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Hirokazu Nishitani - One of the best experts on this subject based on the ideXlab platform.
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multilayer minimum Projection Method with singular point assignment for nonsmooth control lyapunov function design
Conference on Decision and Control, 2010Co-Authors: Hisakazu Nakamura, Nami Nakamura, Yoshiro Fukui, Hirokazu NishitaniAbstract:Control Lyapunov functions (CLFs) design on manifolds is a difficult control problem. For the problem, we have proposed the multilayer minimum Projection Method. The Method requires control Lyapunov functions (CLF) on other manifolds. For the case of “another single-manifold,” we relaxed the condition by desingularization of the function on the other manifold. However, the “multilayer-case” is not discussed. This paper focuses on the problem of desingularization via the multilayer minimum Projection Method. We show that the functions on other manifolds need not to be CLFs on these manifolds by considering desingularization. Based on the advantage of desingularization, we propose a CLF design Method by singular point assignment. The Method enables us to merge local CLFs into the global CLF. We confirm the effectiveness of the proposed CLF design Method by an example of obstacle avoidance control of a mobile robot.
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multilayer minimum Projection Method for nonsmooth strict control lyapunov function design
Systems & Control Letters, 2010Co-Authors: Hisakazu Nakamura, Nami Nakamura, Yoshiro Fukui, Hirokazu NishitaniAbstract:Asymptotic stabilization on noncontractible manifolds is known as a difficult control problem. To address this problem, we had proposed the minimum Projection Method to design nonsmooth control Lyapunov functions. This Method, however, has some problems: difficult etale-surjection design, undesirable resulting control Lyapunov functions, etc. In this paper, we propose a new nonsmooth control Lyapunov function design Method called the ‘Multilayer minimum Projection Method’ for nonsmooth control Lyapunov function design on general manifolds. The Method considers many simple-structured smooth manifolds associated with the original manifold by etale mappings, and then a function on the original manifold is obtained by projecting control Lyapunov functions defined on the simple-structured manifolds onto the original manifold. In this paper, we prove that the resulting function by the proposed Method is a nonsmooth control Lyapunov function on the original manifold. Moreover, we prove that if all control Lyapunov functions defined on simple-structured manifolds are strict, the control Lyapunov function on the original manifold is a strict control Lyapunov function. Finally, the effectiveness of the proposed Method and the advantage over the conventional minimum Projection Method are confirmed by an example.
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minimum Projection Method for nonsmooth control lyapunov function design on general manifolds
Systems & Control Letters, 2009Co-Authors: Hisakazu Nakamura, Yuh Yamashita, Hirokazu NishitaniAbstract:Abstract Asymptotic stabilization on noncontractible manifolds is known as a difficult control problem. On the other hand, an important fact is every control system that is globally asymptotically stabilizable at a desired equilibrium must have nonsmooth control Lyapunov functions. This paper considers the problem of construction of nonsmooth control Lyapunov functions on general manifolds, and we propose a nonsmooth control Lyapunov function design Method called the ‘Minimum Projection Method’. The proposed Method considers a simple-structured smooth manifold associated with the original manifold by a surjective immersion, and then a control Lyapunov function defined on the simple-structured manifold is projected to the original manifold. A function on the original manifold is thus obtained. In this paper, we prove that the control system on another manifold associated with a surjective immersion is determined uniquely, and the resulting function by the proposed Method is a nonsmooth control Lyapunov function on the original manifold. The effectiveness of the proposed Method is confirmed by examples.
Hisakazu Nakamura - One of the best experts on this subject based on the ideXlab platform.
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global nonsmooth control lyapunov function design for path following problem via minimum Projection Method
IFAC-PapersOnLine, 2016Co-Authors: Hisakazu NakamuraAbstract:Abstract: Path-following and trajectory-tracking problems are important control problems. For the path-following problem the paper proposes a locally semiconcave path-following control Lyapunov function (PF-CLF). Moreover, the paper proposes the minimum Projection Method for PF-CLF design by using tracking control Lyapunov function. Furthermore, a static feedback controller for a path-following problem is proposed. Finally, we confirm the effectiveness of the proposed Method by computer simulation.
