The Experts below are selected from a list of 3711 Experts worldwide ranked by ideXlab platform
Marco Spadini - One of the best experts on this subject based on the ideXlab platform.
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Branches of Forced Oscillations Induced by a Delayed Periodic Force
Advanced Nonlinear Studies, 2019Co-Authors: Alessandro Calamai, Maria Patrizia Pera, Marco SpadiniAbstract:Abstract We study global continuation properties of the set of T-periodic solutions of parameterized second order delay differential equations with constant time lag on smooth manifolds. We apply our results to get multiplicity of T-periodic solutions. Our topological approach is mainly based on the notion of degree of a Tangent Vector Field.
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About the notion of non‐T‐resonance and applications to topological multiplicity results for ODEs on differentiable manifolds
Mathematical Methods in the Applied Sciences, 2015Co-Authors: Luca Bisconti, Marco SpadiniAbstract:By using topological methods, mainly the degree of a Tangent Vector Field, we establish multiplicity results for $T$-periodic solutions of parametrized $T$-periodic perturbations of autonomous ODEs on a differentiable manifold $M$. In order to provide insights into the key notion of $T$-resonance, we consider the elementary situations $M = \mathbb{R}$ and $M = \mathbb{R}^2$. So doing, we provide more comprehensive analysis of those cases and find improved conditions.
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ABOUT THE NOTION OF NON-T-RESONANCE AND APPLICATIONS TO TOPOLOGICAL MULTIPLICITY RESULTS FOR ODES ON
2014Co-Authors: Luca Bisconti, Marco SpadiniAbstract:By using topological methods, mainly the degree of a Tangent Vector Field, we establish multiplicity results for T-periodic solutions of parametrized T-periodic pertur- bations of autonomous ODEs on a differentiable manifold M. In order to provide insights into the key notion of T-resonance, we consider the elementary situations M = R and M = R2. So doing, we provide more comprehensive analysis of those cases and find improved conditions.
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Branches of forced oscillations for a class of constrained ODEs: a topological approach
Nonlinear Differential Equations and Applications NoDEA, 2012Co-Authors: Alessandro Calamai, Marco SpadiniAbstract:We apply topological methods to obtain global continuation results for harmonic solutions of some periodically perturbed ordinary differential equations on a k -dimensional differentiable manifold $${M \subseteq \mathbb{R}^m}$$ . We assume that M is globally defined as the zero set of a smooth map and, as a first step, we determine a formula which reduces the computation of the degree of a Tangent Vector Field on M to the Brouwer degree of a suitable map in $${\mathbb{R}^m}$$ . As further applications, we study the set of harmonic solutions to periodic semi-explicit differential-algebraic equations.
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On a class of differential-algebraic equations with infinite delay
Electronic Journal of Qualitative Theory of Differential Equations, 2011Co-Authors: Luca Bisconti, Marco SpadiniAbstract:We study the set of T-periodic solutions of a class of T-periodically perturbed Differential-Algebraic Equations, allowing the perturbation to contain a distributed and possibly infinite delay. Under suitable assumptions, the perturbed equations are equivalent to Retarded Functional (Ordinary) Differential Equations on a manifold. Our study is based on known results about the latter class of equations and on a “reduction” formula for the degree of a Tangent Vector Field to implicitly defined differentiable manifolds.
Yingmin Jia - One of the best experts on this subject based on the ideXlab platform.
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Tangent Vector Field approach for curved path following with input saturation
Systems & Control Letters, 2017Co-Authors: Yueqian Liang, Yingmin JiaAbstract:Abstract Path following is an indispensable function for autonomous vehicles. Desired paths may be of arbitrary shape, not just the mostly investigated straight lines and circles. This paper addresses the path following problem of arbitrary twice differentiable curves using Vector-Field-based approach. A Tangent Vector Field is constructed through coordinate transformation, and a sufficient condition for its feasibility concerning the input saturation is given out. A saturated turning velocity controller is designed and its Lyapunov stability is discussed in detail. Numerical simulation results show us that the path following performance of the proposed approach is comparable with that of the literature while involving 5 less parameters to be set.
