Region Of Attraction Research Articles

Stability Analysis Using Quadratic Constraints for Systems With Neural Network Controllers

A method is presented to analyze the stability of feedback systems with neural network controllers. Two stability theorems are given to prove asymptotic stability and to compute an ellipsoidal innerapproximation to the region of attraction (ROA). The first theorem addresses linear time-invariant systems, and merges Lyapunov theory with local (sector) quadratic constraints to bound the nonlinear activation functions in the neural network. The second theorem allows the system to include perturbations such as unmodeled dynamics, slope-restricted nonlinearities, and time delay, using integral quadratic constraint (IQCs) to capture their input/output behavior. This in turn allows for off-by-one IQCs to refine the description of activation functions by capturing their slope restrictions. Both results rely on semidefinite programming to approximate the ROA. The method is illustrated on systems with neural networks trained to stabilize a nonlinear inverted pendulum as well as vehicle lateral dynamics with actuator uncertainty.

Instability of dwell-time constrained switched nonlinear systems

Analyzing the stability of switched nonlinear systems under dwell-time constraints, this article investigates different scenarios where all the subsystems have a common globally asymptotically stable (GAS) equilibrium, but for the switched system, the equilibrium is not uniformly GAS for arbitrarily large values of dwell-time. We motivate our study with the help of examples showing that, if near the origin all the vector fields decay at a rate slower than the linear vector fields, then the trajectories are ultimately bounded for large enough dwell-time. On the other hand, if away from the origin, the vector fields do not grow as fast as the linear vector fields, then we can only guarantee local asymptotic stability for large enough dwell-times, with region of attraction depending on the dwell-time itself. We formalize our observations for homogeneous systems, and show that, even if the origin is not uniformly GAS with dwell-time switching for nonlinear systems, it still holds that the trajectories starting from a bounded set converge to a neighborhood of the origin if the dwell-time is large enough.

Computation of Regions of Attraction for Hybrid Limit Cycles Using Reachability: An Application to Walking Robots

Contact-rich robotic systems, such as legged robots and manipulators, are often represented as hybrid systems. However, the stability analysis and region-of-attraction computation for these systems are often challenging because of the discontinuous state changes upon contact (also referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">state resets</i> ). In this work, we cast the computation of region-of-attraction as a Hamilton-Jacobi (HJ) reachability problem. This enables us to leverage HJ reachability tools that are compatible with general nonlinear system dynamics, and can formally deal with state and input constraints as well as bounded disturbances. Our main contribution is the generalization of HJ reachability framework to account for the discontinuous state changes originating from state resets, which has remained a challenge until now. We apply our approach for computing region-of-attractions for several underactuated walking robots and demonstrate that the proposed approach can (a) recover a bigger region-of-attraction than state-of-the-art approaches, (b) handle state resets, nonlinear dynamics, external disturbances, and input constraints, and (c) also provides a stabilizing controller for the system that can leverage the state resets for enhancing system stability.

Regional consensus in discrete-time multi-agent systems subject to time-varying delays and saturating actuators

This paper deals with consensus in discrete-time multi-agent systems under directed networks subject to time-varying delays and input saturation. Because saturation might prevent multi-agent systems from attaining consensus, system analysis and controller design require the characterization of the allowed region for the initial conditions. The main contributions of this work are sufficient conditions for consensus analysis and design of distributed protocols for discrete-time systems. Moreover, the conditions lead to a procedure allowing an estimate of the region of attraction. Such a procedure considers the effect of current and delayed states separately, yielding broader estimates of the allowed region for initial conditions. The results follow from the transformation of the consensus problem into a stability problem, with the subsequent employment of the Lyapunov-Krasovskii theory. The conditions are formulated as convex optimization problems. Finally, the paper presents examples and comparisons with previous approaches to illustrate the validity of the proposed methods.

