Publications

Under Review

2024

1. TAC

   Matrix-Scheduling of QSR-Dissipative Systems

   Sepehr Moalemi, and James R. Forbes

   IEEE Transactions on Automatic Control (TAC), May 2024

   [Under Review | Submitted May 2024]

   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 \(\mathcal{L}_2\) 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.

2. L-CSS

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

   Sepehr Moalemi, and James R. Forbes

   IEEE Control Systems Letters (L-CSS), Sep 2024

   [Under Review | Submitted Sep 2024]

   Abstract

   This paper presents a 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. To demonstrate the utility of this passivity-based analysis, a gain-scheduling interpretation of the gradient descent method with time-varying step size is presented using Kronecker delta scheduling functions. Finally, a new variation of the gradient descent method is proposed, where the input and output of the gradient are scaled using the scheduling functions.

Conference Papers

2024

1. CCTA

   Passivity-Based Gain-Scheduled Control with Scheduling Matrices

   Sepehr Moalemi, and James R. Forbes

   IEEE Conference on Control Technology and Applications (CCTA), Feb 2024

   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},
     month = feb,
     doi = {0.1109/CCTA60707.2024.10666540},
   }