Near-optimal feedback strategies for optimal control and pursuit-evasion games: A spatial statistical approach

Pradipto Ghosh, Bruce A. Conway

Research output: Chapter in Book/Report/Conference proceedingConference contribution


This paper presents a new extremal-field approach for synthesizing nearly-optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general non-linear differential equations. The proposed method utilizes a spatial statistical technique called universal kriging to construct the surrogate model of a feedback controller, which is capable of quickly predicting an optimal control estimate based on current state (and time) information. The kriging framework estimates an unknown function by observing its input-output behavior at a number of neighboring 'training' sites. In universal kriging, a feedback map is considered to be the linear combination of a deterministic regression polynomial model and Gaussian random function. The parameters of the kriging model are computed based on data from offline-computed open-loop extremals, generated by a direct or indirect method. Numerical examples involving both autonomous and nonautonomous systems are presented to evaluate the effectiveness of this methodology. For each solved problem, the performance of the feedback controller is ascertained by comparing the feedback solutions with open-loop ones. The numerical accuracy of the feedback solutions is very encouraging, and the low computational overhead of this approach makes it a suitable candidate for real-time applications.

Original languageEnglish (US)
Title of host publicationAIAA/AAS Astrodynamics Specialist Conference 2012
StatePublished - 2012
EventAIAA/AAS Astrodynamics Specialist Conference 2012 - Minneapolis, MN, United States
Duration: Aug 13 2012Aug 16 2012

Publication series

NameAIAA/AAS Astrodynamics Specialist Conference 2012


ConferenceAIAA/AAS Astrodynamics Specialist Conference 2012
CountryUnited States
CityMinneapolis, MN

ASJC Scopus subject areas

  • Aerospace Engineering
  • Astronomy and Astrophysics

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