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Strong observability as a sufficient condition for non-singularity and lossless convexification in optimal control with mixed constraints
SherilKunhippurayil1,MatthewW.Harris2
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(1 Torc Robotics, Inc., 405 Partnership Drive, Blacksburg 24060, Virginia, USA;2 Department of Mechanical and Aerospace Engineering, Utah State University, 4130 Old Main Hill, Logan 84322, Utah, USA)
摘要:
This paper analyzes optimal control problems with linear time-varying dynamics defined on a smooth manifold in addition to mixed constraints and pure control constraints. The main contribution is the identification of sufficient conditions for the optimal controls to be non-singular, which enables exact (or lossless) convex relaxations of the control constraints. The problem is analyzed in a geometric framework using a recent maximum principle on manifolds, and it is shown that strong observability of the dual system on the cotangent space is the key condition. Two minimum time problems are analyzed and solved. A minimum fuel planetary descent problem is then analyzed and relaxed to a convex form. Convexity enables its efficient solution in less than one second without any initial guess.
关键词:  Optimal control · Strong observability · Lossless convexification
DOI:https://doi.org/10.1007/s11768-022-00115-w
基金项目:The second author was partially funded by ONR Grant N00014-22-1-2131.
Strong observability as a sufficient condition for non-singularity and lossless convexification in optimal control with mixed constraints
Sheril Kunhippurayil1,Matthew W. Harris2
(1 Torc Robotics, Inc., 405 Partnership Drive, Blacksburg 24060, Virginia, USA;2 Department of Mechanical and Aerospace Engineering, Utah State University, 4130 Old Main Hill, Logan 84322, Utah, USA)
Abstract:
This paper analyzes optimal control problems with linear time-varying dynamics defined on a smooth manifold in addition to mixed constraints and pure control constraints. The main contribution is the identification of sufficient conditions for the optimal controls to be non-singular, which enables exact (or lossless) convex relaxations of the control constraints. The problem is analyzed in a geometric framework using a recent maximum principle on manifolds, and it is shown that strong observability of the dual system on the cotangent space is the key condition. Two minimum time problems are analyzed and solved. A minimum fuel planetary descent problem is then analyzed and relaxed to a convex form. Convexity enables its efficient solution in less than one second without any initial guess.
Key words:  Optimal control · Strong observability · Lossless convexification