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Adaptive control can be applied to robotic systems with parameter uncertainties, but improving its performance is usually difficult, especially under discontinuous friction. Inspired by the human motor learning control mechanism, an…
Numerical solutions to Newton's equations of motion for chaotic self gravitating systems of more than 2 bodies are often regarded to be irreversible. This is due to the exponential growth of errors introduced by the integration scheme and…
Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity,…
The surface of a liquid near a moving contact line is highly curved owing to diverging viscous forces. Thus, microscopic physics must be invoked at the contact line and matched to the hydrodynamic solution farther away. This matching has…
Deep learning has provided new ways of manipulating, processing and analyzing data. It sometimes may achieve results comparable to, or surpassing human expert performance, and has become a source of inspiration in the era of artificial…
For more than a century and a half it has been widely-believed (but was never rigorously shown) that the physics of diffraction imposes certain fundamental limits on the resolution of an optical system. However our understanding of what…
Differential equations need boundary conditions (BC's) for their solution. It is commonly acknowledged that differential equations and BC's are representative of independent physical processes, and no correlations between them is required.…
We present a task-centered formal analysis of the relative power of several robot designs, inspired by the unique properties and constraints of micro-scale robotic systems. Our task of interest is object manipulation because it is a…
A linear elastic circular disc is analyzed under a self-equilibrated system of loads applied along its boundary. A distinctive feature of the investigation, conducted using complex variable analysis, is the assumption that the material is…
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…
This paper is concerned with mismatched disturbance rejection control for the second-order discrete-time systems.Different from previous work, the controllability of the system is applied to design the disturbance compensation gain, which…
Characterizing the risk of operations is a fundamental requirement in robotics, and a crucial ingredient of safe planning. The problem is multifaceted, with multiple definitions arising in the vast recent literature fitting different…
The nonlinear convection terms in the governing equations of compressible fluid flows are hyperbolic in nature and are nontrivial for modelling and numerical simulation. Many numerical methods have been developed in the last few decades for…
We revisit the computation of a probability of collision in the context of automotive collision avoidance (also referred to as conflict detection in other contexts). After reviewing existing approaches to the definition and computation of a…
This work investigates the inverse drift problem in the one-dimensional parabolic equation with the final time data. The authors construct an operator first, whose fixed points are the unknown drift, and then apply it to prove the…
In recent years, machine learning has been used to create data-driven solutions to problems for which an algorithmic solution is intractable, as well as fine-tuning existing algorithms. This research applies machine learning to the…
Ductile damage models and cohesive laws incorporate the material plasticity entailing the growth of irrecoverable deformations even after complete failure. This unrealistic growth remains concealed until the unilateral effects arising from…
A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned…
Robustness is a basic property of any control system. In the context of linear output regulation, it was proved that embedding an internal model of the exogenous signals is necessary and sufficient to achieve tracking of the desired…
Diffusion, a fundamental internal mechanism emerging in many physical processes, describes the interaction among different objects. In many learning tasks with limited training samples, the diffusion connects the labeled and unlabeled data…