Sepehr Moalemi

M.Sc. Mechanical Engineering
McGill University DECAR Group

I’m finishing my Master’s degree in Mechanical Engineering (Thesis) under the supervision of Prof. James Richard Forbes at McGill’s DECAR research group. My research focuses on studying optimization algorithms through the lens of control theory. More specifically, I’m interested in analyzing the stability and robustness of popular optimization algorithms using input-output theory. Within the context of gain-scheduling dissipative systems, I have also worked on extending the existing gain-scheduling architecture to a more general class of scheduling functions and dissipative systems.

I obtained my B.Eng. in Mechanical Engineering (Honors) from McGill, with a minor in Computer Science and a minor in Mathematics. For my undergraduate thesis, I was part of the McGill Computational Aerodynamics Group under the supervision of Prof. Siva Nadarajah.

News

Feb 01, 2025 Journal		Our paper, Matrix-Scheduling of QSR-Dissipative Systems, has been accepted as a full paper in TAC and is tentatively scheduled to appear in the August 2025 issue! Abstract This paper considers gain-scheduling of QSR-dissipative subsystems using scheduling matrices. The corresponding QSR-dissipative properties of the overall matrix-gain-scheduled system, which depends on the QSR properties of the subsystems scheduled, are explicitly derived. The use of scheduling matrices is a generalization of the scalar scheduling signals used in the literature, and allows for greater design freedom when scheduling systems, such as in the case of gain-scheduled control. Furthermore, this work extends the existing gain-scheduling results to a broader class of QSR-dissipative systems. The matrix-scheduling of important special cases, such as passive, input strictly passive, output strictly passive, finite L2 gain, very strictly passive, and conic systems are presented. The proposed gain-scheduling architecture is used in the context of controlling a planar three-link robot subject to model uncertainty. A novel control synthesis technique is used to design QSR-dissipative subcontrollers that are gain-scheduled using scheduling matrices. Numerical simulation results highlight the greater design freedom of scheduling matrices, leading to improved performance. PDF
Jan 27, 2025 Conference		Our paper proposing the Input-Output Stability of Gradient Descent: A Discrete-Time Passivity-Based Approach has been accepted to ACC 2025. Abstract This paper presents a discrete-time passivity-based analysis of the gradient descent method for a class of functions with sector-bounded gradients. Using a loop transformation, it is shown that the gradient descent method can be interpreted as a passive controller in negative feedback with a very strictly passive system. The passivity theorem is then used to guarantee input-output stability, as well as the global convergence, of the gradient descent method. Furthermore, provided that the lower and upper sector bounds are not equal, the input-output stability of the gradient descent method is guaranteed using the weak passivity theorem for a larger choice of step size. Finally, to demonstrate the utility of this passivity-based analysis, a new variation of the gradient descent method with variable step size is proposed by gain-scheduling the input and output of the gradient. PDF
Sep 25, 2024 Workshop		I Led an introduction to MATLAB workshop session for McGill Biomedical Engineering students. Files
Aug 21, 2024 Presentation		I presented our work on the Passivity-Based Gain-Scheduled Control with Scheduling Matrices at CCTA 2024. Abstract This paper considers gain-scheduling of very strictly passive (VSP) subcontrollers using scheduling matrices. The use of scheduling matrices, over scalar scheduling signals, realizes greater design freedom, which in turn can improve closed-loop performance. The form and properties of the scheduling matrices such that the overall gain-scheduled controller is VSP are explicitly discussed. The proposed gain-scheduled VSP controller is used to control a rigid two-link robot subject to model uncertainty where robust input-output stability is assured via the passivity theorem. Numerical simulation results highlight the greater design freedom, resulting in improved performance, when scheduling matrices are used over scalar scheduled signals. PDF Slides Code
Jul 24, 2024 Presentation		I presented our preliminary work on the Input-Output Stability of First-Order Optimization Algorithms: A Passivity Approach at ISMP 2024. I also chaired the Optimal Control, PDE Constrained Optimization, and Multi-level Methods 1 session! Abstract In this presentation, the stability of popular first-order optimization algorithms is examined through the lens of passivity. The passivity theorem ensures input-output stability of a passive plant connected in a negative feedback loop with a very strictly passive (VSP) system. Combining existing work on control interpretation of first-order optimization algorithms with loop transformation techniques, it is shown that gradient descent (GD) can be rendered passive, while the more recent triple momentum (TM) method is input strictly passive (ISP). It is shown that the sector boundedness of the gradient of an L-smooth, m-strongly convex function renders it being VSP. Therefore, the passivity theorem can ensure input-output stability of GD when the gradient is L-smooth, m-strongly convex. Slides

