Related papers: A characterization of normal forms for control sys…
The Pontryagin's Maximum Principle allows, in most cases, the design of optimal controls of affine nonlinear control systems by considering the sign of a smooth function. There are cases, although, where this function vanishes on a whole…
Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic…
A crucial problem in shape deformation analysis is to determine a deformation of a given shape into another one, which is optimal for a certain cost. It has a number of applications in particular in medical imaging. In this article we…
In some previous works, two of the authors have introduced a strategy to develop high-order numerical methods for systems of balance laws that preserve all the stationary solutions of the system. The key ingredient of these methods is a…
Mechanical systems are usually modeled by second-order Ordinary Differential Equations (ODE) which take the form $\ddot{q} = f(t, q, \dot{q})$. While simulation methods tailored to these equations have been studied, using them in direct…
Since 2023, through the detailed examination of numerous concrete examples, the author and his collaborators have identified a recurring pattern. Building upon this observation, they introduced the concept of the normalized remainder. They…
In this paper we present a pure algebraic construction of the normal factorization of multimode squeezed states and calculate their inner products. This procedure allows one to orthonormalize bases generated by squeezed states. We calculate…
Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…
The Macdonald polynomials with prescribed symmetry are obtained from the nonsymmetric Macdonald polynomials via the operations of $t$-symmetrisation, $t$-antisymmetrisation and normalisation. Motivated by corresponding results in Jack…
First-order iterative optimization methods play a fundamental role in large scale optimization and machine learning. This paper presents control interpretations for such optimization methods. First, we give loop-shaping interpretations for…
This paper explores the fundamental limits of a simple system, inspired by the intermittent Kalman filtering model, where the actuation direction is drawn uniformly from the unit hypersphere. The model allows us to focus on a fundamental…
We study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential equations under two new conditions. We first consider the…
As a counterpart of the well-known generalized Wick theorem by Bais et. al. in 1988 for interacting fields in two dimensional conformal field theory, we present a new contour integral formula for the operator product expansion of a normally…
In this paper we consider the normal map of a closed plane curve as a vector field on the cylinder. We interpret the critical points geometrically and study their Poincar\'{e} index, including the points at infinity. After projecting the…
The paper is an attempt to generalize a methodology, which is similar to the bounded-input bounded-output method currently widely used for the system stability studies. The presented earlier methodology allows decomposition of input space…
This paper examines an averaging technique in which the nonlinear flux term is expanded and the convective velocities are passed through a low-pass filter. It is the intent that this modification to the nonlinear flux terms will result in…
Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular, intrinsic formulas allowing to…
A common theme in all the above areas is designing a dynamical system to accomplish desired objectives, possibly in some predefined optimal way. Since control theory advances the idea of suitably modifying the behavior of a dynamical…
We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key idea is to develop a new control-theoretic regularizer for dynamics fitting rooted in the notion of…
In this paper we deal with analytic nonautonomous vector fields with a periodic time-dependancy, that we study near an equilibrium point. In a first part, we assume that the linearized system is split in two invariant subspaces E0 and E1.…