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Vector Field guidance for three dimensional curved path following with fixed wing uavs
Advances in Computing and Communications, 2015Co-Authors: Yueqian Liang, Yingmin Jia, Jun ZhangAbstract:This paper investigates the three-dimensional (3D) curved path following problem using fixed-wing unmanned aerial vehicles (UAVs) in the presence of constant wind disturbance. Vector Field based approaches are used as the solution. Two Vector Fields are first developed, one is the Tangent Vector Field based on path Tangent Vector and coordinate transformation, and the other is the combined Vector Field based on the combination of a conservative Vector Field and a solenoidal Vector Field. A unified jointly saturated course rate and saturated climb rate controller is designed based on the proposed Vector Fields. Simulations are conducted to demonstrate the effectiveness of the proposed approach.
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ACC - Vector Field guidance for three-dimensional curved path following with fixed-wing UAVs
2015 American Control Conference (ACC), 2015Co-Authors: Yueqian Liang, Yingmin Jia, Jun ZhangAbstract:This paper investigates the three-dimensional (3D) curved path following problem using fixed-wing unmanned aerial vehicles (UAVs) in the presence of constant wind disturbance. Vector Field based approaches are used as the solution. Two Vector Fields are first developed, one is the Tangent Vector Field based on path Tangent Vector and coordinate transformation, and the other is the combined Vector Field based on the combination of a conservative Vector Field and a solenoidal Vector Field. A unified jointly saturated course rate and saturated climb rate controller is designed based on the proposed Vector Fields. Simulations are conducted to demonstrate the effectiveness of the proposed approach.
Yueqian Liang - One of the best experts on this subject based on the ideXlab platform.
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Tangent Vector Field approach for curved path following with input saturation
Systems & Control Letters, 2017Co-Authors: Yueqian Liang, Yingmin JiaAbstract:Abstract Path following is an indispensable function for autonomous vehicles. Desired paths may be of arbitrary shape, not just the mostly investigated straight lines and circles. This paper addresses the path following problem of arbitrary twice differentiable curves using Vector-Field-based approach. A Tangent Vector Field is constructed through coordinate transformation, and a sufficient condition for its feasibility concerning the input saturation is given out. A saturated turning velocity controller is designed and its Lyapunov stability is discussed in detail. Numerical simulation results show us that the path following performance of the proposed approach is comparable with that of the literature while involving 5 less parameters to be set.
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Vector Field guidance for three dimensional curved path following with fixed wing uavs
Advances in Computing and Communications, 2015Co-Authors: Yueqian Liang, Yingmin Jia, Jun ZhangAbstract:This paper investigates the three-dimensional (3D) curved path following problem using fixed-wing unmanned aerial vehicles (UAVs) in the presence of constant wind disturbance. Vector Field based approaches are used as the solution. Two Vector Fields are first developed, one is the Tangent Vector Field based on path Tangent Vector and coordinate transformation, and the other is the combined Vector Field based on the combination of a conservative Vector Field and a solenoidal Vector Field. A unified jointly saturated course rate and saturated climb rate controller is designed based on the proposed Vector Fields. Simulations are conducted to demonstrate the effectiveness of the proposed approach.
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ACC - Vector Field guidance for three-dimensional curved path following with fixed-wing UAVs
2015 American Control Conference (ACC), 2015Co-Authors: Yueqian Liang, Yingmin Jia, Jun ZhangAbstract:This paper investigates the three-dimensional (3D) curved path following problem using fixed-wing unmanned aerial vehicles (UAVs) in the presence of constant wind disturbance. Vector Field based approaches are used as the solution. Two Vector Fields are first developed, one is the Tangent Vector Field based on path Tangent Vector and coordinate transformation, and the other is the combined Vector Field based on the combination of a conservative Vector Field and a solenoidal Vector Field. A unified jointly saturated course rate and saturated climb rate controller is designed based on the proposed Vector Fields. Simulations are conducted to demonstrate the effectiveness of the proposed approach.
Teng-teng Yao - One of the best experts on this subject based on the ideXlab platform.
