Stability Analysis Of Systems Research Articles

The Dynamic Behavior of a Stochastic SEIRM Model of COVID-19 with Standard Incidence Rate

This paper studies the dynamic behavior of a stochastic SEIRM model of COVID-19 with a standard incidence rate. The existence of global solutions for dynamic system models is proven by integrating stochastic process theory and the concept of stopping times, together with the contradiction method. Moreover, we construct appropriate Lyapunov functions to analyze system stability and apply Dynkin’s formula and Fatou’s lemma to handle stopping times and expectations of stochastic processes. Notably, the extinction study provides mathematical proof that under the given system dynamics, the total population does not grow indefinitely but tends to stabilize over time. The properties of the diffusion matrix are harnessed to guarantee the system’s stationary distribution. Conclusively, numerical simulations confirm the model’s extinction outcomes.

Optimal Control of Underdamped Systems: An Analytic Approach

Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an open and challenging research frontier, with a spectrum of applications ranging from stochastic thermodynamics to biophysics and data science. Among these, the design of nanoscale electronic components motivates the study of underdamped dynamics, leading to practical and conceptual difficulties. In this work, we develop analytic techniques to determine protocols steering finite time transitions at a minimum thermodynamic cost for stochastic underdamped dynamics. As cost functions, we consider two paradigmatic thermodynamic indicators. The first is the Kullback–Leibler divergence between the probability measure of the controlled process and that of a reference process. The corresponding optimization problem is the underdamped version of the Schrödinger diffusion problem that has been widely studied in the overdamped regime. The second is the mean entropy production during the transition, corresponding to the second law of modern stochastic thermodynamics. For transitions between Gaussian states, we show that optimal protocols satisfy a Lyapunov equation, a central tool in stability analysis of dynamical systems. For transitions between states described by general Maxwell-Boltzmann distributions, we introduce an infinite-dimensional version of the Poincaré-Lindstedt multiscale perturbation theory around the overdamped limit. This technique fundamentally improves the standard multiscale expansion. Indeed, it enables the explicit computation of momentum cumulants, whose variation in time is a distinctive trait of underdamped dynamics and is directly accessible to experimental observation. Our results allow us to numerically study cost asymmetries in expansion and compression processes and make predictions for inertial corrections to optimal protocols in the Landauer erasure problem at the nanoscale.

A new quasi-finite-rank approximation of compression operators on [formula omitted] with applications to sampled-data and time-delay systems: Piecewise linear kernel approximation approach

This paper provides a new quasi-finite-rank approximation (QFRA) of infinite-rank compression operators defined on the Banach space L∞[0,H), which are associated with tractable representations of infinite-dimensional systems such as time-delay and sampled-data systems. We first formulate the QFRA by an optimization problem with a matrix-valued parameter X to minimize the associated error in terms of the L∞[0,H)-induced norm. To facilitate solving the optimization problem, we next employ the piecewise linear kernel approximation (PLKA) technique, by which the optimization problem is then converted to a linear programming (LP) problem. The solution of the LP problem is shown to converge to the optimal solution of the original QFRA with the order of 1/M, where M is the PLKA parameter. The PLKA-based QFRA is shown to lead to practical methods of the stability analysis for time-delay systems and the L1 optimal controller synthesis for sampled-data systems. Finally, the overall arguments developed in this paper are demonstrated through some numerical and experimental studies.

Proportional-derivative control and motion stability analysis of a 16-pole legs rotor-active magnetic bearings system

This paper analyzes the motion stability of a 16-pole rotor-active magnetic bearings (rotor-AMB) system and investigates the complex vibrations under a proportional-derivative (PD) controller. First, electromagnetic theory and Newton’s second law are applied to derive the two-degree-of-freedom differential governing equations for the 16-pole rotor-AMB system, incorporating the PD control terms. The resulting differential equations include parametrically excited, quadratic nonlinear, and cubic nonlinear terms. Subsequently, the multiple time scales perturbation analysis method is performed on the obtained governing equations, yielding four-dimensional averaged equations in both Cartesian and polar coordinates. Finally, numerical simulations including the amplitude–frequency response characteristics, motion trajectories, energy–amplitude relationships, as well as bifurcation and chaotic motion of the system are studied. The results indicate that the PD controller affects the softening and hardening spring characteristics of the system and has significant control effects on the system’s amplitude, energy, and stability. Additionally, increasing the differential gain coefficient [Formula: see text] can change the system’s motion from chaotic to periodic.

