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Yubiao Zhang

Publications and source records attributed to Yubiao Zhang.

14 recordsLinked to original sources
arXiv2026

Vision-Force Admittance Learning for Peg Insertion into a Movable Hole

Precise manipulation in dynamic environments, whether induced by a mobile robot base or a target with unknown motion, remains a major challenge in robotics. Manipulation in dynamic environments introduces substantial uncertainty, which fundamentally conflicts with the tight precision requirement of precise tasks such as peg-in-the-hole. We propose a Vision-Force Admittance Learning (VFAL) framework that fuses asynchronous visual feedback with a high-frequency force-based model, using visual pose estimations as a regularization term. VFAL adapts insertion strategies online to dynamic motion while maintaining millimeter-level precision. To obtain robust, low-frequency pose information, we employ state-of-the-art vision foundation models for visual pose estimation. Additionally, we incorporate failure recovery mechanisms to enhance overall robustness. We validate our approach in real-world experiments, demonstrating high success rates and strong adaptability to various pegs and dynamic environments.

cs.RO↗
arXiv2026

A Structure-Preserving Numerical Scheme for Optimal Control and Design of Mixing in Incompressible Flows

We develop a structure-preserving computational framework for optimal mixing control in incompressible flows. Our approach exactly conserves the continuous system's key invariants (mass and $L^2$-energy), while also maintaining discrete state-adjoint duality at every time step. These properties are achieved by integrating a centered finite-volume discretization in space with a time-symmetric Crank-Nicolson integrator for both the forward advection and its adjoint, all inside a gradient-based optimization loop. The result is a numerical solver that is faithful to the continuous optimality conditions and efficiently computes mixing-enhancing controls. In our numerical tests, the optimized time-dependent stirring produces a nearly exponential decay of a chosen mix-norm, achieving orders-of-magnitude faster mixing than any single steady flow. To our knowledge, this work provides the first evidence that enforcing physical structure at the discrete level can lead to both exact conservation and highly effective mixing outcomes in optimal flow design.

math.NA↗
arXiv2025

Periodic propagation of singularities for heat equations with time delay

This paper presents two remarkable phenomena associated with the heat equation with a time delay: namely, the propagation of singularities and periodicity. These are manifested through a distinctive mode of propagation of singularities in the solutions. Precisely, the singularities of the solutions propagate periodically in a bidirectional fashion along the time axis. Furthermore, this propagation occurs in a stepwise manner. More specifically, when propagating in the positive time direction, the order of the joint derivatives of the solution increases by 2 for each period; conversely, when propagating in the reverse time direction, the order of the joint derivatives decreases by 2 per period. Additionally, we elucidate the way in which the initial data and historical values impact such a propagation of singularities. The phenomena we have discerned not only corroborate the pronounced differences between heat equations with and without time delay but also vividly illustrate the substantial divergence between the heat equation with a time delay and the wave equation, especially when viewed from the point of view of singularity propagation.

math.AP↗
arXiv2024

Sampling Observability for Heat Equations with Memory

This paper studies the sampling observability for the heat equations with memory in the lower-order term, where the observation is conducted at a finite number of time instants and on a small open subset at each time instant. We present a two-sided sampling observability inequality and give a sharp sufficient condition to ensure the aforementioned inequality. We also provide a method to select the time instants and then to design the observation regions, based on a given memory kernel, such that the above-mentioned inequality holds for these time instants and observation regions. Additionally, we demonstrate that the positions of these time instants depend significantly on the memory kernel.

math.OC↗
arXiv2023

Observability for heat equations with time-dependent analytic memory

This paper presents a complete analysis of the observability property of heat equations with time-dependent real analytic memory kernels. More precisely, we characterize the geometry of the space-time measurable observation sets ensuring sharp observability inequalities, which are relevant both for control and inverse problems purposes. Despite the abundant literature on the observation of heat-like equations, existing methods do not apply to models involving memory terms. We present a new methodology and observation strategy, relying on the decomposition of the flow, the time-analyticity of solutions and the propagation of singularities. This allows us to obtain a sufficient and necessary geometric condition on the measurable observation sets for sharp two-sided observability inequalities. In addition, some applications to control and relevant open problems are presented.

math.OC↗
arXiv2021

Flow decomposition for heat equations with memory

We build up a decomposition for the flow generated by the heat equation with a real analytic memory kernel. It consists of three components: The first one is of parabolic nature; the second one gathers the hyperbolic component of the dynamics, with null velocity of propagation; the last one exhibits a finite smoothing effect. This decomposition reveals the hybrid parabolic-hyperbolic nature of the flow and clearly illustrates the significant impact of the memory term on the parabolic behavior of the system in the absence of memory terms.

