The structural properties of LM-g splines are investigated by optimization and optimal control theory. The continuity and structure of LM-g splines are derived by using a class of necessary conditions with state constraints of optimal control and the relationship between LM-g interpolating splines and the corresponding L-g interpolating splines. This work provides a new method for further exploration of LM-g interpolating splines and its applications in the optimal control.
Xiongwei Liu. Xinjian Zhang. Lizhi Cheng. "The Derivation of Structural Properties of LM-g Splines by Necessary Condition of Optimal Control." Abstr. Appl. Anal. 2014 (SI10) 1 - 5, 2014. https://doi.org/10.1155/2014/641435