Stability Analysis of Spacecraft Phase Plane Control Systems: A Brief Overview and Some Problems

Chen, Zhihua; Xie, Yongchun; Guo, Yong; Guo, Jin-hua; Zhang, Kai; Liu, Wangkui; Li, Yong; Li, Guangxu; Zhou, Zhiyong

doi:10.1109/cac51589.2020.9327724

Cited by 4 publications

(6 citation statements)

References 37 publications

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“…For timely detection of a hazardous emotional state of a person in an extreme situation, it is proposed to use the phase plane method [38], the remedy of which is to build phase trajectories for differential equations in the coordinate system: the deviation of the monitored parameter x and the rate of its change y=dx/dt. To do this, it is necessary to perform the inverse conversion: to obtain the equations of the person's movements for spontaneous, emotional and reasonable control from the existing phase portraits.…”

Section: Remote Monitoring and Diagnosis Of A Person's Emotional Statementioning

confidence: 99%

Section: Variance Calculationmentioning

confidence: 99%

“…One of the frequency criteria was proposed in 1932 by the American physicist H. Nyquist, who studied the properties of electronic amplifiers with feedback. This criterion later became one of the most widely used in studies on the stability of automatic systems [38].…”

Section: Variance Calculationmentioning

confidence: 99%

“…In the theory of automatic control, another effective method for assessing stability is the use of stability criteria -generalized indicators that do not require solving the system equations. Algebraic and frequency criteria are used[38].Algebraic criteria establish necessary and sufficient conditions for stability based on determinants consisting of the coefficients of the characteristic equation of the system. The English mathematician E. Rouse (1877) and the Swiss mathematician A. Hurwitz (1893) proposed a criterion in different forms, according to which the stability conditions are reduced to the fulfillment of inequalities that link the coefficients of the system equation.…”

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confidence: 99%

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Real-time monitoring and diagnostics of the person’s emotional state and decision-making in extreme situations for healthcare

Shmelova,

Smolanka,

Sikirda

et al. 2024

Decision Making and Analysis

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Monitoring and diagnosing the emotional state is important for varied professional groups, especially, those involve in hazardous work, risks, and high responsibility (pilots, astronauts, miners, sailors, firefighters, military personnel, law enforcement officers, etc.). These professions are definitely extreme. Moreover, the number of these professions and people engaged in them is constantly increasing. Unfortunately, disorders of the emotional state are not easily recognized by visible symptoms, so prompt remote diagnosis and monitoring of a person's emotional state is important, especially in conditions of complex geography, lack of transportation and mobility of patients, reduced financial resources, or lack of medical staff. In many cases, effective supports from various participants involved in a difficult situation that could become dangerous are required to make a timely decision. The authors, who have aviation experience in operational detection of deviations in the pilot's emotional state and decision making under risk, propose to apply the concept of mental activity, which is based on the property of the mind to slow down or speed up the flow of subjective time in relation to the real one, for the monitoring and diagnosing the emotional state of a person. For the timely detection of a hazardous emotional state of a person in an extreme situation, the phase plane method is used, the essence of which is to build phase trajectories for differential equations in the coordinate system. The identification of a person's emotional state in real time is based on the variance analysis of the models of spontaneous (optimal), emotional and rational activities. The deformity of the emotional state is determined using a priori person’s models based on the actual material of a posteriori research of the accident investigations. The Nyquist criterion is used to measure the functional stability of a person. The method of real-time diagnostics of the person’s emotional state is presented. A software “Diagnostics of the emotional state of a human-operator” is developed. The problem of effective monitoring and diagnostics of a person's emotional state can be solved with the help of an Intelligent Remote Monitoring System (IRMS) built on the basis of dynamic modeling principles, when the subsystems are formalized in the form of transfer functions. A person is considered as a control object, and the monitoring and diagnostics of the emotional state are based on the analysis of the phase portrait obtained by the control device. The conceptual model and the functional diagram of medical IRMS are worked out. The algorithm for monitoring and diagnosing the person’s emotional state is presented. Mikhailov and Nyquist criteria are used to determine the IRMS stability; Mikhailov and Nyquist hodographs are built. IRMS is proposed for monitoring the emotional state of a person in medicine, sports, treatment, and for automated monitoring of persons in hazardous environments, for example, in an aeroplane (passengers), in a smart home (people), in medicine (patients), etc. Prompt monitoring and diagnosis enables timely adjustment and improvement of a person's emotional state and prevents the development of an extreme situation towards worsening. Based on the objective-subjective collaborative decision-making method under uncertainty, the problem of urgent delivery of medical cargo using UAV from the point of departure to the destination is solved. The optimal decision with minimum risk and maximum safety according to the Wald-Wald, Wald-Laplace, and Wald-Hurwitz criteria and with the consideration of all participants’ opinions on UAV transportation, is found. Based on the dynamic programming method, the task of finding a route with minimum cost is solved when it is necessary to urgently deliver medicines to a seriously ill patient using UAV.

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Section: Remote Monitoring and Diagnosis Of A Person's Emotional Statementioning

confidence: 99%

Section: Variance Calculationmentioning

confidence: 99%

Section: Variance Calculationmentioning

confidence: 99%

mentioning

confidence: 99%

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Real-time monitoring and diagnostics of the person’s emotional state and decision-making in extreme situations for healthcare

Shmelova,

Smolanka,

Sikirda

et al. 2024

Decision Making and Analysis

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“…Meanwhile, this method involves with large calculations when we calculate the time derivative of the Lyapunov candidate function [83][84][85][86][87][88][89]. The graphical phase plane approach is a better choice to analyze the stability of an equilibrium point if quantitative result is not needed [90][91][92], and this approach is a visualization-based method, which can give the conclusion without being getting into calculation, and it is faster than the Lyapunov method when determining the stability of an equilibrium point. However, this method most of the time is limited to the two-dimensional systems and can only be applied to autonomous systems, not non-autonomous systems.…”

Section: Advantages Disadvantagesmentioning

confidence: 99%

Stability Analysis of Equilibrium Point and Limit Cycle of Two-Dimensional Nonlinear Dynamical Systems—A Tutorial

Wei

2023

Applied Sciences

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The equilibrium state of a dynamical system can be divided into the equilibrium point and limit cycle. In this paper, the stability analysis of the equilibrium point and limit cycle of dynamical systems are presented through different and all possible approaches, and those approaches are compared as well. In particular, the author presented the stability analysis of the equilibrium point through phase plane approach, Lyapunov–LaSalle energy-based approach, and linearization approach, respectively, for two-dimensional nonlinear system, while the stability analysis of the limit cycle is analyzed by using the LaSalle local invariant set theorem and Poincaré–Bendixson theorem, which is only valid in two-dimensional systems. Different case studies are used to demonstrate the stability analysis of equilibrium point and limit cycle.

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Stability Analysis of A Class of Second-Order Phase Plane Control Systems: A Simulation Study

Chen¹,

Xie²,

Guo

et al. 2021

2021 33rd Chinese Control and Decision Conference (CCDC)

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Stability Analysis of Spacecraft Phase Plane Control Systems: A Brief Overview and Some Problems

Cited by 4 publications

References 37 publications

Real-time monitoring and diagnostics of the person’s emotional state and decision-making in extreme situations for healthcare

Real-time monitoring and diagnostics of the person’s emotional state and decision-making in extreme situations for healthcare

Stability Analysis of Equilibrium Point and Limit Cycle of Two-Dimensional Nonlinear Dynamical Systems—A Tutorial

Stability Analysis of A Class of Second-Order Phase Plane Control Systems: A Simulation Study

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