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Hamiltonian Representation of Higher Order Partial Differential Equations with Boundary Energy Flows

Journal of Applied Mathematics and Physics 2015年第11期3卷 1472-1490页

作者： gou nishida Department of Mechanical and Environmental Informatics Graduate School of Information Science and Engineering Tokyo Institute of Technology Tokyo Japan

This paper presents a system representation that can be applied to the description of the interaction between systems connected through common boundaries. The systems consist of partial differential equations that are first order with respect to time, but spatially higher order. The representation is derived from the instantaneous multisymplectic Hamiltonian formalism;therefore, it possesses the physical consistency with respect to energy. In the interconnection, particular pairs of control inputs and observing outputs, called port variables, defined on the boundaries are used. The port variables are systematically introduced from the representation.

关键词： Symplectic Structure Dirac Structure Hamiltonian Systems Passivity Partial Differential Equations Nonlinear Systems

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Symplectic Numerical Approach for Nonlinear Optimal Control of Systems with Inequality Constraints

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International Journal of Modern Nonlinear Theory and Application 2015年第4期4卷 234-248页

作者： Yoshiki Abe gou nishida Noboru Sakamoto Yutaka Yamamoto Department of Applied Analysis and Complex Dynamical Systems Graduate School of Informatics Kyoto University Kyoto Japan Department of Mechanical and Environmental informatics Graduate School of Information Science and Engineering Tokyo Institute of Technology Tokyo Japan Department of Mechatronics Faculty of Science and Engineering Nanzan University Nagoya Japan

This paper proposes a system representation for unifying control design and numerical calculation in nonlinear optimal control problems with inequality constraints in terms of the symplectic structure. The symplectic structure is derived from Hamiltonian systems that are equivalent to Hamilton-Jacobi equations. In the representation, the constraints can be described as an input-state transformation of the system. Therefore, it can be seamlessly applied to the stable manifold method that is a precise numerical solver of the Hamilton-Jacobi equations. In conventional methods, e.g., the penalty method or the barrier method, it is difficult to systematically assign the weights of penalty functions that are used for realizing the constraints. In the proposed method, we can separate the adjustment of weights with respect to objective functions from that of penalty functions. Furthermore, the proposed method can extend the region of computable solutions in a state space. The validity of the method is shown by a numerical example of the optimal control of a vehicle model with steering limitations.

关键词： Optimal Controls Nonlinear Systems Constrained Systems Symplectic Numerical Methods Stable Manifold Method

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