Related papers: State-Dependent Lyapunov Method for Rank-1 Matrix …
We investigate the problem of verifying different properties of discrete time dynamical systems, namely, reachability, safety and reach-while-avoid. To achieve this, we adopt a data driven perspective and, using past system trajectories as…
In the design and operation of complex dynamical systems, it is essential to ensure that all state trajectories of the dynamical system converge to a desired equilibrium within a guaranteed stability region. Yet, for many practical systems…
Two common approaches in low-rank optimization problems are either working directly with a rank constraint on the matrix variable, or optimizing over a low-rank factorization so that the rank constraint is implicitly ensured. In this paper,…
This paper presents a safe learning framework that employs an adaptive model learning algorithm together with barrier certificates for systems with possibly nonstationary agent dynamics. To extract the dynamic structure of the model, we use…
We develop a finite-dimensional sensitivity framework for studying stability in learning systems whose states include representations, parameters, and update variables. The central object is the \emph{Learning Stability Profile}, a…
Before 2025, no open-source system existed that could learn Lyapunov stability certificates directly from noisy, real-world flight data. This work addresses that gap by proposing a data-driven approach that learns Lyapunov functions from…
Monotone systems preserve a partial ordering of states along system trajectories and are often amenable to separable Lyapunov functions that are either the sum or the maximum of a collection of functions of a scalar argument. In this paper,…
We augment the Slotine--Li adaptive controller for Euler--Lagrange systems with three learned components: a structured-quadratic Lyapunov function \(V_\psi\) whose positive-definiteness follows from a Cholesky parameterization, a residual…
Linear parameter-varying (LPV) systems with uncertainty in time-varying delays are subject to performance degradation and instability. In this line, we investigate the stability of such systems invoking an input-output stability approach.…
The problem of safely learning and controlling a dynamical system - i.e., of stabilizing an originally (partially) unknown system while ensuring that it does not leave a prescribed 'safe set' - has recently received tremendous attention in…
The paper concerns the $d$-dimensional stochastic approximation recursion, $$ \theta_{n+1}= \theta_n + \alpha_{n + 1} f(\theta_n, \Phi_{n+1}) $$ where $ \{ \Phi_n \}$ is a stochastic process on a general state space, satisfying a…
In this paper we study the semi-global (approximate) state feedback stabilization of an infinite dimensional quantum stochastic system towards a target state. A discrete-time Markov chain on an infinite-dimensional Hilbert space is used to…
We consider change-point tests based on rank statistics to test for structural changes in long-range dependent observations. Under the hypothesis of stationary time series and under the assumption of a change with decreasing change-point…
We present a novel recursive algorithm for reducing a symmetric matrix to a triangular factorization which reveals the rank profile matrix. That is, the algorithm computes a factorization $\mathbf{P}^T\mathbf{A}\mathbf{P} =…
We study the problem of solving fixed-point equations for seminorm-contractive operators and establish foundational results on the non-asymptotic behavior of iterative algorithms in both deterministic and stochastic settings. Specifically,…
We show that the factor graph and certifiable estimation paradigms, which have thus far been treated as essentially independent in the literature, can be naturally synthesized into a unified framework for certifiable factor graph…
Reinforcement learning (RL) can be highly effective at learning goal-reaching policies, but it typically does not provide formal guarantees that the goal will always be reached. A common approach to provide formal goal-reaching guarantees…
In this work, we introduce a novel gradient descent-based approach for optimizing control systems, leveraging a new representation of stable closed-loop dynamics as a function of two matrices i.e. the step size or direction matrix and value…
Certifying the stability of dynamical systems is a central and challenging task in control theory and systems analysis. To tackle these problems we present an algorithmic approach to finding polynomial Lyapunov functions. Our method relies…
We introduce for the first time a neural-certificate framework for continuous-time stochastic dynamical systems. Autonomous learning systems in the physical world demand continuous-time reasoning, yet existing learnable certificates for…