Related papers: Geometry of Control-Affine Systems
For a map $f:X \to M$ into a manifold $M$, we study the sets of deficient and multiple points of $f$. In case of the set of deficient points, we estimate its dimension. For multiple points, we study its density in $X$, and we also provide…
Prediction-based transformation is applied to control-affine systems with distributed input delays. Transformed system state is calculated as a prediction of the system's future response to the past input with future input set to zero.…
The concept of quasi-affine frame in Euclidean spaces was introduced to obtain translation invariance of the discrete wavelet transform. We extend this concept to a local field $K$ of positive characteristic. We show that the affine system…
A four-variable distribution on permutations is derived, with two dual combinatorial interpretations. The first one includes the number of fixed points "fix", the second the so-called "pix" statistic. This shows that the duality between…
In this article we study optimal control problems for systems that are affine in one part of the control variable. Finitely many equality and inequality constraints on the initial and final values of the state are considered. We investigate…
We consider the decentralized control of radial distribution systems with controllable photovoltaic inverters and energy storage resources. For such systems, we investigate the problem of designing fully decentralized controllers that…
This work investigates the optimal control of the variable-exponent subdiffusion, which extends the work [Gunzburger and Wang, {\it SIAM J. Control Optim.} 2019] to the variable-exponent case to account for the multiscale and crossover…
We study affine invariant 2D triangulation methods. That is, methods that produce the same triangulation for a point set $S$ for any (unknown) affine transformation of $S$. Our work is based on a method by Nielson [A characterization of an…
Using a coordinate free characterization of hyperplanes intersection, we provide explicitly a set of local generators for a smooth affine distribution given by those smooth vector fields $X\in\mathfrak{X}(U)$ defined eventually on an open…
Congruences, or $2$-parameter families of lines in $3$-space are of interest in many situations, in particular in geometric optics. In this paper we consider elements of their geometry which are invariant under affine changes of…
We study formation control problems. Our approach is to let a group of systems maximize their pairwise distances whilst bringing them all to a given submanifold, determining the shape of the formation. The algorithm we propose allows to…
In this letter, we derive minimum-energy controls for a broad class of control-affine systems using a Lagrange multiplier fixed-point equation and a generally non-symmetric Gramian-like matrix. In feasible coercivity classes, this fixed…
In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order $\alpha\in(0,1)$ in time. The…
This paper studies a data-driven predictive control for a class of control-affine systems which is subject to uncertainty. With the accessibility to finite sample measurements of the uncertain variables, we aim to find controls which are…
We investigate optimal control of dynamical systems which are affine, i.e., linear in control, but nonlinear in state. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible, a task…
In dynamical systems, shrinking target sets and pointwise recurrent sets are two important classes of dynamically defined subsets. In this article we introduce a mild condition on the linear parts of the affine mappings that allow us to…
We introduce an image based algorithmic tool for analyzing multi-component shapes here. Due to the generic concept of multi-component shapes, our method can be applied to the analysis of a wide spectrum of applications where real objects…
This paper is concerned with error estimates for the numerical approximation for affine optimal control problems subject to semilinear elliptic PDEs. To investigate the error estimates, we focus on local minimizers that satisfy certain…
We consider the problem of computing optimal linear control policies for linear systems in finite-horizon. The states and the inputs are required to remain inside pre-specified safety sets at all times despite unknown disturbances. In this…
In this paper, we study a regularised relaxed optimal control problem and, in particular, we are concerned with the case where the control variable is of large dimension. We introduce a system of mean-field Langevin equations, the invariant…