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multilayer minimum Projection Method with singular point assignment for nonsmooth control lyapunov function design
Asian Journal of Control, 2013Co-Authors: Hisakazu Nakamura, Nami NakamuraAbstract:Control Lyapunov function (CLF) design on a manifold is a difficult problem in control theory. To address this problem, we have proposed the multilayer minimum Projection Method. The Method requires CLFs on different manifolds from the manifold where the control problem is defined. In this paper, we relax the requirement by desingularization of the functions on the manifolds. The paper focuses on the problem of desingularization in the multilayer minimum Projection Method. We show that the functions on other manifolds need not be CLFs by consideration of desingularization. Moreover, we propose a CLF design Method by singular point assignment based on the advantage of desingularization. The Method enables us to merge local CLFs into the global CLF. This paper proposes two CLF design Methods: desingularization and singular point assignment. A CLF design example is provided for each Method; the advantages of the proposed Methods are confirmed by those two examples.
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multilayer minimum Projection Method with singular point assignment for nonsmooth control lyapunov function design
Conference on Decision and Control, 2010Co-Authors: Hisakazu Nakamura, Nami Nakamura, Yoshiro Fukui, Hirokazu NishitaniAbstract:Control Lyapunov functions (CLFs) design on manifolds is a difficult control problem. For the problem, we have proposed the multilayer minimum Projection Method. The Method requires control Lyapunov functions (CLF) on other manifolds. For the case of “another single-manifold,” we relaxed the condition by desingularization of the function on the other manifold. However, the “multilayer-case” is not discussed. This paper focuses on the problem of desingularization via the multilayer minimum Projection Method. We show that the functions on other manifolds need not to be CLFs on these manifolds by considering desingularization. Based on the advantage of desingularization, we propose a CLF design Method by singular point assignment. The Method enables us to merge local CLFs into the global CLF. We confirm the effectiveness of the proposed CLF design Method by an example of obstacle avoidance control of a mobile robot.
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multilayer minimum Projection Method for nonsmooth strict control lyapunov function design
Systems & Control Letters, 2010Co-Authors: Hisakazu Nakamura, Nami Nakamura, Yoshiro Fukui, Hirokazu NishitaniAbstract:Asymptotic stabilization on noncontractible manifolds is known as a difficult control problem. To address this problem, we had proposed the minimum Projection Method to design nonsmooth control Lyapunov functions. This Method, however, has some problems: difficult etale-surjection design, undesirable resulting control Lyapunov functions, etc. In this paper, we propose a new nonsmooth control Lyapunov function design Method called the ‘Multilayer minimum Projection Method’ for nonsmooth control Lyapunov function design on general manifolds. The Method considers many simple-structured smooth manifolds associated with the original manifold by etale mappings, and then a function on the original manifold is obtained by projecting control Lyapunov functions defined on the simple-structured manifolds onto the original manifold. In this paper, we prove that the resulting function by the proposed Method is a nonsmooth control Lyapunov function on the original manifold. Moreover, we prove that if all control Lyapunov functions defined on simple-structured manifolds are strict, the control Lyapunov function on the original manifold is a strict control Lyapunov function. Finally, the effectiveness of the proposed Method and the advantage over the conventional minimum Projection Method are confirmed by an example.
