Physical systems with symmetry arise abundantly in applications, and are endowed with interesting mathematical structures. The present paper focusses on linear reciprocal and input-output Hamiltonian systems. Their ch...
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Finding Nash equilibria in non-cooperative games can be, in general, an exceptionally challenging task. This is owed to various factors, including but not limited to the cost functions of the game being nonconvex/nonc...
Finding Nash equilibria in non-cooperative games can be, in general, an exceptionally challenging task. This is owed to various factors, including but not limited to the cost functions of the game being nonconvex/nonconcave, the players of the game having limited information about one another, or even due to issues of computational complexity. The present tutorial draws motivation from this harsh reality and provides methods to approximate Nash or min-max equilibria in non-ideal settings using both optimization- and learning-based techniques. The tutorial acknowledges, however, that such techniques may not always converge, but instead lead to oscillations or even chaos. In that respect, tools from passivity and dissipativity theory are provided, which can offer explanations about these divergent behaviors. Finally, the tutorial highlights that, more frequently than often thought, the search for equilibrium policies is simply vain; instead, bounded rationality and non-equilibrium policies can be more realistic to employ owing to some players’ learning imperfectly or being relatively naive – "bounded rational." The efficacy of such plays is demonstrated in the context of autonomous driving systems, where it is explicitly shown that they can guarantee vehicle safety.
Groundbreaking applications such as ChatGPT have heightened research interest in generative artificial intelligence (GAI). Essentially, GAI excels not only in content generation but also signal processing, offering su...
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Mild cognitive impairment (MCI) is an early stage of non-age-related cognitive decline with an increased risk of progressing to dementia. Early detection of MCI is essential for implementing preventative strategies th...
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In pursuit-evasion the objective of the pursuer is to capture the evader. In this work, the faster pursuer is modeled to have limited range and therefore optimal strategies for the pursuer and evader change. Depending...
In pursuit-evasion the objective of the pursuer is to capture the evader. In this work, the faster pursuer is modeled to have limited range and therefore optimal strategies for the pursuer and evader change. Depending upon the range limits of the pursuer the evader may evade capture by the pursuer. This paper describes the optimal strategies and nuances that appear for point-capture or when the pursuer is endowed with a non-zero capture radius.
With the vigorous development of electricity spot market and the rapid transformation of energy structure in China, market risks have significantly increased, making the risk early warning mechanism an essential tool ...
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ISBN:
(数字)9798350365573
ISBN:
(纸本)9798350365580
With the vigorous development of electricity spot market and the rapid transformation of energy structure in China, market risks have significantly increased, making the risk early warning mechanism an essential tool for guaranteeing the safe operation of the market. This paper proposes a data-driven risk identification and comprehensive risk level early warning model for the electricity spot market. Firstly, based on the characteristics of the market, Latin hypercube sampling is utilized to construct a diverse set of scenarios which simulate the market operations. Multiple risk indicators are established, and risks are quantified through a market clearing model. Subsequently, the matter-element extension cloud model (MEECM) improved by the cloud entropy optimization algorithm is employed to classify the risks into five levels, ranging from I to V, for each time period. Finally, multiple deep neural networks are constructed to accurately predict single risk indicators for a single time period, and the MEECM is utilized to achieve an overall operational risk rating and early warning for the market. The results of case study demonstrate the effectiveness of the proposed model in risk early warning.
There are many models of memristors, but there are no reports on exponential memristors. In this paper, a three- dimension memristor Rucklidge system with exponential memristor is proposed by introducing exponential f...
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In this paper, we investigate the problem of reference tracking for a class of linear systems subject to actuator saturation and propose a performance-based model recovery anti-windup strategy. We adopt the classic mo...
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ISBN:
(数字)9798350382655
ISBN:
(纸本)9798350382662
In this paper, we investigate the problem of reference tracking for a class of linear systems subject to actuator saturation and propose a performance-based model recovery anti-windup strategy. We adopt the classic model recovery anti-windup framework and regard the states or one of the outputs of the anti-windup compensator as the tracking error, by which the difference between the unconstrained system and the saturated system is quantified. Then, instead of employing the commonly used
$\mathcal{L}_{2}$
gain, we present the prescribed performance functions (PPFs) to characterize the real-time tracking error such that the system performance can be captured more specifically. In particular, to avoid singular issues arising from the occurrence of saturation, we modify the existing PPFs with an auxiliary system when saturation occurs. Based on these modified performance functions, we follow a modified prescribed performance control approach and design the remaining output of the anti-windup compensator. Such a design procedure is constructive, making it more promising for extension to nonlinear systems. Theoretical results establish the boundedness of all signals in the closed-loop system. Simulation results verify the effectiveness of our design strategy.
In planar pursuit-evasion differential games considering a faster pursuer and slower evader, the interception points resulting from equilibrium strategies lie on the Apollonius circle. This property is instrumental fo...
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ISBN:
(数字)9798350316339
ISBN:
(纸本)9798350316346
In planar pursuit-evasion differential games considering a faster pursuer and slower evader, the interception points resulting from equilibrium strategies lie on the Apollonius circle. This property is instrumental for leveraging geometric approaches for solving multiple pursuit-evasion scenarios in the plane. Here, we study a pursuit-evasion differential game on a sphere and generalize the planar Apollonius set to the spherical domain. We find that the interception point from the equilibrium strategies can leave the Apollonius set boundary and present a condition to keep the intercept point on the boundary. This condition allows for generalizing planar pursuitevasion strategies to the sphere.
In this article, two methods of addressing path planning for a Dubins vehiclemoving on a sphere are considered, wherein either spherical coordinates or amoving frame are considered to describe the vehicle's motion...
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