Static output‐feedback stabilization of discrete‐time linear parameter‐varying systems under actuator saturation

AbstractThis paper introduces a novel local synthesis condition for gain‐scheduling static output‐feedback control of discrete‐time linear parameter‐varying (LPV) systems under actuator saturation and state constraints. The proposed condition is formulated as a set of parameter‐dependent linear matrix inequalities that are incorporated into a convex optimization procedure to provide an enlarged estimate of the region of attraction of the closed‐loop equilibrium. In contrast with related works, the proposed approach allows handling a wider class of LPV systems since no rank condition is required to employ the so‐called equality constraints.

Stability conditions for some classes of time-varying switched systems

In the paper, some classes of time-varying nonlinear switched systems are considered. The stability problem is investigated. The Lyapunov direct method and the theory of differential inequalities are used. The non-stationary switched comparison equation with hybrid degrees is constructed for the considered system. Switching in the comparison equation can be caused by changing the operating modes, as well as changing non-stationary parameters of the system. Sufficient conditions of the asymptotic and finite-time stability are obtained. The region of attraction for the given equilibrium position is estimated. Some examples are presented to illustrate the results. In particular, some classes of nonlinear mechanical system are studied.

Image Quality Evaluation Based on Gradient, Visual Saliency, and Color Information

This paper proposes an image quality evaluation (IQE) metric by considering gradient, visual saliency, and color information. Visual saliency and gradient information are two types of effective features for quality evaluation research. Different regions within an image are not uniformly important for IQE. Visual saliency can find the most attractive regions to the human visual system in a given image. These attractive image regions are more strongly correlated with image quality results. In addition, the degradation of gradient information is related to the structure distortion which is a very important factor for image quality. However, the two types of features cannot accurately evaluate the color distortion of images. In order to evaluate chromatic distortion, this paper proposes the color similarity which is measured in the YIQ color space. The computation of the proposed method begins with the similarity calculation of local gradient information, visual saliency, and color information. Then, the final quality score is obtained by the standard deviation on each similarity component. The experimental results on five benchmark databases (i.e., CSIQ, IVC, LIVE, TID2013, and TID2008) show that the proposed IQE method performs better than other methods in the correlation with subjective quality judgment.

Neural Lyapunov Control for Power System Transient Stability: A Deep Learning-Based Approach

Power system control and transient stability analysis play essential roles in secure system operation. Control of power systems typically involves highly nonlinear and complex dynamics. Most of the existing works address such problems with additional assumptions in system dynamics, leading to a requirement for a complete and general solution. This paper, therefore, proposes a novel control framework for various power system control and stability problems leveraging a learning-based approach. The proposed framework includes a two-module structure that iteratively and jointly learns the candidate Lyapunov function and control law via deep neural networks in a learning module. Meanwhile, it guides the learning procedure towards valid results satisfying Lyapunov conditions in a falsification module. The introduced termination criteria ensure provable system stability. This control framework is verified through several studies handling different types of power system control problems. The results show that the proposed framework is generalizable and can simplify the control design for complex power systems with the stability guarantee and enlarged region of attraction.

On the dynamics of the diffusive Field-Noyes model for the Belousov-Zhabotinskii reaction

In this paper, a diffusive Field-Noyes model for the Belousov-Zhabotinskii reaction is considered. We are mainly concerned with the global existence, boundedness and the asymptotic behaviors of the solutions. Of our particular interests, we focus on the existence of attraction region which attracts all the solutions of the system (regardless of the initial values), the global asymptotic stability of the constant positive equilibrium solution, the lumped parameter phenomenon, as well as Turing instability of the spatially homogeneous periodic solutions. In particular, a general formula in terms of the diffusion rates for the general 3×3 reaction-diffusion system is derived to determine Turing instability of the Hopf bifurcating periodic solutions, which extends our earlier results on general 2×2 reaction-diffusion system.

