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The escape dynamics around the triangular Lagrangian point L5 in the real Sun-Earth-Moon-Spacecraft system is investigated. Appearance of the finite time chaotic behaviour suggests that widely used methods and concepts of dynamical system…
We consider the problem of optimally controlling stochastic, Markovian systems subject to joint chance constraints over a finite-time horizon. For such problems, standard Dynamic Programming is inapplicable due to the time correlation of…
This paper focuses on the invariance control problem for discrete-time switched nonlinear systems. The proposed approach computes controlled invariant sets in a finite number of iterations and directly yields a partition-based invariance…
In this contribution, we introduce a general class of car-following models with an input-state-output port-Hamiltonian structure. We derive stability conditions and long-term behavior of the finite system with periodic boundaries and…
In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
Many systems contain latent variables that make their dynamics partially unidentifiable or cause distribution shifts in the observed statistics between offline and online data. However, existing control techniques often assume access to…
Any strategy used to distribute a robot ensemble over a set of sequential tasks is subject to inaccuracy due to robot-level uncertainties and environmental influences on the robots' behavior. We approach the problem of inaccuracy during…
The encounter situation between marine vessels determines how they should navigate to obey COLREGs, but time-varying and stochastic uncertainty in estimation of angles of encounter, and of closest point of approach, easily give rise to…
We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…
Computing control invariant sets is paramount in many applications. The families of sets commonly used for computations are ellipsoids and polyhedra. However, searching for a control invariant set over the family of ellipsoids is…
In this paper, we study the optimal control problem for steering the state covariance of a discrete-time linear stochastic system over a finite time horizon. First, we establish the existence and uniqueness of the optimal control law for a…
This paper investigates stochastic invariance for control systems through probabilistic controlled invariant sets (PCISs). As a natural complement to robust controlled invariant sets~(RCISs), we propose finite- and infinite-horizon PCISs,…
The optimal control of epidemic-like stochastic processes is important both historically and for emerging applications today, where it can be especially important to include time-varying parameters that impact viral epidemic-like…
Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their…
The stability of solutions to evolution equations with respect to small stochastic perturbations is considered. The stability of a stochastic dynamical system is characterized by the local stability index. The limit of this index with…
On timescales that greatly exceed an orbital period, typical planetary orbits evolve in a stochastic yet stable fashion. On even longer timescales, however, planetary orbits can spontaneously transition from bounded to unbound chaotic…
We uncover a dynamical entanglement transition in a monitored quantum system that is heralded by a local order parameter. Classically, chaotic systems can be stochastically controlled onto unstable periodic orbits and exhibit controlled and…
This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…
Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant…