The Experts below are selected from a list of 16143 Experts worldwide ranked by ideXlab platform
Noboru Sakamoto - One of the best experts on this subject based on the ideXlab platform.
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nonlinear optimal control for swing up and stabilization of the acrobot via Stable Manifold approach theory and experiment
IEEE Transactions on Control Systems and Technology, 2019Co-Authors: Takamasa Horibe, Noboru SakamotoAbstract:This paper presents a solution for the swing-up and stabilization problem for the Acrobot. The method employed is the Stable Manifold method for optimal control, which numerically solves Hamilton–Jacobi equations (HJEs). It is shown that the feedback controller derived from the HJE for the optimal control problem exploits an inherent motion in the Acrobot using reactions of arms effectively and, therefore, the control input is kept low. Both the simulation and the experiment confirm the effectiveness and robustness of the controller. This is the first experimental result of a swing-up control for the Acrobot with a single continuous controller. This paper also discusses the comparison with existing approaches for the same problem. It is also shown that nonunique solutions exist for the HJE and the experiment is conducted with one of those.
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numerical computational improvement of the Stable Manifold method for nonlinear optimal control
IFAC-PapersOnLine, 2017Co-Authors: Yasuaki Oishi, Noboru SakamotoAbstract:Abstract Two numerical computational techniques are presented for improvement of the Stable-Manifold method, which is effective for nonlinear optimal control. The first technique is for generation of points on the Stable Manifold in a robust way against numerical errors. There, a special numerical method that preserves Hamiltonian is used to solve a differential equation sensitive to numerical errors. The second technique is a sort of shooting method to generate a point corresponding to the desired system state. Again, numerical robustness is an issue there. The two techniques are applied to an example system and shown to be effective.
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case studies on the application of the Stable Manifold approach for nonlinear optimal control design
Automatica, 2013Co-Authors: Noboru SakamotoAbstract:This paper presents application results of a recently developed method for approximately solving the Hamilton-Jacobi equation in nonlinear control theory. The method is based on Stable Manifold theory and consists of a successive approximation algorithm which is suitable for computer calculations. Numerical approach for this algorithm is advantageous in that the computational complexity does not increase with respect to the accuracy of approximation and non-analytic nonlinearities such as saturation can be handled. First, the Stable Manifold approach for approximately solving the Hamilton-Jacobi equation is reviewed from the computational viewpoint and next, the detailed applications are reported for the problems such as swing up and stabilization of a 2-dimensional inverted pendulum (simulation), stabilization of systems with input saturation (simulation) and a (sub)optimal servo system design for magnetic levitation system (experiment).
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iterative methods to compute center and center Stable Manifolds with application to the optimal output regulation problem
Conference on Decision and Control, 2011Co-Authors: Noboru Sakamoto, Branislav RehakAbstract:This paper presents iterative methods for computing center and center-Stable Manifolds. The methods are based on the contraction mapping theorem and compute flows on the invariant Manifolds. An important application includes the design of optimal output regulators. It will be shown that the center Manifold algorithm solves the regulator equation and the center-Stable Manifold algorithm computes controllers for optimal output regulation.
Michael Scheutzow - One of the best experts on this subject based on the ideXlab platform.
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the Stable Manifold theorem for non linear stochastic systems with memory ii the local Stable Manifold theorem
Journal of Functional Analysis, 2004Co-Authors: Salaheldin A Mohammed, Michael ScheutzowAbstract:Abstract We state and prove a Local Stable Manifold Theorem (Theorem 4.1) for non-linear stochastic differential systems with finite memory (viz. stochastic functional differential equations (sfde's)). We introduce the notion of hyperbolicity for stationary trajectories of sfde's. We then establish the existence of smooth Stable and unStable Manifolds in a neighborhood of a hyperbolic stationary trajectory. The Stable and unStable Manifolds are stationary and asymptotically invariant under the stochastic semiflow. The proof uses infinite-dimensional multiplicative ergodic theory techniques developed by D. Ruelle, together with interpolation arguments.
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the Stable Manifold theorem for non linear stochastic systems with memory i existence of the semiflow
Journal of Functional Analysis, 2003Co-Authors: Salaheldin A Mohammed, Michael ScheutzowAbstract:Abstract We consider non-linear stochastic functional differential equations (sfde's) on Euclidean space. We give sufficient conditions for the sfde to admit locally compact smooth cocycles on the underlying infinite-dimensional state space. Our construction is based on the theory of finite-dimensional stochastic flows and a non-linear variational technique. In Part II of this article, the above result will be used to prove a Stable Manifold theorem for non-linear sfde's.
Biaosong Chen - One of the best experts on this subject based on the ideXlab platform.
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multi objective transfer to libration point orbits via the mixed low thrust and invariant Manifold approach
Nonlinear Dynamics, 2014Co-Authors: Haijun Peng, Biaosong ChenAbstract:The multi-objective optimization of transfer trajectories from an orbit near Earth to a periodic libration-point orbit in the Sun–Earth system using the mixed low-thrust and invariant-Manifold approach is investigated in this paper. A two-objective optimization model is proposed based on the mixed low-thrust and invariant-Manifold approach. The circular restricted three-body model (CRTBP) is utilized to represent the motion of a spacecraft in the gravitational field of the Sun and Earth. The transfer trajectory is broken down into several segments; both low-thrust propulsion and Stable Manifolds are utilized based on the CRTBP in different segments. The fuel cost, which is generated only by the low-thrust trajectory for transferring the spacecraft from an orbit near Earth to a Stable Manifold, is minimized. The total flight time, which includes the time during which the spacecraft is controlled by the low-thrust trajectory and the time during which the spacecraft is moving on the Stable Manifold, is also minimized. Using the nondominated sorting genetic algorithm for the resulting multi-objective optimization problem, highly promising Pareto-optimal solutions for the transfer of the spacecraft are found. Via numerical simulations, it is shown that tradeoffs between time of flight and fuel cost can be quickly evaluated using this approach. Furthermore, for the same time of flight, transfer trajectories based on the mixed-transfer method can save a larger amount of fuel than the low-thrust method alone.
Vn Biktashev - One of the best experts on this subject based on the ideXlab platform.
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Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system
'AIP Publishing', 2017Co-Authors: Bezekci B., Vn BiktashevAbstract:This is the author accepted manuscript. The final version is available from AIP Publishing via the DOI in this record.We study the problem of initiation of propagation of excitation waves in the FitzHugh-Nagumo model. Our approach is based on earlier works, based on the idea of approximating of the boundary between basins of attraction of propagating wave solutions and of decaying solutions as the Stable Manifold of the critical solution. Here, we obtain analytical expressions for the essential ingredients of the theory by singular perturbation using two small parameters, the separation of time scales of the activator and inhibitor, and the threshold in the activator's kinetics. This results in a closed analytical expression for the strength-duration curve.VNB gratefully acknowledges the current financial support of the EPSRC via grant EP/N014391/1 (UK
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Initiation of Excitation Waves: An Analytical Approach
2016Co-Authors: Vn Biktashev, I IdrisAbstract:We consider the problem of initiation of a propagat-ing wave in a one-dimensional excitable fibre. In the Zeldovich-Frank-Kamenetsky equation, a.k.a. Nagumo equation, the key role is played by the “critical nucleus” solution whose Stable Manifold is the threshold surface separating initial conditions leading to initiation of propa-gation and to decay. In ionic models of cardiac excitation fronts, the same role is played by the center-Stable man-ifold of the “critical ” front solution. Approximations of these Manifolds by their tangent linear spaces yield an-alytical criteria of initiation. These criteria give a good quantitative appoximation for simplified models and a use-ful qualitatively correct answer for the ionic models. 1
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critical fronts in initiation of excitation waves
Physical Review E, 2007Co-Authors: I Idris, Vn BiktashevAbstract:We consider the problem of initiation of propagating waves in a one-dimensional excitable fiber. In the FitzHugh-Nagumo theory, the key role is played by "critical nucleus" and "critical pulse" solutions whose (center-) Stable Manifold is the threshold surface separating initial conditions leading to propagation and those leading to decay. We present evidence that in cardiac excitation models, this role is played by "critical front" solutions.
Salaheldin A Mohammed - One of the best experts on this subject based on the ideXlab platform.
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the Stable Manifold theorem for semilinear stochastic evolution equations and stochastic partial differential equations
2008Co-Authors: Salaheldin A Mohammed, Tusheng Zhang, Huaizhong ZhaoAbstract:The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see's) and stochastic partial differential equations (spde's) near stationary solutions. Such characterization is realized through the long-term behavior of the solution field near stationary points. The analysis falls in two parts 1, 2. In Part 1, we prove general existence and compactness theorems for Ck-cocycles of semilinear see's and spde's. Our results cover a large class of semilinear see's as well as certain semilinear spde's with Lipschitz and non-Lipschitz terms such as stochastic reaction diffusion equations and the stochastic Burgers equation with additive infinite- dimensional noise. In Part 2, stationary solutions are viewed as cocycle-invariant random points in the infinite-dimensional state space. The pathwise local structure of solutions of semilinear see's and spde's near stationary solutions is described in terms of the almost sure longtime behavior of trajectories of the equation in relation to the stationary solution. More specifically, we establish local Stable Manifold theorems for semilinear see's and spde's (Theorems 2.4.1-2.4.4). These results give smooth Stable and unStable Manifolds in the neighborhood of a hyperbolic stationary solution of the underlying stochastic equation. The Stable and unStable Manifolds are stationary, live in a stationary tubular neighborhood of the stationary solution and are asymptotically invariant under the stochastic semiflow of the see/spde. Furthermore, the local Stable and unStable Manifolds intersect transversally at the stationary point, and the unStable Manifolds have fixed finite dimension. The proof uses infinite-dimensional multiplicative ergodic theory techniques, interpolation and perfection arguments (Theorem 2.2.1).
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the Stable Manifold theorem for non linear stochastic systems with memory ii the local Stable Manifold theorem
Journal of Functional Analysis, 2004Co-Authors: Salaheldin A Mohammed, Michael ScheutzowAbstract:Abstract We state and prove a Local Stable Manifold Theorem (Theorem 4.1) for non-linear stochastic differential systems with finite memory (viz. stochastic functional differential equations (sfde's)). We introduce the notion of hyperbolicity for stationary trajectories of sfde's. We then establish the existence of smooth Stable and unStable Manifolds in a neighborhood of a hyperbolic stationary trajectory. The Stable and unStable Manifolds are stationary and asymptotically invariant under the stochastic semiflow. The proof uses infinite-dimensional multiplicative ergodic theory techniques developed by D. Ruelle, together with interpolation arguments.
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the Stable Manifold theorem for non linear stochastic systems with memory i existence of the semiflow
Journal of Functional Analysis, 2003Co-Authors: Salaheldin A Mohammed, Michael ScheutzowAbstract:Abstract We consider non-linear stochastic functional differential equations (sfde's) on Euclidean space. We give sufficient conditions for the sfde to admit locally compact smooth cocycles on the underlying infinite-dimensional state space. Our construction is based on the theory of finite-dimensional stochastic flows and a non-linear variational technique. In Part II of this article, the above result will be used to prove a Stable Manifold theorem for non-linear sfde's.