Selected Publications

CCTA
Passivity-Based Gain-Scheduled Control with Scheduling Matrices

Sepehr Moalemi, and James R. Forbes

IEEE Conference on Control Technology and Applications (CCTA)

Abstract PDF Code Slides BibTeX

This paper considers gain-scheduling of very strictly passive (VSP) subcontrollers using scheduling matrices. The use of scheduling matrices, over scalar scheduling signals, realizes greater design freedom, which in turn can improve closed-loop performance. The form and properties of the scheduling matrices such that the overall gain-scheduled controller is VSP are explicitly discussed. The proposed gain-scheduled VSP controller is used to control a rigid two-link robot subject to model uncertainty where robust input-output stability is assured via the passivity theorem. Numerical simulation results highlight the greater design freedom, resulting in improved performance, when scheduling matrices are used over scalar scheduled signals.
@inproceedings{moalemi_forbes_vsp_gs_ccta, author = {Moalemi, Sepehr and Forbes, James R.}, title = {Passivity-Based Gain-Scheduled Control with Scheduling Matrices}, booktitle = {IEEE Conference on Control Technology and Applications (CCTA)}, pages = {7--13}, year = {2024}, doi = {0.1109/CCTA60707.2024.10666540}, }

To Appear

TAC

Matrix-Scheduling of QSR-Dissipative Systems

Sepehr Moalemi, and James R. Forbes

IEEE Transactions on Automatic Control (TAC)

Abstract PDF Code

This paper considers gain-scheduling of QSR-dissipative subsystems using scheduling matrices. The corresponding QSR-dissipative properties of the overall matrix-gain-scheduled system, which depends on the QSR properties of the subsystems scheduled, are explicitly derived. The use of scheduling matrices is a generalization of the scalar scheduling signals used in the literature, and allows for greater design freedom when scheduling systems, such as in the case of gain-scheduled control. Furthermore, this work extends the existing gain-scheduling results to a broader class of QSR-dissipative systems. The matrix-scheduling of important special cases, such as passive, input strictly passive, output strictly passive, finite \(\mathcal{L}_2\) gain, very strictly passive, and conic systems are presented. The proposed gain-scheduling architecture is used in the context of controlling a planar three-link robot subject to model uncertainty. A novel control synthesis technique is used to design QSR-dissipative subcontrollers that are gain-scheduled using scheduling matrices. Numerical simulation results highlight the greater design freedom of scheduling matrices, leading to improved performance.
ACC

Input-Output Stability of Gradient Descent: A Discrete-Time Passivity-Based Approach

Sepehr Moalemi, and James R. Forbes

American Control Conference (ACC)

Abstract PDF

This paper presents a discrete-time passivity-based analysis of the gradient descent method for a class of functions with sector-bounded gradients. Using a loop transformation, it is shown that the gradient descent method can be interpreted as a passive controller in negative feedback with a very strictly passive system. The passivity theorem is then used to guarantee input-output stability, as well as the global convergence, of the gradient descent method. Furthermore, provided that the lower and upper sector bounds are not equal, the input-output stability of the gradient descent method is guaranteed using the weak passivity theorem for a larger choice of step size. Finally, to demonstrate the utility of this passivity-based analysis, a new variation of the gradient descent method with variable step size is proposed by gain-scheduling the input and output of the gradient.