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minimum Projection Method for nonsmooth control lyapunov function design on general manifolds
Systems & Control Letters, 2009Co-Authors: Hisakazu Nakamura, Yuh Yamashita, Hirokazu NishitaniAbstract:Abstract Asymptotic stabilization on noncontractible manifolds is known as a difficult control problem. On the other hand, an important fact is every control system that is globally asymptotically stabilizable at a desired equilibrium must have nonsmooth control Lyapunov functions. This paper considers the problem of construction of nonsmooth control Lyapunov functions on general manifolds, and we propose a nonsmooth control Lyapunov function design Method called the ‘Minimum Projection Method’. The proposed Method considers a simple-structured smooth manifold associated with the original manifold by a surjective immersion, and then a control Lyapunov function defined on the simple-structured manifold is projected to the original manifold. A function on the original manifold is thus obtained. In this paper, we prove that the control system on another manifold associated with a surjective immersion is determined uniquely, and the resulting function by the proposed Method is a nonsmooth control Lyapunov function on the original manifold. The effectiveness of the proposed Method is confirmed by examples.
Markus Kraft - One of the best experts on this subject based on the ideXlab platform.
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a joint moment Projection Method and maximum entropy approach for simulation of soot formation and oxidation in diesel engines
Applied Energy, 2020Co-Authors: Shaohua Wu, Jethro Akroyd, Sebastian Mosbach, Wenming Yang, Markus KraftAbstract:Abstract A joint moment Projection Method and maximum entropy approach for treating the soot population balance equations is developed and presented in this work. The moment Projection Method is used to solve the population balance equations and generate moments that are supplied to the maximum entropy approach as a post-processing technique to reconstruct the soot particle size distribution. The particle size range required by the maximum entropy for particle size distribution reconstruction is determined based on the weighted particles generated in the moment Projection Method. The performance of the joint approach is first evaluated by solving a set of simplified population balance equations in MatLab, then it is implemented into a Stochastic Reactor Model engine code to simulate the formation and oxidation of soot particles in a single-cylinder direct injection diesel engine. Results suggest that the joint approach has the advantages of ease of implementation, high accuracy and low computational cost. It enables a detailed analysis on the soot formation and oxidation processes in diesel engines. Complete information on the soot particle size distribution can be provided with little CPU cost induced.
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bivariate extension of the moment Projection Method for the particle population balance dynamics
Computers & Chemical Engineering, 2019Co-Authors: Casper S Lindberg, Jethro Akroyd, Wenming Yang, Markus KraftAbstract:Abstract This work presents a bivariate extension of the moment Projection Method (BVMPM) for solving the two-dimensional population balance equations involving particle inception, growth, shrinkage, coagulation and fragmentation. A two–dimensional Blumstein and Wheeler algorithm is proposed to generate a set of weighted particles that approximate the number density function. With this algorithm, the number of the smallest particles can be directly tracked, closing the shrinkage and fragmentation moment source terms. The performance of BVMPM has been tested against the hybrid Method of moments (HMOM) and the stochastic Method. Results suggest that BVMPM can achieve higher accuracy than HMOM in treating shrinkage and fragmentation processes where the number of the smallest particles plays an important role.
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a moment Projection Method for population balance dynamics with a shrinkage term
Journal of Computational Physics, 2017Co-Authors: Edward Kien Yee Yapp, Jethro Akroyd, Sebastian Mosbach, Wenming Yang, Markus KraftAbstract:A new Method of moments for solving the population balance equation is developed and presented. The moment Projection Method (MPM) is numerically simple and easy to implement and attempts to address the challenge of particle shrinkage due to processes such as oxidation, evaporation or dissolution. It directly solves the moment transport equation for the moments and tracks the number of the smallest particles using the algorithm by Blumstein and Wheeler (1973) 41. The performance of the new Method is measured against the Method of moments (MOM) and the hybrid Method of moments (HMOM). The results suggest that MPM performs much better than MOM and HMOM where shrinkage is dominant. The new Method predicts mean quantities which are almost as accurate as a high-precision stochastic Method calculated using the established direct simulation algorithm (DSA).
E Weinan - One of the best experts on this subject based on the ideXlab platform.