Strongly Nonlinear Diffusion in Turbulent Environment: A Problem with Infinitely Many Couplings

The field theoretic renormalization group is applied to the strongly nonlinear stochastic advection-diffusion equation. The turbulent advection is modelled by the Kazantsev–Kraichnan “rapid-change” ensemble. As a requirement of the renormalizability, the model necessarily involves infinite number of coupling constants (“charges”). The one-loop counterterm is calculated explicitly. The corresponding renormalization group equation demonstrates existence of a pair of two-dimensional surfaces of fixed points in the infinite-dimensional parameter space. If the surfaces contain infrared attractive regions, the problem allows for the large-scale, long-time scaling behaviour. For the first surface (advection is irrelevant), the critical dimensions of the scalar field Δθ, the response field Δθ′ and the frequency Δω are nonuniversal (through the dependence on the effective couplings) but satisfy certain exact identities. For the second surface (advection is relevant), the dimensions are universal and they are found exactly.

Regional sampled-data synchronization of chaotic neural networks using piecewise-continuous delay dependent Lyapunov functional

In this paper, a regional sampled-data synchronization criterion is proposed for the chaotic neural networks (CNNs) with input saturation using the piecewise-continuous delay dependent Lyapunov functional (PDDLF) approach. The aim of this work is to enlarge the region of attraction (ROA) of the synchronous state for CNNs with input saturation. Unlike existing works, the Lyapunov functional in the proposed approach is constructed from a polynomial with respect to the piecewise-continuous delay. Moreover, the proposed Lyapunov functional is combined with looped-functionals to derive the sufficient condition. The synchronization criterion is formulated in terms of sum of squares (SOS) programs, which reduces the infinite-dimensional linear matrix inequality (LMI) conditions to a finite number of SOS conditions. A numerical example is presented to illustrate the effectiveness and advantages of the proposed approach.

Geographical Analysis for the Population Attraction Area in Kirkuk City

It is possible to know the direction of the population movementor the direction of the cities development through indicating the population attraction region of the city. It means the fair distribution of people around this certain region. To explain the regional discrepancy, it depends on two alternatives which are population and the urban invested area and the amount of alterative through sequences of time It gives a vivid image of actual value in the city in present time and future which is taken to be a guidance for the urban Planner to design a plan to the current use and the probable use inside or at the edges. The population use is necessary to provide service which is by the urban inhabitant to create environment away from complication.

Hamilton-Based Stability Criterion and Attraction Region Estimation for Grid-Tied Inverters Under Large-Signal Disturbances

As the crucial interface of renewable energy integration, the stable operation of power converters under grid faults and external disturbances has become much more important. However, synchronization instability of grid-tied inverters has been found caused by the phase-locked loop (PLL) under some critical operating conditions, such as the grid voltage sag, current surge, and transmission line faults. Due to the strong nonlinearity, transient stability analysis of inverters with PLL becomes much more complicated under large-signal perturbations and weak grid conditions. In this article, the large-signal synchronization stability of grid-tied inverters is investigated from the energy perspective. Based on the structural resemblance between the PLL and synchronous generator, the energy function is constructed to establish a port-Hamiltonian model for the grid-tied inverter. For the nonlinear inverter system, an explicit Hamilton-based stability criterion is developed for grid-tied converters according to the concept of dissipativity and LaSalle&#x2019;s theorem. Moreover, the analytical stability boundary is acquired based on the proposed stability criterion and attraction region estimation, covering both controller parameters and grid parameters. To verify the effectiveness of the proposed analysis approach, extensive simulation and experimental results are presented. Compared with the conventional large-signal methods, the proposed Hamilton-based approach has explicit physical meaning and high accuracy.