math.AP↗
arXiv2018

Asymptotic observability identity for the heat equation in R^d

We build up an asymptotic observability identity for the heat equation in the whole space. It says that one can approximately recover a solution, through observing it over some countable lattice points in the space and at one time. This asymptotic identity is a natural extension of the well-known Shannon-Whittaker sampling theorem \cite{Shannon,Whittaker}. According to it, we obtain a kind of feedback null approximate controllability for impulsively controlled heat equations. We also obtain a weak asymptotic observability identity with finitely many observation lattice points. This identity holds only for some solutions to the heat equation.

math.AP↗
arXiv2017

Observable set, observability, interpolation inequality and spectral inequality for the heat equation in $\mathbb{R}^n$

This paper studies connections among observable sets, the observability inequality, the Hölder-type interpolation inequality and the spectral inequality for the heat equation in $\mathbb R^n$. We present a characteristic of observable sets for the heat equation. In more detail, we show that a measurable set in $\mathbb{R}^n$ satisfies the observability inequality if and only if it is $γ$-thick at scale $L$ for some $γ>0$ and $L>0$.We also build up the equivalence among the above-mentioned three inequalities. More precisely, we obtain that if a measurable set $E\subset\mathbb{R}^n$ satisfies one of these inequalities, then it satisfies others. Finally, we get some weak observability inequalities and weak interpolation inequalities where observations are made over a ball.

math.OC↗
arXiv2017

Time optimal sampled-data controls for heat equations

In this paper, we first design a time optimal control problem for the heat equation with sampled-data controls, and then use it to approximate a time optimal control problem for the heat equation with distributed controls. Our design is reasonable from perspective of sampled-data controls. And it might provide a right way for the numerical approach of a time optimal distributed control problem, via the corresponding semi-discretized (in time variable) time optimal control problem. The study of such a time optimal sampled-data control problem is not easy, because it may have infinitely many optimal controls. We find connections among this problem, a minimal norm sampled-data control problem and a minimization problem. And obtain some properties on these problems. Based on these, we not only build up error estimates for optimal time and optimal controls between the time optimal sampled-data control problem and the time optimal distributed control problem, in terms of the sampling period, but also prove that such estimates are optimal in some sense.

math.OC↗
arXiv2016

Observability and unique continuation inequalities for the Schrödinger equation

In this paper, we present several observability and unique continuation inequalities for the free Schrödinger equation in the whole space. The observations in these inequalities are made either at two points in time or one point in time. These inequalities correspond to different kinds of controllability for the free Schrödinger equation. We also find that the observability inequality at two points in time is equivalent to the uncertainty principle built up in [18].

math.OC↗
arXiv2016

Decompositions and bang-bang properties

In this paper, minimal time and minimal norm control problems are studied. The target sets considered are the origin of state spaces and controls are point-wisely bounded functions. The system stuided in this paper is assumed to have no the null controllability or the backward uniqueness property. In this study, minimal time and minimal norm control problems depend on two parameters, respectively. Whether these problems hold the bang-bang property also depend on the parameters. We study the bang-bang property for different parameters for minimal time and minimal norm control problems, by assuming some kinds of weak controllability and unique continuation property. These two properties automatically hold for general time-invariant finitely dimensional controlled systems.

math.OC↗
arXiv2015

Impulse and sampled-data optimal control of heat equations, and error estimates

We consider the optimal control problem of minimizing some quadratic functional over all possible solutions of an internally controlled multi-dimensional heat equation with a periodic terminal state constraint. This problem has a unique optimal solution, which can be characterized by an optimality system derived from the Pontryagin maximum principle. We define two approximations of this optimal control problem. The first one is an impulse approximation, and consists of considering a system of linear heat equations with impulse control. The second one is obtained by the sample-and-hold procedure applied to the control, resulting into a sampled-data approximation of the controlled heat equation. We prove that both problems have a unique optimal solution, and we establish precise error estimates for the optimal controls and optimal states of the initial problem with respect to its impulse and sampled-data approximations.

math.OC↗
arXiv2014

Attainable subspaces and the bang-bang property of time optimal controls for heat equations

In this paper, we study two subjects on internally controlled heat equations with time varying potentials: the attainable subspaces and the bang-bang property for some time optimal control problems. We present some equivalent characterizations on the attainable subspaces, and provide a sufficient conditions to ensure the bang-bang property. Both the above-mentioned characterizations and the sufficient condition are closely related to some function spaces consisting of some solutions to the adjoint equations. It seems for us that the existing ways to derive the bang-bang property for heat equations with time-invariant potentials (see, for instance, [4],[7],[16],[26]) do not work for the case where the potentials are time-varying. We provide another way to approach it in the current paper.

math.OC↗