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Formal language techniques have been used in the past to study autonomous dynamical systems. However, for controlled systems, new features are needed to distinguish between information generated by the system and input control. We show how…
Topological metamaterials have invaded the mechanical world, demonstrating acoustic cloaking and waveguiding at finite frequencies and variable, tunable elastic response at zero frequency. Zero frequency topological states have previously…
We evaluate the localization length of the wave (or Schroedinger) equation in the presence of a disordered speckle potential. This is relevant for experiments on cold atoms in optical speckle potentials. We focus on the limit of large…
Autoresonance is a phenomenon of physical interest that may take place when a nonlinear oscillator is forced at a frequency that varies slowly. The stroboscopic averaging method (SAM), which provides an efficient numerical technique for the…
Understanding the continuous states of objects is essential for task learning and planning in the real world. However, most existing task learning benchmarks assume discrete (e.g., binary) object goal states, which poses challenges for the…
A class of nonlinear control-affine systems with bounded time-varying drift is considered. It is assumed that the control vector fields together with their iterated Lie brackets satisfy Hormander's condition in a neighborhood of the origin.…
Offline preference optimization offers a simpler and more stable alternative to RLHF for aligning language models. However, their effectiveness is critically dependent on ranking accuracy, a metric where further gains are highly impactful.…
We study a diagnosis scheme to reliably detect the active mode of discrete-time, switched affine systems in the presence of measurement noise and asynchronous switching. The proposed scheme consists of two parts: (i) the construction of a…
Normal modes provide a fundamental basis for understanding crucial properties of solids, such as the thermal conductivity, the heat capacity and the sound propagation. While the normal modes are excellently described by plane waves in…
We consider disordered pinning models, when the return time distribution of the underlying renewal process has a polynomial tail with exponent $\alpha \in (1/2,1)$. This corresponds to a regime where disorder is known to be relevant, i.e.…
We develop a new method to isolate localized defects from extended vibrational modes in disordered solids. This method augments particle interactions with an artificial potential that acts as a high-pass filter: it preserves small-scale…
Jailbreaking in Large Language Models (LLMs) is a major security concern as it can deceive LLMs to generate harmful text. Yet, there is still insufficient understanding of how jailbreaking works, which makes it hard to develop effective…
In this paper, we consider the problem of controlling a dynamical system such that its trajectories satisfy a temporal logic property in a given amount of time. We focus on multi-affine systems and specifications given as syntactically…
Safe reinforcement learning (RL) agents accomplish given tasks while adhering to specific constraints. Employing constraints expressed via easily-understandable human language offers considerable potential for real-world applications due to…
We consider a constrained Markov Decision Problem (CMDP) where the goal of an agent is to maximize the expected discounted sum of rewards over an infinite horizon while ensuring that the expected discounted sum of costs exceeds a certain…
The problem of tracking an arbitrary curve in the state space is considered for underactuated driftless control-affine systems. This problem is formulated as the stabilization of a time-varying family of sets associated with a neighborhood…
In this paper, we seek to learn a robot policy guaranteed to satisfy state constraints. To encourage constraint satisfaction, existing RL algorithms typically rely on Constrained Markov Decision Processes and discourage constraint…
Nonautonomous driving of an oscillator has been shown to enlarge the Arnold tongue in parameter space, but little is known about the analogous effect for a network of oscillators. To test the hypothesis that deterministic nonautonomous…
When driving a disordered elastic manifold through quenched disorder, the pinning forces exerted on the center of mass are fluctuating, with mean $f_c=-\overline{F_w} $ and variance $\Delta(w)=\overline{F_w F_0}^c$, where $w$ is the…
In this work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the…