A frequency‐constrained geometric Pontryagin maximum principle on matrix Lie groups. (22nd July 2020)

• Record Type: Journal Article
• Authors: Paruchuri, Pradyumna; Kotpalliwar, Shruti; Phogat, Karmvir Singh; Chatterjee, Debasish; Banavar, Ravi
• Other Names: Piga Dario guestEditor.; Bemporad Alberto guestEditor.
• Is Part Of: International journal of robust and nonlinear control. Volume 30:Number 15(2020)
• Page Start: 6281
• Page End: 6297
• Publication Date: 2020-07-22
• Subjects: constrained optimal control -- motion planning -- mechanical systems; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.5085
• Languages: English
• ISSNs: 1049-8923

Abstract

Abstract: We present a geometric discrete‐time Pontryagin maximum principle (PMP) on matrix Lie groups that incorporates frequency constraints on the control trajectories in addition to pointwise constraints on the states and control actions directly at the stage of the problem formulation. This PMP gives first‐order necessary conditions for optimality and leads to two‐point boundary value problems that may be solved by numerical techniques to arrive at optimal trajectories. We demonstrate our theoretical results with numerical simulations on the optimal trajectory generation of a wheeled inverted pendulum and an attitude control problem of a spacecraft on the Lie group SO (3).