研究会 (2026 年 02 月 28 日)

Abstract:

1. Modern engineering and scientific discovery increasingly rely on the
   ability to model complex, nonlinear dynamical systems. While traditional
   first-principles models offer interpretability, they often fail to capture
   unmodeled dynamics. Conversely, pure black-box machine learning models
   excel at data fitting but often lack physical consistency and fail in
   long-term forecasting.
   This seminar presents a unified modeling framework designed to bridge
   this gap. By integrating partial physical knowledge with corrective
   data-driven components (such as sparse basis functions or kernel methods),
   we achieve models that are both physically grounded and high-performing.
   The proposed methodology shifts from classical one-step-ahead identification
   to a multi-step framework that minimizes cumulative error over extended
   horizons, ensuring reliability for control and forecasting applications.
   To capture missing dynamics without loosing interpretability, we introduce
   a sparse augmentation strategy that isolates residual effects through
   theoretical bounds and sparsity recovery. This approach is further
   hardened against the irregularities of real-world data, such as missing
   samples and aggregated measurements, by deriving robust estimation bounds
   for non-uniform observations. The effectiveness of these methods is
   demonstrated through diverse applications, ranging from spacecraft inertia
   identification and chemical reactors to ecological population dynamics.

   Bio: Cesare received the B.Sc. degree in Computer Engineering and the
   M.Sc. degree (cum laude) in Computer Engineering from Politecnico di
   Torino, Italy, where he also completed his Ph.D. in Electrical,
   Electronics, and Communication Engineering in early 2026. In 2024,
   he was a Visiting Scholar at The Pennsylvania State University.
   He is currently a postdoctoral research fellow at the Institute of
   Electronics, Computer and Telecommunication Engineering of the Italian
   National Research Council (CNR-IEIIT). He is a member of the IEEE
   committee on System Identification and Adaptive Control. His research
   interests include system identification, physics-based modeling, machine
   learning, filtering/estimation, and optimization.

2. Piecewise affine (PWA) dynamical models arise in a wide range of
   applications, including hybrid systems, model predictive control, neural
   networks, and non-linear circuit design and simulation. In this talk, we
   motivate the use of a ramp-based implicit representation of PWA systems,
   which avoids explicit enumeration of polyhedral regions and simplifies the
   study of system properties such as stability. We then introduce the Linear
   Complementarity Problem (LCP) and show how the ramp-based implicit PWA
   systems can be formulated as a Linear Complementarity System (LCS). The
   well-posedness of the underlying LCP is guaranteed when an associated
   matrix satisfies the P-matrix property. To certify P-matricity, we present
   a semidefinite programming (SDP)-based test relying on a Sum-Of-Squares
   (SOS) feasibility formulation. We show that the first relaxation yields
   known sufficient conditions for P-matricity, while higher relaxations
   allow us to certify a larger set of P-matrices.

   Bio: Pieter Van Holm is a Ph.D. student at the L2S laboratory of
   Centralesupelec, which is part of the Paris-Saclay University in France.
   He obtained his Bachelor in Electromechanical engineering from the Vrije
   Universiteit Brussel (VUB), Belgium. He obtained his master in Aeronautical
   engineering from the Vrije Universiteit Brussels (VUB) and the Universite
   Libre de Bruxelles (ULB), Belgium. He spent his second master year at
   ISAE-Supaero in Toulouse. His thesis topic is titled "Learning and
   Observing Linear Complementarity Systems."

3. We present a method of reducing the number of activation functions of a
   continuous-time recurrent neural network for its stability analysis.
   The proposed method takes advantages of the Lyapunov stability theory
   for perturbed systems. An SDP-based method of reducing the conservatism
   of the proposed reduction method is also presented.

   Bio: Tsuyoshi Yuno received his B.Eng. degree from Kumamoto University,
   Japan, in 2010. He received his M.Eng. degree and Ph.D. degree from
   Osaka University, Japan, in 2012 and 2015, respectively. In 2015, he
   joined Kyushu University, Japan, as an assistant professor at the
   Faculty of Information Science and Electrical Engineering. His research
   interests include algebraic methods in nonlinear control theory, real-time
   optimization in vehicle control, and stability analysis of neural networks.
   He is a member of IEEE, SICE, and JSAE.