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Sufficient Conditions for Optimal Co...

Bhan, Sankalp Kishan.

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Sufficient Conditions for Optimal Control Problems with Terminal Constraints and Free Terminal Times with Applications to Aerospace.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Sufficient Conditions for Optimal Control Problems with Terminal Constraints and Free Terminal Times with Applications to Aerospace./
作者:	Bhan, Sankalp Kishan.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
面頁冊數:	163 p.
附註:	Source: Dissertations Abstracts International, Volume: 80-10, Section: B.
Contained By:	Dissertations Abstracts International80-10B.
標題:	Applied Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13862113
ISBN:	9781392074763

Sufficient Conditions for Optimal Control Problems with Terminal Constraints and Free Terminal Times with Applications to Aerospace.
Bhan, Sankalp Kishan.

Sufficient Conditions for Optimal Control Problems with Terminal Constraints and Free Terminal Times with Applications to Aerospace. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 163 p.

Source: Dissertations Abstracts International, Volume: 80-10, Section: B.

Thesis (D.Sc.)--Washington University in St. Louis, 2019.

This item must not be sold to any third party vendors.

Motivated by the flight control problem of designing control laws for a Ground Collision Avoidance System (GCAS), this thesis formulates sufficient conditions for a strong local minimum for a terminally constrained optimal control problem with a free-terminal time. The conditions develop within the framework of a construction of a field of extremals by means of the method of characteristics, a procedure for the solution of first-order linear partial differential equations, but modified to apply to the Hamilton-Jacobi-Bellman equation of optimal control. Additionally, the thesis constructs these sufficient conditions for optimality with a mathematically rigorous development. The proof uses an approach which generalizes and differs significantly from procedures outlined in the classical literature on control engineering, where similar formulas are derived, but only in a cursory, formal and sometimes incomplete way. Additionally, the thesis gives new arrangements of the relevant expressions arising in the formulation of sufficient conditions for optimality that lead to more concise formulas for the resulting perturbation feedback control schemes. These results are applied to an emergency perturbation-feedback guidance scheme which recovers an aircraft from a dangerous flight-path angle to a safe one. Discussion of required background material contrasts nonlinear and linear optimal control theory are contrasted in the context of aerospace applications. A simplified version of the classical model for an F-16 fighter aircraft is used in numerical computation to very, by example, that the sufficient conditions for optimality developed in this thesis can be used off-line to detect possible failures in perturbation feedback control schemes, which arise if such methods are applied along extremal controlled trajectories and which only satisfy the necessary conditions for optimality without being locally optimal. The sufficient conditions for optimality developed in this thesis, on the other hand, guarantee the local validity of such perturbation feedback control schemes. This thesis presents various graphs that compare the neighboring extremals which were derived from the perturbation feedback control scheme with optimal ones that start from the same initial condition. Future directions for this work include extending the perturbation feedback control schemes to optimization problems that are further constrained, possibly through control constraints, state-space constraints or mixed state-control constraints.

ISBN: 9781392074763Subjects--Topical Terms:

1669109
Applied Mathematics.

Sufficient Conditions for Optimal Control Problems with Terminal Constraints and Free Terminal Times with Applications to Aerospace.
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