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Equivalences of Nonlinear Higher Order Fractional Differential Equations With Integral Equations
Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6930-6942, April 2025.ABSTRACT Equivalences of initial value problems (IVPs) of both nonlinear higher order (Riemann–Liouville type) fractional differential equations (FDEs) and Caputo FDEs with the corresponding integral equations are studied in this paper. It is proved that the nonlinearities in the FDEs can be L1$$ {L}^1 $$‐Carathéodory with suitable conditions.
Kunquan Lan
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Novel Bernstein‐Kantorovich Type Operators
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT In this paper, we introduce a novel class of Bernstein‐Kantorovich operators, denoted as Kβn,θ$$ {K}_{\beta}^{n,\theta } $$, parameterized by 0<β<1$$ 0<\beta <1 $$ and θ>0$$ \theta >0 $$. We first derive a recurrence formula that facilitates the computation of moments and central moments and provide explicit expressions for Kβn,θ(tm;x)$$ {K}_{\
Pembe Sabancigil, Nazim I. Mahmudov
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Optimal Control Applications and Methods, EarlyView.Computational governor is shown which simultaneously adjusts the reference and adjusts the constraints. ABSTRACT The paper considers a computational governor strategy to facilitate the implementation of Model Predictive Control (MPC) based on inexact optimization when the time available to compute the solution may be insufficient.
Steven van Leeuwen, Ilya Kolmanovsky
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Exact Robust Filtering and Differentiation Based on Sliding Modes and Homogeneity
International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT This article addresses the problem of online estimation of the derivatives of a signal corrupted by measurement noise. The measured signal is modeled as the sum of a smooth nominal component and a uniformly bounded noise term. A key objective is to attenuate the effect of high‐frequency noise.
Jaime A. Moreno, Arie Levant
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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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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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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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Fixed Point Theory and Applications, 2011 Approximate optimality conditions for a class of nonconvex semi-infinite programs involving support functions are given. The objective function and the constraint functions are locally Lipschitz functions on .
Son TaQuang, Kim DoSang
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State estimation for MISO non–linear systems in controller canonical form
International Journal of Applied Mathematics and Computer Science, 2016 We propose a new observer where the model, decomposed in generalized canonical form of regulation described by Fliess, is dissociated from the part assuring error correction.
Schwaller Benoît +3 more
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Symmetry of solutions to singular fractional elliptic equations and applications
Comptes Rendus. Mathématique, 2020 In this article, we study the symmetry of positive solutions to a class of singular semilinear elliptic equations whose prototype is \begin{align*} (P) \quad \left\lbrace \begin{array}{ll} (-\Delta )^{s}u = \frac{1}{u^\delta } + f(u), \; u>0\quad ...
Arora, Rakesh +3 more
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