Adeel Akhtar

selected publications

1. IEEE ACC

   Global Accelerated Nonconvex Geometric Optimization Methods on SO(3)

   Akhtar, Adeel, and Sanfelice, Ricardo G.

   In 2023 American Control Conference (ACC), 2023

   Abs Bib HTML

   This paper proposes global accelerated nonconvex geometric (GANG) optimization algorithms for optimizing a class of nonconvex functions on the compact Lie group SO(3). Nonconvex optimization is a challenging problem because the objective function may have multiple critical points, including saddle points. We propose two accelerated geometric algorithms to escape maxima and saddle points using random perturbations. The first algorithm uses the value of the Hessian of the objective function and random perturbations to escape the undesired critical points. In contrast, the second algorithm uses only the gradient information and random perturbations to escape maxima and saddle points. The efficacy of these geometric algorithms is verified in simulations.

   @inproceedings{AkhSan2023,
     author = {Akhtar, Adeel and Sanfelice, Ricardo G.},
     booktitle = {2023 American Control Conference (ACC),},
     title = {Global Accelerated Nonconvex Geometric Optimization Methods on SO(3)},
     html = {https://ieeexplore.ieee.org/abstract/document/10155919},
     year = {2023},
     volume = {},
     number = {},
     pages = {3554-3559},
     publisher = {IEEE},
     abbr = {IEEE ACC},
     bibtex_show = {true},
     selected = {true},
     doi = {10.23919/ACC55779.2023.10155919}
   }

2. IEEE CDC

   Hybrid Geometric Controllers for Fully-Actuated Left-invariant Systems on Matrix Lie Groups

   Akhtar, Adeel, and Sanfelice, Ricardo G.

   In 2022 IEEE 61st Conference on Decision and Control (CDC) 2022

   Bib

   @inproceedings{AkhSan2022,
     author = {Akhtar, Adeel and Sanfelice, Ricardo G.},
     booktitle = {2022 IEEE 61st Conference on Decision and Control (CDC)},
     title = {Hybrid Geometric Controllers for Fully-Actuated Left-invariant Systems on Matrix Lie Groups},
     year = {2022},
     volume = {},
     number = {},
     pages = {1855-1860},
     abbr = {IEEE CDC},
     bibtex_show = {true},
     selected = {true},
     doi = {10.1109/CDC51059.2022.9992659}
   }

3. IEEE ACC

   A Class of Hybrid Geometric Controllers for Robust Global Asymptotic Stabilization on S^1

   Akhtar, A., and Sanfelice, R.

   IEEE American Control Conference (ACC), 2022

   Abs Bib

   This paper proposes a hybrid geometric control scheme for the classical problem of globally stabilizing a pointmass system on a unit circle, as it is impossible to design a smooth globally asymptotically stable controller for this problem. Unlike most existing solutions that rely on coordinates and rely on a particular controller construction, our proposed solution is coordinate free (or geometric) and belongs to a class of controllers that we also characterize. Specifically, we propose a geometric hybrid controller that uses a local geometric controller (from the said class) and an open-loop geometric controller. The system achieves global asymptotic stability when each controller from the local geometric class is combined with the geometric open-loop controller using a hybrid systems framework. Moreover, the hybrid geometric controller guarantees robust asymptotic stability. Simulations validate the stability properties of the proposed hybrid geometric controller.

   @article{AkhRic2022,
     title = {A Class of Hybrid Geometric Controllers for Robust Global Asymptotic
     Stabilization on S^1},
     author = {Akhtar, A. and Sanfelice, R.},
     journal = {IEEE American Control Conference (ACC),},
     year = {2022},
     doi = {10.23919/ACC53348.2022.9867666},
     publisher = {IEEE},
     selected = {true},
     abbr = {IEEE ACC},
     bibtex_show = {true}
   }

4. IEEE ACC

   Coordinated Path Following for a Class of Underactuated Multi-agent System using Nested Set Stabilization

   Akhtar, A.