Research of Eastern Siberia Oils with the Use of Infrared Spectroscopy Method

Oil is a multicomponent mixture and infrared spectroscopy may be one of the most instant methods for determining the classes of hydrocarbon compounds. Oil consists of organic and mineral compounds. It is found in all types of rocks and can be met in the most unexpected places. The rate and volume of oil and gas production depends on many factors involving natural and man-made ones. The forecast for the development of fluid systems of various types and for their regimes plays an important part in assessing water resources, their management conditions, and for designing and developing hydrocarbon deposits. Currently, Eastern Siberia is one of the most attractive regions for investors [1-3]. There is one of the largest Russian oil and gas basins belonging to the Siberian platform in the Irkutsk region [4-6]. This work presents the study of Eastern Siberia oils with the use of infrared spectroscopy in order to determine the chemical group composition and spectral indices of oils.

Stability conditions and estimation of the region of attraction for a class of nonlinear switched systems

Stability conditions and estimation of the region of attraction for a class of nonlinear switched systems

Learning‐based robust control methodologies under information constraints

Learning‐based robust control methodologies under information constraints

CONTEMPORARY GEOPOLITICS OF EURASIA AND THE BELT AND ROAD INITIATIVE

In 2013, Chinese President Xi Jinping launched the Belt and Road Initiative. This modern initiative aims to revive the ancient Silk Road and connect China with many neighboring and distant countries and economic blocs. China invests mainly in infrastructure by developing a network of land and maritime roads, facilitating communication, trade and transportation. The various projects under this initiative will make China a leader in international trade and an attractive region for giant partners. This paper analyzes the Chinese presence in Eurasia after the launch of the Belt and Road Initiative and the contemporary geopolitics of Eurasia in light of the great Chinese expansion. This study contributes to clarifying the China-Central Asia relationship and represents this relationship within the framework of the Belt and Road Initiative. This study is based on data issued by governmental institutions and international research centers, which makes it an important reference in Central Asian studies. This paper concluded that the Belt and Road Initiative will have a significant impact on the economy of Central Asia and its geopolitical position through the great Chinese openness and dependence on Central Asia in China’s regional and international trade. The paper also discusses the Sino-Russian contrast that may arise with the Chinese penetration into Central Asia.

Resilient perimeter control for hyper-congested two-region networks with MFD dynamics

Understanding the resilience of transportation networks has received considerable research attention. Nevertheless in the field of network traffic flow control, few control approaches target the mitigation from hyper-congestion, and the control objective has rarely touched the system resilience requirement which focuses on system recovering from hyper-congested state. This paper sheds light on a resilience-oriented network control. We firstly define the traffic resilience as the integral of deviation against optimal state from disturbance generation moment t0 to recovery moment tf. Then, we propose a control method under hyper-congested situations by formulating the analytical problem using a two-reservoir transportation system with parabola-shaped Macroscopic Fundamental Diagrams (MFDs), using phase diagram analysis, attraction region derivation and switched controller design. Afterwards, we evaluate the system resilience performances between two classic perimeter control schemes (constant perimeter control (CPC) and state-feedback control (SFC)) and the proposed resilient control scheme. Results show that proposed controller can ensure the system to recover from hyper-congestion to the optimal state while existing studies failed to recover. This resilience is confirmed in various case study scenarios, e.g., when the level of hyper-congestion is different. More promisingly, the proposed control shows high compatibility with the form of the MFDs, e.g., the recover can be achieved under hysteresis conditions which are common for network-level traffic dynamics. These findings will help to design an intelligent transportation system with enhanced resilience.

Command Governor Strategy Based on Region of Attraction

Command Governor Strategy Based on Region of Attraction

ISS control for continuous‐time systems with filtered time‐varying parameter and saturating actuators

AbstractThis paper presents new convex conditions to design robust and linear parameter varying (LPV) gains for continuous time‐varying systems subject to saturating actuator and energy bounded disturbances. The input‐to‐state stability conditions are used to design controllers ensuring the minimization of the ‐gain between the disturbance input and the controlled output. Furthermore, optimization procedures to maximize the estimate of the region of attraction, and the bound to the control signal as well, are formulated. The efficacy of the proposed methods is illustrated with numerical examples, including a reference tracking problem, where realistic simulations are performed.