A decentralized control approach in hypergraph distributed optimization decomposition cases

We study the main decomposition approaches (primal, dual and primal–dual) for a distributed optimization problem from a dynamical system perspective where the couplings among the variables of the optimization problem are described by an undirected, unweighted hypergraph. We conduct stability analysis for the respective dynamical systems of the decomposition cases by using non linear decentralized control theoretic techniques and spectral properties of the respective communication matrices, i.e., the incidence and the Laplacian matrices of the hypergraph. Finally, we provide numerical simulations under a specific coalitional setting that demonstrate the superiority of the hypergraph compared to its respective graph analogue, the clique expansion graph, for the given decomposition algorithms in terms of convergence rate and information transmission efficiency.

Stability analysis of random fractional-order nonlinear systems and its application

The research on stability analysis and control design for random nonlinear systems have been greatly popularized in recent ten years, but almost no literature focuses on the fractional-order case. This paper explores the stability problem for a class of random Caputo fractional-order nonlinear systems. As a prerequisite, under the globally and the locally Lipschitz conditions, it is shown that such systems have a global unique solution with the aid of the generalized Gronwall inequality and a Picard iterative technique. By resorting to Laplace transformation and Lyapunov stability theory, some feasible conditions are established such that the considered fractional-order nonlinear systems are respectively Mittag-Leffler noise-to-state stable, Mittag-Leffler globally asymptotically stable. Then, a tracking control strategy is established for a class of random Caputo fractional-order strict-feedback systems. The feasibility analysis is addressed according to the established stability criteria. Finally, a power system and a mass–spring-damper system modeled by the random fractional-order method are employed to demonstrate the efficiency of the established analysis approach. More critically, the deficiency in the existing literatures is covered up by the current work and a set of new theories and methods in studying random Caputo fractional-order nonlinear systems is built up.

The static voltage stability analysis of photovoltaic energy storage systems based on NPU algorithm

Although the data-driven static voltage stability problems have been widely studied, most of the classical algorithms focus more on improving the accuracy of the system prediction, ignoring the error classification errors generated during the prediction process. Furthermore, current research ignores the utilization of data-driven voltage stability assessment of energy storage systems. Therefore, this paper proposes a static voltage stability assessment method for photovoltaic energy storage systems based on considering the error classification constraint algorithm using Neyman-Pearson umbrella algorithms. Firstly, the Spearman Correlation Coefficient is employed in the feature selection phase. Secondly, an updated voltage stability assessment (VSA) model is proposed. Compared with the existing data-driven prediction of system static voltage stability in the literature, it can realize voltage stability assessment more quickly. Furthermore, on the basis of rapid voltage stability assessment, the umbrella NP classifier can also effectively limit the first-class error and attenuate the effect of error classification by mirroring the control of the number of cycle splits and the type I classification error threshold. Finally, the simulation and experimental results show that the effectiveness and robustness of the scheme proposed in this paper in grid-connected photovoltaic energy farms.

Adaptive path following control for underactuated surface vessels considering actuator saturation dynamics

ABSTRACT This article studies the path-following problem of underactuated surface vessels with saturated actuator dynamics and unmeasured linear velocities subjected to model uncertainties and unknown environmental disturbances. Firstly, a predictor is designed to estimate linear velocities and an improved predictor-based line-of-sight guidance law is designed to generate a reference heading angle, where the unknown arbitrary sideslip angle is compensated. Secondly, robust adaptive control laws are devised, where auxiliary dynamic systems are introduced to address input saturation and adaptive technique is employed to offset environmental disturbances and model uncertainties. Furthermore, to tackle computational complexity in control design, tracking differentiators are employed. Subsequently, the stability analysis of a closed-loop system is demonstrated by the Lyapunov theory. At last, simulations are applied to verify the validity and superiority of the presented strategy.

