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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 |
|
|
| (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 |
