The work presented in this thesis lies at the intersection of Machine Learning (ML) and control theory.
The first part is dedicated to the design of Deep Neural Network (DNN) architectures with specific numerical properties, inspired by dynamical systems m ...
We consider control of dynamical systems through the lens of competitive analysis. Most prior work in this area focuses on minimizing regret, that is, the loss relative to an ideal clairvoyant policy that has noncausal access to past, present, and future d ...
Two dynamical systems are topologically equivalent when their phase-portraits can be morphed into each other by a homeomorphic coordinate transformation on the state space. The induced equivalence classes capture qualitative properties such as stability or ...
In part I, we address the issue of existence of solutions for Cauchy problems involving nonlinear hyperbolic equations for initial data in Sobolev spaces with scaling subcritical regularity. In particular, we analyse nonlinear estimates for null-forms in t ...
We explore consequences of the Averaged Null Energy Condition (ANEC) for scaling dimensions Delta of operators in four-dimensional N = 1 superconformal field theories. We show that in many cases the ANEC bounds are stronger than the corresponding unitarity ...
We consider the finite-time stabilization of homogeneous quasilinear hyperbolic systems with one side controls and with nonlinear boundary condition at the other side. We present time-independent feedbacks leading to the finite-time stabilization in any ti ...
A feedback control design is proposed for stochastic systems with finite second moment which aims at maximising the region of attraction of the equilibrium point. Polynomial Chaos (PC) expansions are employed to represent the stochastic closed loop system ...
Data-driven modeling and feedback control play a vital role in several application areas ranging from robotics, control theory, manufacturing to management of assets, financial portfolios and supply chains. Many such problems in one way or another are rela ...
We prove that the critical Wave Maps equation with target S2 and origin ℝ2+1 admits energy class blow up solutions of the form u(t,r)=Q(λ(t)r)+ϵ(t,r) where Q:R2→S2 is the ground state harmonic map and $\lambda ...
An algorithmic method is proposed to design stabilizing control laws for a class of nonlinear systems that comprises single-input feedback-linearizable systems and a particular set of single-input non feedback-linearizable systems. The method proceeds iter ...
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