC scheme with low differential calculation and few parameter updates is developed. In the proposed scheme, the feasibility condition generally required in the existing state-constrained control, and the control chattering and singularity problem which are common in the existing FTC schemes are removed and avoided respectively. Finally, complete stability analysis and a set of comparative simulations are presented.

An arbitrary-order discrete rot-rot complex on polygonal meshes with application to a quad-rot problem

Abstract In this work, following the discrete de Rham approach, we develop a discrete counterpart of a two-dimensional de Rham complex with enhanced regularity. The proposed construction supports general polygonal meshes and arbitrary approximation orders. We establish exactness on a contractible domain for both the versions of the complex with and without boundary conditions and, for the former, prove a complete set of Poincaré-type inequalities. The discrete complex is then used to derive a novel discretization method for a quad-rot problem, which, unlike other schemes in the literature, does not require the forcing term to be prepared. We carry out complete stability and convergence analyses for the proposed scheme and provide numerical validation of the results.

Constructive exponential tracking control for mechanical systems via Hamiltonian realization and contraction analysis method

The conventional tracking control of mechanical systems is generally based on the stabilization of error dynamics and most of the results can only guarantee asymptotic tracking of the desired trajectories. Since error dynamics are generally time-varying, it is very difficult to find appropriate Lyapunov functions or control Lyapunov functions to complete stability analysis and controller design. To address this limitation, the novel constructive exponential tracking control method is proposed to mechanical systems by utilizing the Hamiltonian realization and contraction analysis in this paper. Firstly, based on the Hamiltonian realization and use the structural characteristics of port-Hamiltonian systems, the exponential tracking controllers are constructed for fully actuated and under-actuated mechanical systems by combining the pre-feedback with feedback control. The proposed tracking control strategies can be used to discuss fully actuated and under-actuated mechanical systems in a unified framework. Then the exponential decay-rate of tracking controllers and procedure for selecting control parameters for fully actuated and under-actuated mechanical systems are given. Finally, comparative simulations and experiments are carried out to illustrate the effectiveness and robustness of the proposed control strategy.

Robust distributed formation control with prescribed performance for nonlinear multi‐agent systems subjected to compound disturbances

SummaryThis article is concerned with the distributed leader‐following formation control for nonlinear multi‐agent systems (MASs) subject to compound disturbances. Three aspects of the control objective: formation control, collision avoidance and connectivity preservation are achieved by the designed controller composed of three control laws. The formation control law is developed based on the barrier Lyapunov function and the backstepping method, which can prescribe the performance of the close‐loop system to some extent. Within our scheme, an adaptive finite‐time disturbance observer is used to enhance the robustness of the control system against compound disturbances including parameter perturbations, actuator bias faults and external disturbances. Meanwhile, a nonlinear tracking differentiator is introduced for each follower to cancel complex differential calculations and the requirement for the leader's acceleration information. Furthermore, the auxiliary control laws for collision avoidance and connectivity preservation are designed based on the artificial potential field method, which plays an important role during the formation shaping. Finally, complete stability analysis and vivid numerical simulation are carried out.

An Overview of the Stability Analysis of Recurrent Neural Networks With Multiple Equilibria.

The stability analysis of recurrent neural networks (RNNs) with multiple equilibria has received extensive interest since it is a prerequisite for successful applications of RNNs. With the increasing theoretical results on this topic, it is desirable to review the results for a systematical understanding of the state of the art. This article provides an overview of the stability results of RNNs with multiple equilibria including complete stability and multistability. First, preliminaries on the complete stability and multistability analysis of RNNs are introduced. Second, the complete stability results of RNNs are summarized. Third, the multistability results of various RNNs are reviewed in detail. Finally, future directions in these interesting topics are suggested.

Reinforcement Learning-Based Prescribed Performance Motion Control of Pneumatic Muscle Actuated Robotic Arms With Measurement Noises

Featured with high power density, excellent flexibility, shock absorption capacity, etc., pneumatic muscles (PMs) promote the development of exoskeleton robots and rehabilitation equipment. However, the complex nonlinearities of PMs limit efficiency optimization in closed-loop control, while the force-displacement coupling, soft materials, deficient workspace, etc., make it more difficult to simultaneously increase motion speeds and ensure the safety of multiple PM-actuated (PMA) robots. Although force sensors can currently be replaced by applying state estimation techniques, the amplification effects of measurement noises still compromise control accuracy and stability in practice. To this end, this article proposes a reinforcement learning-based robust motion control method with the prescribed performance, which achieves efficient and satisfactory tracking control for PMA robotic arms. In particular, by elaborately incorporating an integral term, a robust generalized proportional integral observer is used to eliminate measurement noises. Meanwhile, by using an actor–critic network to optimize control performance, an error-transformation-based continuous controller is designed to guarantee the uniformly ultimately boundedness of tracking errors. Compared with most existing methods, this article provides the first solution to restrict the entire transient and steady-state performance of PMA robotic arms, improve the noise suppression capability, and optimize the control efficiency simultaneously. Finally, complete stability analysis based on Lyapunov techniques is provided, and several groups of hardware experiments demonstrate the practicability and robustness of the proposed method.

Complete Large-Signal Stability Analysis of DC Distribution Network via Brayton-Moser’s Mixed Potential Theory

For a nonlinear RLC network, Brayton and Moser have proposed the so-called general mixed potential function (GMPF) whose time-derivative is negative semi-definite. Then, the equilibrium of the RLC network is stable if it is a local minimum of the GMPF. Therefore, Brayton-Moser’s mixed potential theory is a powerful methodology, which has been widely used in the stability analysis of DC microgrid. However, most of the results in existing references are flawed and incomplete. This paper carries out the complete stability analysis of the DC distribution network with constant power loads via Brayton-Moser’s mixed potential theory. Firstly, several critical points in this theory that are often mistaken are emphasized. Secondly, based on Brayton-Moser’s mixed potential theory, the condition that the equilibrium is a local minimum is proposed. All the low-voltage equilibria are proved to be unstable, and only the high-voltage equilibrium can be stabilizable and the complete stability conditions are provided. Thirdly, some unsolved problems about the stability issue of DC microgrid via Brayton-Moser’s mixed potential theory are presented. Finally, hardware-in-the-loop (HIL) experimental results verify the proposed stability conditions.

Nondisturbing Extremum Seeking Control for Multiagent Industrial Systems

Industrial applications of extremum seeking control (ESC) can be a hit and miss affair. Although a gain in performance can be achieved, the dither applied to excite the system causes unwanted fluctuations in the performance of the system. The fluctuations in systems with a single extremum seeking loop are generally small. However, for systems with many extremum seeking loops, the fluctuations in each loop may add up to an intolerable amount of fluctuation in the total performance. In this article, we propose a method to cancel the dither-induced fluctuations in the overall system performance to a large extent by smartly constructing the dither signals in each extremum seeking loop using a centralized coordinator. The novelty of our method lies in the direct calculation of the dither signals that avoids the heavy computations required by other methods. Moreover, we provide a solvability analysis for the problem of cancelling dither-induced fluctuations in the total performance of the system. Furthermore, a complete stability analysis of the overall ESC scheme with dither coordination is given.

Error Analysis for a Parabolic PDE Model Problem on a Coupled Moving Domain in a Fully Eulerian Framework

We introduce an unfitted finite element method with Lagrange-multipliers to study an Eulerian time stepping scheme for moving domain problems applied to a model problem where the domain motion is implicit to the problem. We consider a parabolic partial differential equation (PDE) in the bulk domain, and the domain motion is described by an ordinary differential equation (ODE), coupled to the bulk partial differential equation through the transfer of forces at the moving interface. The discretisation is based on an unfitted finite element discretisation on a time-independent mesh. The method-of-lines time discretisation is enabled by an implicit extension of the bulk solution through additional stabilisation, as introduced by Lehrenfeld & Olshanskii (ESAIM: M2AN, 53:585-614, 2019). The analysis of the coupled problem relies on the Lagrange-multiplier formulation, the fact that the Lagrange-multiplier solution is equal to the normal stress at the interface and that the motion of the interface is given through rigid body motion. This paper covers the complete stability analysis of the method and an error estimate in the energy norm, under an assumption on the discrete interface velocity. This includes the dynamic error in the domain motion resulting from the discretised ODE and the forces from the discretised PDE. To the best of our knowledge this is the first error analysis of this type of coupled moving domain problem in a fully Eulerian framework. Numerical examples illustrate the theoretical results.

Dynamic Stability of Tensegrity Structures-Part I: The Time-Independent External Load.

The paper contains a parametric analysis of tensegrity structures subjected to time-independent external loads. A complete dynamic stability analysis is a three-step process. The first stage involves the identification of self-stress states and infinitesimal mechanisms. The next stage concentrates on the static and dynamic behavior of tensegrities under time-independent external loads, whereas the third is under periodic loads. In this paper, the first two stages are carried out. The structures built with the most popular tensegrity modules, Simplex and Quartex, are considered. The effect of the initial prestress on the static parameters and frequency is analyzed. To assess this behavior, a geometrically non-linear model is used.