Small signal analysis of DC voltage control based on a virtual resistance of DC/DC converter integrated in a multiterminal DC grid

AbstractThe future multi‐terminal direct‐current (MTDC) grid will require the interconnection of point‐to‐point high‐voltage (HV) DC links with different specifications such as DC voltage level, system grounding configuration and HVDC technology. To adapt these differences, it is obligatory for DC/DC converters to interconnect HVDC links. Additionally, they are capable of providing supplementary functionalities as they are highly controllable devices. In this article, a primary virtual resistance DC voltage controller associated with DC/DC converter is proposed for managing DC grid voltages of the interconnected HVDC grids, increasing the reliability of the system. The commonly known topology, Front‐to‐Front Modular Multilevel Converter (F2F‐MMC) is adopted for DC/DC converter. Time‐domain simulations are performed using EMTP software for validating the controller behaviour under power disturbances and large events of loss of one converter in a MMC‐based MTDC system. The converters are modelled using reduced order modelling (ROM) methodology. Apart from this, dynamic studies have been carried out using a linear state space model for small‐signal stability analysis of a HVDC system integrating DC/DC converter with a virtual resistance DC voltage controller. The results are examined through parametric sensitivity analysis.

I-CNN-LSTM: An Improved CNN-LSTM for Transient Stability Analysis of More Electric Aircraft Power Systems

I-CNN-LSTM: An Improved CNN-LSTM for Transient Stability Analysis of More Electric Aircraft Power Systems

On hybrid dynamical systems of differential–difference equations

In this paper, we define and study a class of linear hybrid dynamical systems characterized by differential–difference equations. We introduce two operators that facilitate the analysis of these systems and derive explicit formulas for their solutions. We examine the transfer function matrix and characteristic polynomial to assess stability. Our theoretical findings are supported by numerical examples, demonstrating their application in power systems stability analysis. Specifically, we substantiate our theory within the context of power systems stability analysis, incorporating elements of discrete behavior.

An Oscillation Stability Analysis of a Direct-Driven Wind Power Grid-Connected System Considering Low Voltage Ride Though from an Energy Perspective

To solve the problem of the oscillation stability of direct-driven wind-powered grid-connected systems with a low-voltage crossing control, a method of oscillation stability analysis for these systems, based on interactive energy, is proposed in this paper. Firstly, a dynamic energy model of a direct-driven wind-powered grid-connected system is established, considering a low-voltage traverse control. Secondly, the energy is divided into four parts—the line parameter energy, current inner loop energy, PLL energy, and current inner loop–PLL interaction energy—and the conduction path of the energy during a low-voltage crossing is described. On this basis, the aperiodic components of each energy path are analyzed, the stability level of the system is quantified, the influence of the different control parameters on the interactive energy dissipation is deduced, the key interactive control links affecting the stability of the system are screened, and the influence rules of the parameters are expounded. Finally, a direct-driven wind-powered grid-connected system model is built on the Rt-lab platform, and it is verified by a simulation test. The results show that the interaction energy generated by the interaction of the current inner loop and phase-locked loop is a key factor affecting the stability of the direct-driven wind-powered grid-connected system. The simulation test parameters of the control group were adjusted as the current inner loop’s proportion parameter increased from 1.32 to 5.28, the current inner loop’s integral parameter increased from 4.48 to 6.42, the PLL’s proportion parameter decreased from 9.45 to 6.3, and the PLL’s integral parameter decreased from 50.25 to 40.2. Both the theoretical and experimental results show that increasing the current inner loop’s integral and proportion parameters can improve the stability level of the direct-driven wind-powered grid-connected system; reducing the phase-locked loop’s proportion and integral parameters can also improve the stability level of the grid-connected system.

