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We describe a method to analyze and decompose the dynamics of a control system on a Lie group subject to symmetries. The method is based on the concept of generalized Young symmetrizers of representation theory. It naturally applies to the…
We will show that there is a universal connection between the achievable closed-loop dynamics and the corresponding feedback controller that produces it. This connection shows promise to lead to new methods for robust nonlinear control in…
We introduce a new determinantal method to count cycle systems in a directed graph that generalizes Gessel and Viennot's determinantal method on path systems. The method gives new insight into the enumeration of domino tilings of Aztec…
A simple approach is presented to study the asymptotic behavior of some algorithms with an underlying tree structure. It is shown that some asymptotic oscillating behaviors can be precisely analyzed without resorting to complex analysis…
Functional digraphs are unlabelled finite digraphs where each vertex has exactly one out-neighbor. They are isomorphic classes of finite discrete-time dynamical systems. Endowed with the direct sum and product, functional digraphs form a…
The connection between symmetries and linearizations of discrete-time dynamical systems is being inverstigated. It is shown, that existence of semigroup structures related to the vector field and having linear representations enables…
This study propose a continuous pathfinding system based on coupled oscillator systems. We consider acyclic graphs whose vertices are connected by unidirectional edges. The proposed model autonomously finds a path connecting two specified…
Complexity analysis becomes a common task in supervisory control. However, many results of interest are spread across different topics. The aim of this paper is to bring several interesting results from complexity theory and to illustrate…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
In this paper we address the problem of tracking control of nonlinear systems via contraction analysis. The necessary conditions of the systems which can achieve universal asymptotic tracking are studied under several different cases. We…
An algorithm is presented that constructs an acyclic partial matching on the cells of a given simplicial complex from a vector-valued function defined on the vertices and extended to each simplex by taking the least common upper bound of…
In order to find Hamiltonian cycle, algorithm should find edges that creates a Hamiltonian cycle. Higher number of edges creates more possibilities to check to solve the problem. Algorithm rests on analysis of original graph and opposite…
Many engineered as well as naturally occurring dynamical systems do not have an accurate mathematical model to describe their dynamic behavior. However, in many applications, it is possible to probe the system with external inputs and…
We investigate a system of coupled oscillators on the circle, which arises from a simple model for behavior of large numbers of autonomous vehicles. The model considers asymmetric, linear, decentralized dynamics, where the acceleration of…
The paper presents a complete study of simple homoclinic cycles in R^5. We find all symmetry groups Gamma such that a Gamma-equivariant dynamical system in R^5 can possess a simple homoclinic cycle. We introduce a classification of simple…
Both humans and the sensors on an autonomous vehicle have limited sensing capabilities. When these limitations coincide with scenarios involving vulnerable road users, it becomes important to account for these limitations in the motion…
We study a model of colored multiwebs, which generalizes the dimer model to allow each vertex to be adjacent to \(n_v\) edges. These objects can be formulated as a random tiling of a graph with partial dimer covers. We examine the case of a…
Simulation is essential to validate autonomous driving systems. However, a simple simulation, even for an extremely high number of simulated miles or hours, is not sufficient. We need well-founded criteria showing that simulation does…
This is a complementary document to the paper presented in [1], to provide more detailed proofs for some results. The main paper addresses the problem of trajectory tracking control of autonomous rotorcraft in operation scenarios where only…
We show that any semi-algebraic sweeping process admits piecewise absolutely continuous solutions, and any such bounded trajectory must have finite length. Analogous results hold more generally for sweeping processes definable in o-minimal…