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A Riemannian derivative-free Polak–Ribiére–Polyak method for Tangent Vector Field
Numerical Algorithms, 2020Co-Authors: Teng-teng Yao, Zhi Zhao, Zheng-jian Bai, Xiao-qing JinAbstract:This paper is concerned with the problem of finding a zero of a Tangent Vector Field on a Riemannian manifold. We first reformulate the problem as an equivalent Riemannian optimization problem. Then, we propose a Riemannian derivative-free Polak–Ribiere–Polyak method for solving the Riemannian optimization problem, where a non-monotone line search is employed. The global convergence of the proposed method is established under some mild assumptions. To further improve the efficiency, we also provide a hybrid method, which combines the proposed geometric method with the Riemannian Newton method. Finally, some numerical experiments are reported to illustrate the efficiency of the proposed method.
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A Riemannian Derivative-Free Polak-Ribiere-Polyak Method for Tangent Vector Field
arXiv: Numerical Analysis, 2019Co-Authors: Teng-teng Yao, Zhi Zhao, Zheng-jian Bai, Xiao-qing JinAbstract:This paper is concerned with the problem of finding a zero of a Tangent Vector Field on a Riemannian manifold. We first reformulate the problem as an equivalent Riemannian optimization problem. Then we propose a Riemannian derivative-free Polak-Ribi\'ere-Polyak method for solving the Riemannian optimization problem, where a non-monotone line search is employed. The global convergence of the proposed method is established under some mild assumptions. To further improve the efficiency, we also provide a hybrid method, which combines the proposed geometric method with the Riemannian Newton method. Finally, some numerical experiments are reported to illustrate the efficiency of the proposed method.
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A Riemannian nonmonotone spectral method for self-adjoint Tangent Vector Field
Applied Numerical Mathematics, 1Co-Authors: Teng-teng YaoAbstract:Abstract Based on the requirement of specific problems, for instance unconstrained and equality-constrained Rayleigh quotient problems, we consider the problem of finding zeros of a Tangent Vector Field on Riemannian manifold. More precisely, we focus on the study of self-adjoint Tangent Vector Field in this paper. By making full use of the self-adjointness property of the Tangent Vector Field, we propose an effective Riemannian spectral method to solve the problem, which is derivative free with nonmonotone line search employed. Through analysis, we find that the algorithm can achieve global convergence under certain conditions, which is a good result. At the end of the paper, numerical test results of the algorithm are given. We find that the proposed algorithm not only has an improvement in speed and time, but also is applicable to large-scale problems.
Xiao-qing Jin - One of the best experts on this subject based on the ideXlab platform.
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A Riemannian derivative-free Polak–Ribiére–Polyak method for Tangent Vector Field
Numerical Algorithms, 2020Co-Authors: Teng-teng Yao, Zhi Zhao, Zheng-jian Bai, Xiao-qing JinAbstract:This paper is concerned with the problem of finding a zero of a Tangent Vector Field on a Riemannian manifold. We first reformulate the problem as an equivalent Riemannian optimization problem. Then, we propose a Riemannian derivative-free Polak–Ribiere–Polyak method for solving the Riemannian optimization problem, where a non-monotone line search is employed. The global convergence of the proposed method is established under some mild assumptions. To further improve the efficiency, we also provide a hybrid method, which combines the proposed geometric method with the Riemannian Newton method. Finally, some numerical experiments are reported to illustrate the efficiency of the proposed method.
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A Riemannian Derivative-Free Polak-Ribiere-Polyak Method for Tangent Vector Field
arXiv: Numerical Analysis, 2019Co-Authors: Teng-teng Yao, Zhi Zhao, Zheng-jian Bai, Xiao-qing JinAbstract:This paper is concerned with the problem of finding a zero of a Tangent Vector Field on a Riemannian manifold. We first reformulate the problem as an equivalent Riemannian optimization problem. Then we propose a Riemannian derivative-free Polak-Ribi\'ere-Polyak method for solving the Riemannian optimization problem, where a non-monotone line search is employed. The global convergence of the proposed method is established under some mild assumptions. To further improve the efficiency, we also provide a hybrid method, which combines the proposed geometric method with the Riemannian Newton method. Finally, some numerical experiments are reported to illustrate the efficiency of the proposed method.