Small-Signal Stability Analysis of DC Ship Hybrid Power System With Energy Storage Device Based on Hybrid H-Matrix Model

Small-Signal Stability Analysis of DC Ship Hybrid Power System With Energy Storage Device Based on Hybrid H-Matrix Model

Modeling and Stability Analysis of Fuel Cell-Based Marine Hybrid Power Systems

Modeling and Stability Analysis of Fuel Cell-Based Marine Hybrid Power Systems

Stability analysis of systems with delay-dependent coefficients and commensurate delays

Stability analysis of systems with delay-dependent coefficients and commensurate delays

Finite-time stability analysis of homogeneous systems with sector nonlinearities

A class of homogeneous systems with sector nonlinearities is considered in the paper. Sufficient conditions of finite-time (input-to-state) stability are established with the use of new constructive modification of the Implicit Lyapunov Function approach. The proposed conditions are given in the form of linear matrix inequalities. The theoretical results are supported with numerical examples.

Stability analysis of grid-connected inverter under full operating conditions based on small-signal stability region

Impedance analysis is a practical approach for assessing the small-signal stability of renewable energy power systems. However, existing research predominantly focuses on specific operating conditions, neglecting the fundamental principles governing stability evolution under time-varying operating conditions. This paper presents a methodology to develop the small-signal stability region (SSSR) for grid-connected inverters using the impedance method. A comprehensive stability analysis for grid-connected inverter systems is performed based on the stability region. Firstly, the multi-parameter SSSR of the grid-connected inverter is defined according to both the aggregated impedance criterion and the generalized Nyquist criterion. Furthermore, a polynomial approximation expression for the SSSR boundary is derived. Secondly, the sensitivity analysis of operating points and control parameters is performed under full operating conditions to investigate their impact on stability based on the quantified boundary. The analyses reveal that the stability of the grid-connected inverter system near the SSSR boundary decreases with increasing active power and decreasing reactive power but exhibits an initial increase followed by a decrease with a larger PLL bandwidth. Finally, the accuracy of the stability region and the influence of key parameters are verified through case studies and experiments. The study in this paper can be used for quantitative analysis of stability margins and decision guidance of control optimization for grid-connected inverters.

Stability and convergence rate analysis of continuous-time delay-difference systems with both point and distributed delays

This paper studies the exponential stability and convergence rate analysis of continuous-time delay-difference systems. Firstly, stability and convergence rate analysis of delay-difference systems with both point delays and distributed delays having exponential integral kernels are studied by using the weighted Lyapunov–Krasovskii functionals (LKFs) approach and the state transformation approach, respectively. Different sufficient stability conditions expressed by linear matrix inequalities (LMIs) are presented. Secondly, as a particular case, LMIs based conditions and spectral radius based conditions are given to ensure the exponential stability with a guaranteed convergence rate for delay-difference systems with both point delays and distributed delays having constant integral kernels, respectively. Finally, numerical examples illustrate the effectiveness of the obtained results.

The stability analysis of a dynamical system equipped with a piezoelectric energy harvester device near resonance

The stability analysis of a dynamical system equipped with a piezoelectric energy harvester device near resonance

Dynamic event-triggered neuro-optimal control for uncertain nonlinear systems with unknown dead-zone constraint

In this article, we propose a dynamic event-triggered neuro-optimal control scheme (DETNOC) for uncertain nonlinear systems subject to unknown dead-zone and disturbances through the design of a composite control law. An integral sliding mode-based discontinuous control law is utilized to compensate for the effects of unknown dead-zone, disturbance, and a component of uncertainties. As a result, a system dynamics that evolves free of these effects during the sliding mode is obtained. Then, an adaptive dynamic programming-based dynamic event-triggered optimal control law is designed to stabilize the sliding mode dynamics with the help of critic-only neural network architecture. Finally, stability analysis of the closed-loop system is provided and the effectiveness of the developed DETNOC scheme is verified.