The scope of this article is the well-known wall pursuit game, which has been used in the literature to illustrate the existence of a singular surface (dispersal line) and the associated game ...dilemma. We derive an analytical expression for the value function of the game, which is the viscosity solution of the Hamilton-Jacobi-Isaacs equation. Then, we introduce a hold time analysis and the rate of change for the loss of time to capture along the dispersal line, and show that the rate has a well-defined saddle point along the dispersal line, which can be used to resolve the dilemma. Moreover, we prove that the saddle point of the rate characterizes optimal game actions not only on the dispersal line, but also for all other states of the game. Finally, we analyze the same game in a version with a nonzero hold time and show that in that case, the actions from the dispersal line have to be applied both on the dispersal line and in a narrow band around it. To illustrate that, we use an example to compute the band around the line.
In this article an <inline-formula><tex-math notation="LaTeX">N</tex-math></inline-formula>-pursuer versus <inline-formula><tex-math notation="LaTeX">M</tex-math></inline-formula>-evader team ...conflict is studied. This article extends classical differential game theory to simultaneously address weapon assignments and multiplayer pursuit-evasion scenarios. Saddle-point strategies that provide guaranteed performance for each team regardless of the actual strategies implemented by the opponent are devised. The players' optimal strategies require the codesign of cooperative optimal assignments and optimal guidance laws. A representative measure of performance is employed and the Value function of the attendant game is obtained. It is shown that the Value function is continuously differentiable and that it satisfies the Hamilton-Jacobi-Isaacs equation-the curse of dimensionality is overcome and the optimal strategies are obtained. The cases of <inline-formula><tex-math notation="LaTeX">N=M</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">N>M</tex-math></inline-formula> are considered. In the latter case, cooperative guidance strategies are also developed in order for the pursuers to exploit their numerical advantage. This article provides a foundation to formally analyze complex and high-dimensional conflicts between teams of <inline-formula><tex-math notation="LaTeX">N</tex-math></inline-formula> pursuers and <inline-formula><tex-math notation="LaTeX">M</tex-math></inline-formula> evaders by means of differential game theory.
Purpose - This paper aims to investigate the barriers for adopting mobile banking services. From a methodological perspective, this paper seeks to build on two widely used models for technology ...adoption, the Technology Acceptance Model (TAM) and Innovation Diffusion Theory and to test a model that is better able to predict consumers' intention to use mobile banking.Design methodology approach - A research model extends the TAM model by additionally examining the effects of compatibility, trust, credibility, perceived risk and cost on behavioural intention. The empirical approach was based on an online survey of 263 young people in Germany, undertaken during August September 2009. The data were analysed using structural equation modelling.Findings - The results of the study indicated that compatibility, perceived usefulness, and risk are significant indicators for the adoption of m-banking services. Compatibility not only had a strong direct effect but was also identified as an important antecedent for perceived ease of use, perceived usefulness and credibility. Trust and credibility are crucial in reducing the overall perceived risk of m-banking.Originality value - The results of this study have implications for researchers and practitioners. The proposed model explains 65 per cent of the variance in intention to adopt mobile phone banking, which is more than the 40 per cent of variance typically found in other studies using the TAM. This study provides a basis for further refinement of models to predict technology adoption, in particular the inclusion of compatibility as a predictor of behavioural intention. In terms of behavioural and demographic data, the study focuses on segments of individuals who are most likely to adopt m-banking.
Circular Target Defense Differential Games Von Moll, Alexander; Pachter, Meir; Shishika, Daigo ...
IEEE transactions on automatic control,
07/2023, Letnik:
68, Številka:
7
Journal Article
Recenzirano
In this paper, the problem of guarding a circular target wherein the Defender(s) is constrained to move along its perimeter is posed and solved using a differential game theoretic approach. Both the ...one-Defender and two-Defender scenarios are analyzed and solved. The mobile Attacker seeks to reach the perimeter of the circular target, whereas the Defender(s) seeks to align itself with the Attacker, thereby ending the game. In the former case, the Attacker wins, and the Attacker and Defender play a zero-sum differential game where the payoff/cost is the terminal angular separation. In the latter case, the Defender(s) wins, and the Attacker and Defender play a zero-sum differential game where the cost/payoff is the Attacker's terminal distance to the target. This formulation is representative of a scenario in which the Attacker inflicts damage on the target as a function of its terminal distance. The state-feedback equilibrium strategies and Value functions for the Attacker-win and Defender(s)-win scenarios are derived for both the one- and two-Defender cases, thus providing a solution to the Game of Degree. Analytic expressions for the separating surfaces between the various terminal scenarios are derived, thus providing a solution to the Game of Kind. An alternative game is formulated and solved in the case of Attacker win wherein the Attacker seeks to minimize time to reach the target.