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a gauss seidel Projection Method for micromagnetics simulations
Journal of Computational Physics, 2001Co-Authors: Xiaoping Wang, Carlos J Garcicervera, E WeinanAbstract:Abstract One of the main difficulties in micromagnetics simulation is the severe time step constraint introduced by the exchange field. Using standard explicit integrators leads to a physical time step of sub-pico seconds, which is often two orders of magnitude smaller than the fastest physical time scales. Direct implicit integrators require solving complicated, coupled systems. In this paper, we introduce an implicit Method whose complexity is comparable to solving the scalar heat equation implicitly. This Method is based on a combination of a Gauss–Seidel implementation of a fractional step implicit solver for the gyromagnetic term, and the Projection Method for the heat flow of harmonic maps. This Method allows us to carry out fully resolved calculations for the switching of the magnetization in micron-sized elements.
Nami Nakamura - One of the best experts on this subject based on the ideXlab platform.
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multilayer minimum Projection Method with singular point assignment for nonsmooth control lyapunov function design
Asian Journal of Control, 2013Co-Authors: Hisakazu Nakamura, Nami NakamuraAbstract:Control Lyapunov function (CLF) design on a manifold is a difficult problem in control theory. To address this problem, we have proposed the multilayer minimum Projection Method. The Method requires CLFs on different manifolds from the manifold where the control problem is defined. In this paper, we relax the requirement by desingularization of the functions on the manifolds. The paper focuses on the problem of desingularization in the multilayer minimum Projection Method. We show that the functions on other manifolds need not be CLFs by consideration of desingularization. Moreover, we propose a CLF design Method by singular point assignment based on the advantage of desingularization. The Method enables us to merge local CLFs into the global CLF. This paper proposes two CLF design Methods: desingularization and singular point assignment. A CLF design example is provided for each Method; the advantages of the proposed Methods are confirmed by those two examples.
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multilayer minimum Projection Method with singular point assignment for nonsmooth control lyapunov function design
Conference on Decision and Control, 2010Co-Authors: Hisakazu Nakamura, Nami Nakamura, Yoshiro Fukui, Hirokazu NishitaniAbstract:Control Lyapunov functions (CLFs) design on manifolds is a difficult control problem. For the problem, we have proposed the multilayer minimum Projection Method. The Method requires control Lyapunov functions (CLF) on other manifolds. For the case of “another single-manifold,” we relaxed the condition by desingularization of the function on the other manifold. However, the “multilayer-case” is not discussed. This paper focuses on the problem of desingularization via the multilayer minimum Projection Method. We show that the functions on other manifolds need not to be CLFs on these manifolds by considering desingularization. Based on the advantage of desingularization, we propose a CLF design Method by singular point assignment. The Method enables us to merge local CLFs into the global CLF. We confirm the effectiveness of the proposed CLF design Method by an example of obstacle avoidance control of a mobile robot.
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multilayer minimum Projection Method for nonsmooth strict control lyapunov function design
Systems & Control Letters, 2010Co-Authors: Hisakazu Nakamura, Nami Nakamura, Yoshiro Fukui, Hirokazu NishitaniAbstract:Asymptotic stabilization on noncontractible manifolds is known as a difficult control problem. To address this problem, we had proposed the minimum Projection Method to design nonsmooth control Lyapunov functions. This Method, however, has some problems: difficult etale-surjection design, undesirable resulting control Lyapunov functions, etc. In this paper, we propose a new nonsmooth control Lyapunov function design Method called the ‘Multilayer minimum Projection Method’ for nonsmooth control Lyapunov function design on general manifolds. The Method considers many simple-structured smooth manifolds associated with the original manifold by etale mappings, and then a function on the original manifold is obtained by projecting control Lyapunov functions defined on the simple-structured manifolds onto the original manifold. In this paper, we prove that the resulting function by the proposed Method is a nonsmooth control Lyapunov function on the original manifold. Moreover, we prove that if all control Lyapunov functions defined on simple-structured manifolds are strict, the control Lyapunov function on the original manifold is a strict control Lyapunov function. Finally, the effectiveness of the proposed Method and the advantage over the conventional minimum Projection Method are confirmed by an example.
