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This article describes the control behavior of any linear control systems on the group of proper motions $SE(2)$. It characterizes the controllability property and the control sets of the system.
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
We consider a finite-dimensional model for the motion of microscopic organisms whose propulsion exploits the action of a layer of cilia covering its surface. The model couples Newton's laws driving the organism, considered as a rigid body,…
Determining the reachable set for a given nonlinear control system is crucial for system control and planning. However, computing such a set is impossible if the system's dynamics are not fully known. This paper is motivated by a scenario…
Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical…
The steering control of an autonomous unicycle is considered. The underlying dynamical model of a single rolling wheel is discussed regarding the steady state motions and their stability. The unicycle model is introduced as the simplest…
For affine control systems with bounded control range the control sets, i.e., the maximal subsets of complete approximate controllability, are studied using spectral properties. For hyperbolic systems there is a unique control set with…
Ensemble control offers rich and diverse opportunities in mathematical systems theory. In this paper, we present a new paradigm of ensemble control, referred to as distributional control, for ensemble systems. We shift the focus from…
Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical…
This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…
We describe a particular control method for a system controlled by several actuators with the same control constants. We show under certain assumptions that the control constants for the whole system can be obtained immediately from the…
The purpose of this review paper is to present some recent results on the modeling and control of large systems of agents. We focus on particular applications where the agents are capable of independent actions instead of simply reacting to…
The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…
Game dynamics structure (e.g., endogenous cycle motion) in human subjects game experiments can be predicted by game dynamics theory. However, whether the structure can be controlled by mechanism design to a desired goal is not known. Here,…
This paper deals with controllability of dynamical networks. It is often unfeasible or unnecessary to fully control large-scale networks, which motivates the control of a prescribed subset of agents of the network. This specific form of…
This chapter focuses on the self-driving technology from a control perspective and investigates the control strategies used in autonomous vehicles and advanced driver-assistance systems from both theoretical and practical viewpoints. First,…
The purpose of this paper is to present a universal approach to the study of controllability/observability problems for infinite dimensional systems governed by some stochastic/deterministic partial differential equations. The crucial…
This paper is mainly concerned with the robustly stable adaptive control of single-input single-output impulse-free linear time-invariant singular dynamic systems of known order and unknown parameterizations subject to single external point…
We study the controlled dynamics of the {\it ensembles of points} of a Riemannian manifold $M$. Parameterized ensemble of points of $M$ is the image of a continuous map $\gamma:\Theta \to M$, where $\Theta$ is a compact set of parameters.…
This paper deals with fractional-order controlled systems and fractional-order controllers in the discrete domain. The mathematical description by the fractional difference equations and properties of these systems are presented. A…