Pure Pursuit with an Effector Von Moll, Alexander; Pachter, Meir; Fuchs, Zachariah
Dynamic games and applications,
09/2023, Letnik:
13, Številka:
3
Journal Article
Recenzirano
The study of pursuit curves is valuable in the context of air-to-air combat as pure pursuit guidance (heading directly at the target) is oftentimes implemented. The problems considered in this paper ...concern a Pursuer, implementing pure pursuit (i.e., line of sight guidance), chasing an Evader who holds course. Previous results are applicable to the case in which capture is defined as the two agents being coincident, i.e., point capture. The focus here is on obtaining results for the more realistic case where the pursuer is endowed with an effector whose range is finite. The scenario in which the Evader begins
inside
the Pursuer’s effector range is also considered (i.e., escape from persistent surveillance, among other potential applications). Questions herein addressed include: does the engagement end in head-on collision or tail chase, will the Evader be captured or escape, what is the minimum distance the Pursuer will attain, for two Pursuers, is simultaneous capture/escape optimal and, if so, what is the optimal heading for the Evader (max time to capture, or min time to escape), and the feasibility for a fast Evader to escape from many Pursuers. Where possible, closed-form, analytic results are obtained, otherwise attention is given to computability with an eye towards real-time, on-board implementation.
A scenario is considered in which two cooperative Attackers aim to infiltrate a circular target guarded by a Turret. The engagement plays out in the two-dimensional plane; the holonomic Attackers ...have the same speed and move with simple motion and the Turret is stationary, located at the target circle's center, and has a bounded turn rate. When the Turret's look angle is aligned with an Attacker, that Attacker is neutralized. In this article, we focus on a region of the state space, wherein only one of the Attackers is able to reach the target circle-and even then, only with the help of its partner Attacker. The Runner distracts the Turret until it is neutralized, which allows the Penetrator to gain a positional advantage and guarantee success in hitting the target circle. We formulate the Turret-Runner-Penetrator scenario as a differential game over the value of the subsequent game of min/max terminal angle, which takes place between the Turret and Penetrator once the Runner has been neutralized. The solution to the game of degree, including equilibrium Turret, Runner, and Penetrator strategies, as well as the Value function is given. The case in which the Penetrator can reach the target before the Turret can neutralize the Runner is formulated and solved. Finally, the assumption of a priori defined roles/goals is relaxed and the minimum of the solutions to the two fixed-role games is shown to be a global stackelberg equilibrium (GSE).
Abstract
In this paper, we determine two asymptotic results for Jack measures $M(v^{\textrm {out}}, v^{\textrm {in}})$, a measure on partitions defined by two specializations $v^{\textrm {out}}, ...v^{\textrm {in}}$ of Jack polynomials proposed by Borodin–Olshanski in 10. Assuming $v^{\textrm {out}} = v^{\textrm {in}}$, we derive limit shapes and Gaussian fluctuations for the anisotropic profiles of these random partitions in three asymptotic regimes associated to vanishing, fixed, and diverging values of the Jack parameter. To do so, we introduce a generalization of Motzkin paths we call “ribbon paths,” show for arbitrary $v^{\textrm {out}}, v^{\textrm {in}}$ that certain Jack measure joint cumulants ${\kappa _n}$ are weighted sums of connected ribbon paths on $n$ sites with $n-1+g$ pairings, and derive our two results from the contributions of $(n,g)=(1,0)$ and $(2,0)$, respectively. Our analysis makes use of Nazarov–Sklyanin’s spectral theory for Jack polynomials. As a consequence, we give new proofs of several results for Schur measures, Plancherel measures, and Jack–Plancherel measures. In addition, we relate our weighted sums of ribbon paths to the weighted sums of ribbon graphs of maps on non-oriented real surfaces recently introduced by Chapuy–Dołęga.
Surveillance of a Faster Fixed-Course Target Weintraub, Isaac E.; Von Moll, Alexander; Garcia, Eloy ...
IEEE transactions on aerospace and electronic systems,
08/2023, Letnik:
59, Številka:
4
Journal Article
Recenzirano
Odprti dostop
The maximum surveillance of a target which is holding course is considered, wherein an observer vehicle aims to maximize the time that a faster target remains within a fixed-range of the observer. ...This entails two coupled phases: an approach phase and observation phase. In the approach phase, the observer strives to make contact with the faster target, such that in the observation phase, the observer is able to maximize the time where the target remains within range. Using Pontryagin's Minimum Principle, the optimal control laws for the observer are found in closed-form. Example scenarios highlight various aspects of the engagement.
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