Lie algebroids and optimal control: abnormality

Lie Geometric Methods in the Study of Driftless Control Affine Systems with Holonomic Distribution and Economic Applications

“…In the same way, considering Equations ( 32) and ( 35), obtain (23). Using u 1 = ẋ1 , u 2 = ẋ2 , we obtain (24) and (25).…”

“…The Pontryagin Maximum Principle on Lie algebroids is presented in [21] and later extended on almost Lie algebroids in [22]. Some aspects regarding the abnormality problem in control theory on Lie algebroids are presented in [23]. The link between optimal control and connection theory on Lie algebroids can be found in [24][25][26].…”

Optimal control of affine connection control systems from the point of view of Lie algebroids

“…The geometric description of the problem we develop here follows the formulation of Pontryagin's maximum principle proposed in [13]. The geometry provided by Lie algebroids has already been used in [3], for the purpose of characterizing abnormal critical trajectories for this kind of optimal control problem.…”