Results 51 to 60 of about 1,759 (215)
Feedback Linearisation with State Constraints
International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT Feedback Linearisation (FBL) is a widely used technique that applies feedback laws to transform input‐affine nonlinear control systems into linear control systems, allowing for the use of linear controller design methods such as pole placement.
Songlin Jin, Yuanbo Nie, Morgan Jones
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Lipschitz maps with prescribed local Lipschitz constants
Let $Γ$ be a closed subset of a complete Riemannian manifold $M$ of dimension $\geq 2$, let $f: M \to N$ be a Lipschitz map to a complete Riemannian manifold $N$, and let $ψ$ be a continuous function which dominates the local Lipschitz constant of $f$. We construct a Lipschitz map which agress with $f$ on $Γ$ and whose local Lipschitz constant is $ψ$.
Backus, Aidan, Ze-An, Ng
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Initial State Privacy of Nonlinear Systems on Riemannian Manifolds
International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT In this paper, we investigate initial state privacy protection for discrete‐time nonlinear closed systems. By capturing Riemannian geometric structures inherent in such privacy challenges, we refine the concept of differential privacy through the introduction of an initial state adjacency set based on Riemannian distances.
Le Liu, Yu Kawano, Antai Xie, Ming Cao
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Locally Lipschitz perturbations of bisemigroups
Communications on Pure and Applied Analysis, 2010 In this work we study the ill posed semilinear system $\dot{x}= Lx + f(\xi,t), \dot{y}= Ry + g(\xi,t)$, $\xi=(x,y)$, in Banach spaces where $L$ and $R$ are the infinitesimal generators of two $C_o$ semigroups $\{\mathcal{L}(t), t\geq 0\}$ and $\{\mathcal{R}(-t), t\geq 0\}$ respectively. The nonlinearity $h=(f,g)$
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CAAI Transactions on Intelligence Technology, EarlyView.ABSTRACT This paper proposes a boundary control method for nonlinear distributed parameter systems (DPSs) with limited boundary measurements (BMs), as typically encountered in networked cyber‐physical processes with spatially distributed dynamics such as thermal and biomedical diffusion systems.
Yanlin Li +5 more
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Homoclinic solutions for a differential inclusion system involving the p(t)-Laplacian
Advances in Nonlinear Analysis, 2022 The aim of this article is to study nonlinear problem driven by the p(t)p\left(t)-Laplacian with nonsmooth potential. We establish the existence of homoclinic solutions by using variational principle for locally Lipschitz functions and the properties of ...
Cheng Jun, Chen Peng, Zhang Limin
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SDFs from Unoriented Point Clouds using Neural Variational Heat Distances
Computer Graphics Forum, EarlyView.We propose a novel variational approach for computing neural Signed Distance Fields (SDF) from unoriented point clouds. We first compute a small time step of heat flow (middle) and then use its gradient directions to solve for a neural SDF (right). Abstract We propose a novel variational approach for computing neural Signed Distance Fields (SDF) from ...
Samuel Weidemaier +5 more
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Characterization of Strict Convexity for Locally Lipschitz Functions
Rocky Mountain Journal of Mathematics, 2009 It is well known that a smooth function \(f: X\to\mathbb{R}\) is convex iff \(f''(x;h, h)\geq 0\) for all \(x\in X\) and all \(h\in X\). The function \(f\) is strictly convex iff \(f''(x;h,h)> 0\) for ``almost'' all \(x\in X\) and all \(h\in X\). Here \[ f''(x;u,v)= \lim_{t\to 0} \frac{\langle\nabla f(x+ tu)-\nabla f(x),v\rangle}{t}, \] where \(\nabla ...
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A Characterization of bi-Lipschitz embeddable metric spaces in terms of local bi-Lipschitz embeddability [PDF]
Mathematical Research Letters, 2011 We characterize uniformly perfect, complete, doubling metric spaces which embed bi- Lipschitzly into Euclidean space. Our result applies in particular to spaces of Grushin type equipped with Carnot-Carathéodory distance. Hence we obtain the first example of a sub-Riemannian mani- fold admitting such a bi-Lipschitz embedding.
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A Non‐Parametric Framework for Correlation Functions on Product Metric Spaces
International Statistical Review, EarlyView.Summary We propose a non‐parametric framework for analysing data defined over products of metric spaces, a versatile class encountered in various fields. This framework accommodates non‐stationarity and seasonality and is applicable to both local and global domains, such as the Earth's surface, as well as domains evolving over linear time or time ...
Pier Giovanni Bissiri +3 more
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