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Let $G$ be a semidirect product of a simply connected nilpotent Lie group and $\R$. For a left invariant control system on $G$ with a convex cone as a control domain, it is proved that the attainable sets coincides with a "halfspace" if the…
In this paper, the notion of contraction is used to solve the trajectory-tracking problem for a class of mechanical systems. Additionally, we propose a dynamic extension to remove velocity measurements from the controller while rejecting…
Finite-state models of control systems were proposed by several researchers as a convenient mechanism to synthesize controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main…
In this paper we study a problem of looking for an optimal solution of a system of the differential equations with a control and an optimized function. The system of differential equations is changed for two systems with the upper and lower…
We investigate the set of limit points of averages of rearrangements of a given sequence. We study how the properties of the sequence determine the structure of that set and what type of sets we can expect as the set of such accessible…
We address consecutively two problems. First we introduce a class of so called Fre'chet generalized controls for a multi-input control-affine system with non-commuting controlled vector fields. For each control of the class one is able to…
This paper deals with formulas of set theory which force the infinity. For such formulas, we provide a technique to infer satisfiability from a finite assignment.
We summarise three applications of the obstacle problem to membrane contact, elastoplastic torsion and cavitation modelling, and show how the resulting models can be solved using mixed finite elements. It is challenging to construct fixed…
We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…
The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…
We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…
Adaptive dynamical systems arise in a multitude of contexts, e.g., optimization, control, communications, signal processing, and machine learning. A precise characterization of their fundamental limitations is therefore of paramount…
Starting with a sigma finite measure on an algebra, we define a pseudometric and show how measurable sets from the Caratheodory Extension Theorem can be thought of as limit points of Cauchy sequences in the algebra.
This paper studies the informativity problem for reachability and null-controllability of constrained systems. To be precise, we will focus on an unknown linear systems with convex conic constraints from which we measure data consisting of…
We show how geometric methods from the general theory of fractal dimensions and iterated function systems can be deployed to study symbolic dynamics in the zero entropy regime. More precisely, we establish a dimensional characterization of…
The inf-convolution of risk measures is directly related to risk sharing and general equilibrium, and it has attracted considerable attention in mathematical finance and insurance problems. However, the theory is restricted to finite sets…
Intuitively, if we can prove that a program terminates, we expect some conclusion regarding its complexity. But the passage from termination proofs to complexity bounds is not always clear. In this work we consider Monotonicity Constraint…
We provide a constructive way of defining new elicitable risk measures that are characterised by a multiplicative scoring function. We show that depending on the choice of the scoring function's components, the resulting risk measure…
In this paper we propose a data-driven distributionally robust Model Predictive Control framework for constrained stochastic systems with unbounded additive disturbances. Recursive feasibility is ensured by optimizing over an linearly…
Longitudinal data tracking repeated measurements on individuals are highly valued for research because they offer controls for unmeasured individual heterogeneity that might otherwise bias results. Random effects or mixed models approaches,…