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In order to minimize a differentiable geodesically convex function, we study a second-order dynamical system on Riemannian manifolds with an asymptotically vanishing damping term of the form $\alpha/t$. For positive values of $\alpha$,…
We provide convex necessary and sufficient conditions for the robust stability of linear positively dominated systems. In particular we show that the structured singular value is always equal to its convex upper bound for nonnegative…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
In a paper by Willems and coauthors it was shown that persistently exciting data can be used to represent the input-output behavior of a linear system. Based on this fundamental result, we derive a parametrization of linear feedback systems…
We present a data-driven approach for distributionally robust chance constrained optimization problems (DRCCPs). We consider the case where the decision maker has access to a finite number of samples or realizations of the uncertainty. The…
Lyapunov stability theory is the bedrock of direct adaptive control. Fundamentally, Lyapunov stability requires constructing a distance-like function which must decrease with time to ensure stability. Feedback linearization, backstepping,…
This work presents a new sufficient condition for synthesizing nonlinear controllers that yield bounded closed-loop tracking error transients despite the presence of unmatched uncertainties that are concurrently being learned online. The…
The stabilization of unstable nonlinear systems and tracking control are challenging engineering problems due to the encompassed nonlinearities in dynamic systems and their scale. In the past decades, numerous observer-based control designs…
In a Hilbert space $H$, in order to develop fast optimization methods, we analyze the asymptotic behavior, as time $t$ tends to infinity, of inertial continuous dynamics where the damping acts as a closed-loop control. The function $f: H…
Modeling and control of high-dimensional, nonlinear robotic systems remains a challenging task. While various model- and learning-based approaches have been proposed to address these challenges, they broadly lack generalizability to…
We study a catching-up algorithm for a class of differential inclusions driven by maximal monotone operators with continuous perturbations. Using a decomposition of the monotone operator into the closed convex hull of its single-valued part…
Robustness is a property of system analyses, namely monotonic maps from the complete lattice of subsets of a (system's state) space to the two-point lattice. The definition of robustness requires the space to be a metric space. Robust…
This paper is concerned with finite element error estimates for Neumann boundary control problems posed on convex and polyhedral domains. Different discretization concepts are considered and for each optimal discretization error estimates…
The fundamental lemma by Willems and coauthors facilitates a parameterization of all trajectories of a linear time-invariant system in terms of a single, measured one. This result plays an important role in data-driven simulation and…
This paper develops a sliding mode control based frame work for equality constrained optimization by reformulation the first order Karush Kuhn Tucker conditions as control affine dynamical system. The optimization variables are treated as…
This paper develops a geometric framework for the stability analysis of differential inclusions governed by maximally monotone operators. A key structural decomposition expresses the operator as the sum of a convexified limit mapping and a…
This paper continues our study of the interconnection between controllability and mixing properties of random dynamical systems. We begin with an abstract result showing that the approximate controllability to a point and a local…
We present a new approach to verifying contraction and $L_2$-gain of uncertain nonlinear systems, extending the well-known method of integral quadratic constraints. The uncertain system consists of a feedback interconnection of a nonlinear…
Robustness of neural networks is commonly quantified via local or global Lipschitz constants. However, Lipschitz continuity can be overly coarse or overly restrictive as global robustness measure, failing to capture nuanced, data-dependent…
Recently, literature on dynamic coherent risk measures has broadened the choices for risk-sensitive performance evaluation. A running example includes Cumulative prospect theory and Conditional variance at risk. Most of them can be can be…