研究会 (2026 年 10 月 24 日)

Abstract:

1. For long the S-variable approach has proved its efficiency for addressing
   robustness issues with respect to matrix-valued bounded, polytopic
   uncertainties. The results are extended in this paper to generic convex
   polyhedra thus allowing robustness analysis with respect to unbounded
   uncertainties. Results apply to rationally-dependent models with respect to
   such polyhedral uncertainties. Moreover the S-variable approach is proved
   to be enhanced thanks to a new affine rows-decoupled descriptor modeling
   of such systems. Examples of application of these results are a
   reinterpretation of the KYP-lemma as well as a reformulation of the links
   between sum-of-squares approach and the S-variable approach.

2. This talk presents a novel computational method for sparse control,
   also known as maximum hands-off control, using non-convex penalty
   functions such as the minimax concave penalty. The sparse control is
   formulated as the L0-optimal control problem, which is difficult to
   directly solve. Conventionally, the L1-norm has been used as a
   surrogate for the L0 norm to numerically obtain the solution.
   However, the L1-norm approximation may not always yield sparse
   control. To overcome this difficulty, we propose non-convex functions
   such as the minimax concave penalty as a surrogate for the L0 norm. We
   establish the equivalence of the original and proposed control
   problems without relying on the normality assumption, which is
   typically required when approximating the L0 norm with the L1 norm.
   Furthermore, we present an effective numerical algorithm for the
   proposed optimal control based on the Alternating Direction Method of
   Multipliers (ADMM). A design example is shown to illustrate the
   effectiveness of the proposed method.