Abstract
Tracking controllers for Euler–Lagrange systems are designed under the assumption that reference trajectories are continuous, and at least twice differentiable with respect to time. However, this assumption precludes several use cases, such as when a robot end-effector must track a path with corners at constant speed. This paper introduces the control design for tracking continuous but non-differentiable trajectories in fully actuated Euler–Lagrange systems that have continuous-time dynamics. The proposed controller combines a continuous feedback law with impulsive inputs, that are intermittently applied at the instants of non-differentiability. A Lyapunov stability analysis establishes global exponential convergence of the tracking error to zero. Since impulsive inputs are an idealized construct, a high-gain feedback design is also presented to approximate their effect for implementation. The control methodology is evaluated on two systems: an RCL circuit, and a two-link robot. Simulations corroborate the theoretical results in both cases, and demonstrate effective tracking of trajectories that are continuous, but not differentiable.
Recommended Citation
N. Kant, "Tracking Continuous Non-differentiable Trajectories in Euler–Lagrange Systems with Continuous Dynamics," Systems and Control Letters, vol. 213, article no. 106438, Elsevier, Jun 2026.
The definitive version is available at https://doi.org/10.1016/j.sysconle.2026.106438
Department(s)
Mechanical and Aerospace Engineering
Publication Status
Full Text Access
Keywords and Phrases
Euler–Lagrange systems; Hybrid system; Impulsive control; Lyapunov analysis; Mechanical systems; Nonlinear systems; Nonsmooth control; Nonsmooth system; Robotics; Tracking
International Standard Serial Number (ISSN)
0167-6911
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2026 Elsevier, All rights reserved.
Publication Date
01 Jun 2026