   IEEE American Control Conference (ACC), 2022

   Abs Bib

   This paper addresses the multi-agent coordinated path following problem consisting of a class of underactuated vehicles capable of following a class of closed embedded curves in the three-dimensional space and proposes a solution using a nested set stabilization approach. The stabilization of the first set restricts each agent to the assigned path following manifold and ensures that each system stays on the path indefinitely when initialized in the neighborhood of the path. Stabilizing the second set, contained inside the first, solves the position, velocity, acceleration, or jerk-related coordination constraints. The third set, contained in the second set, satisfies the yaw, or yaw-rate-related coordination constraints. The reduction theorem establishes the asymptotic stability of each nested set, and as a result, the multi-agent coordinated path following problem is solved.

   @article{Akh2022,
     title = {Coordinated Path Following for a Class of Underactuated Multi-agent System using Nested Set Stabilization},
     author = {Akhtar, A.},
     journal = {IEEE American Control Conference (ACC),},
     year = {2022},
     publisher = {IEEE},
     selected = {true},
     doi = {10.23919/ACC53348.2022.9867249},
     abbr = {IEEE ACC},
     bibtex_show = {true}
   }

5. IEEE TCST

   Path Invariant Controllers for a UAV with a Cable-suspended Payload using a Global Parameterization

   A. Akhtar, S. Saleem, and Shan, J.

   IEEE Transactions on Control Systems Technology, 2021

   Abs Bib

   Payload delivery using unmanned aerial vehicles (UAVs) has attained central importance for smart logistics and transportation systems in the context of the fourth industrial revolution. This work considers the problem of designing a smooth dynamic feedback control law for a point mass payload suspended to a quadrotor and making the load to follow a large class of curves that includes both closed and non-closed curves. Typically, the load path following problem is solved using either a coordinate-free or a local-coordinate-based approach. However, in this article, we adopt an alternative methodology. First, we express the system dynamics in an extended Euclidean space using a global coordinate system. Second, we propose two families of functions that lead to the design of almost-global and local controllers in terms of region of convergence. We cast the load path following the problem in the framework of set stabilization, and as a result, the proposed controllers make the given path an invariant manifold. The resulting controllers guarantee that once the suspended load converges to the path, it stays on the path indefinitely while satisfying other application-specific constraints. Finally, to complement the theoretical results, we provide a successful real-world experimental validation of the proposed controller on a Quanser QDrone UAV platform with a cable-suspended payload.

   @article{AkhSalSha2021,
     title = {Path Invariant Controllers for a UAV with a Cable-suspended Payload using a Global Parameterization},
     author = {A. Akhtar, S. Saleem and Shan, J.},
     volume = {30},
     number = {5},
     pages = {2002-2017},
     journal = {IEEE Transactions on Control Systems Technology,},
     year = {2021},
     publisher = {IEEE},
     doi = {10.1109/TCST.2021.3133693},
     abbr = {IEEE TCST},
     bibtex_show = {true},
     selected = {true}
   }

6. IEEE TAC

   Controller Class for Rigid Body Tracking on SO(3)

   Akhtar, A., and Waslander, S.

   IEEE Transactions on Automatic Control, 2020

   Abs Bib HTML

   In this article, we propose a novel family of Lie algebra valued functions F_R on special orthogonal group SO(3) . Each function belonging to this family induces a novel controller that stabilizes a rigid body attitude. All controllers induced by the family FR form a controller class CR . This novel controller class CR contains both local and almost-global asymptotically stable controllers, and this article presents geometric stability results of the whole controller class C_R.

   @article{AkhWas2020,
     title = {Controller Class for Rigid Body Tracking on SO(3)},
     author = {Akhtar, A. and Waslander, S.},
     journal = {IEEE Transactions on Automatic Control,},
     %volume = {34},
     %number = {4},
     doi = {doi: 10.1109/TAC.2020.3008295.},
     year = {2020},
     publisher = {IEEE},
     abbr = {IEEE TAC},
     html = {https://ieeexplore.ieee.org/document/9137655},
     bibtex_show = {true},
     selected = {true}
   }