First-excursion times have been developed extensively in the literature for oscillators; one major application is structural dynamics of buildings. Using the fact that most closed-loop systems operate with a moderate to high damping ratio, we have derived a new procedure for calculating first-excursion times for a class of linear continuous, time-varying systems. In several examples, we show that the algorithm is both accurate and time-efficient. These are important attributes for real-time path planning in stochastic environments, and hence the work should be useful for autonomous robotic systems involving marine and air vehicles.
A Single Differential Equation for First-Excursion Time in a Class of Linear Systems
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Greytak, M. B., and Hover, F. S. (November 23, 2011). "A Single Differential Equation for First-Excursion Time in a Class of Linear Systems." ASME. J. Dyn. Sys., Meas., Control. November 2011; 133(6): 061020. https://doi.org/10.1115/1.4004602
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