Numerical Calculation of Feedback Law in Quantum Mechanical Theory of Optimal Control

Itami, Teturo

doi:10.1541/ieejeiss.125.1730

Cited by 3 publications

(3 citation statements)

References 7 publications

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“…The Schrödinger equation specifies the wave function ψ of boundary part of the state space Ω as the space boundary condition. The boundary condition is defined as follows Equation (29) shows that the state of object is described as the Schrödinger equation that is restricted in Ω by the potential energy (22) . Then, the boundary conditions are applied to two resonators line circuit.…”

Section: Stochastic Disturbance Reduction With Resonant Filtermentioning

confidence: 99%

Modeling of Stochastic Disturbance Based on Quantum Physics for High-Performance Force Estimation

Takeya

Katsura

2015

IEEJ Journal IA

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Delicate movement with high-precision performance is required in industrial areas such as medical care and semiconductor processing. Taking the expansion of the robotic movement area into account, attainment of force control is the one of the fundamental techniques for working in a microspace. To focus on the force information in a microspace, the transmission of microforce information is important to avoid destruction of the delicate object. However, the quality of force information is deteriorated by the influence of a stochastic disturbance such as quantization noise and sensor noise. In other words, high-precision force control is closely related to a reduction in the influence of the stochastic disturbance. Therefore, this paper focuses on the stochastic disturbance as a quantum fluctuation that is derived as the Schrödinger equation. In order to reduce the stochastic disturbance, a novel modeling method that is focused on quantum fluctuation is proposed. In this paper, a resonant filter is introduced by a complex equivalent electrical circuit of the Schrödinger equation, and a reaction force observer is implemented. The viability of the proposed method and the reduction in the oscillation are confirmed by the displacement of the poles and experiments.

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Section: Stochastic Disturbance Reduction With Resonant Filtermentioning

confidence: 99%

Modeling of Stochastic Disturbance Based on Quantum Physics for High-Performance Force Estimation

Takeya

Katsura

2015

IEEJ Journal IA

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“…For the system defined by Eqs. (1) and (2), we can introduce a linear Hamiltonian operator in the quantum mechanical theory [6]:…”

Section: Quantum Theory Of Nonlinear Optimal Control [1]mentioning

confidence: 99%

“…For that reason, when we form a function this V _ _ is inevitably dependent on the constant H R . Now we can easily show that the phase S q (x, t; H R ) satisfies where the function V _ _ multiplied by H R 2 / 2m appears as a new cost term that we add to the left-hand side of conventional Hamilton-Jacobi equation(6). In the limit H R → 0, this additional cost term tends to zero with the order of H R 2 , at least superficially.…”

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confidence: 91%

Quantum fluctuation in affine optimal control systems

Itami

2007

Electrical Engineering Japan

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SUMMARYQuantum mechanical wave functions are shown to approximate optimal feedback laws of affine control systems, when we set the absolute values of the terminal wave functions positive and with no singular dependence on a control constant H R , which is similar in position to the action constant % introduced by Planck to explain quantum phenomena. Calculation of the wave functions makes use of the path integral representation that we approximate at stationary phase. The phases of the wave functions approximate in H R → 0 to Hamilton-Jacobi value functions, because quantum mechanical fluctuation vanishes in the limit. It is simple to take the terminal absolute value function that meets the condition of having no singularity at H R = 0. The terminal absolute value function without any dependence on the constant H R apparently satisfies the no-singularity condition. Although we restrict ourselves to scalar systems, generalization to systems with higher dimensionality is straightforward. Key words: nonlinear optimal feedback control; linear wave equation; path integral; stationary phase approximation. IntroductionThere have so far been various algorithms and software tools for treating linear systems in mathematical science and technology. Many researchers are still engaged in the development of such linear tools. We therefore have various ideas that allow us to calculate nonlinear control systems within a framework of linear theories. As one such linear theory, the author has developed a quantum mechanical theory of nonlinear optimal control that fully utilizes complex wave equations [1]. The linearity of the wave equations allows us to apply methods that have been developed for linear systems, such as eigenvalue analysis, the path integral method, random walk simulation, and so on. Let us consider an affine nonlinear system with control cost quadratic in control inputs. The real part of the complex wave equation is an extension of the conventional Hamilton-Jacobi equation with an additional term that causes quantum mechanical fluctuation. A control constant H R that has a similar role to Planck's constant % [2] has been brought into our quantum mechanical control theory. It is generally considered that in macroscopic systems, where the constant % is negligible, classical mechanics approximately describes the systems. _ _as a combination of the absolute value R(x, t; H R ) ≡ |ψ(x, t; H R )| of the wave function ψ(x, t; H R ) and its first and second partial derivatives with respect to the spatial variable x. It is necessary to clarify conditions when the absolute value R(x, t; H R ) has no singularity at H R = 0. In optimal control schemes, designers introduce a terminal cost at terminal time t F as one of the control specifications. This terminal cost defines a time boundary condition of a phase of the wave function in our quantum mechanical control theory. On the contrary, we can set a boundary condition R(x, t F ; H R ) freely. What we show in this report is: If the terminal absolute value R(x, t F ; H R ) is ...

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Fluctuation in Quantum Mechanics of Affine Optimal Control System

Itami¹

2006

IEEJ Trans.EIS

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Numerical Calculation of Feedback Law in Quantum Mechanical Theory of Optimal Control

Cited by 3 publications

References 7 publications

Modeling of Stochastic Disturbance Based on Quantum Physics for High-Performance Force Estimation

Modeling of Stochastic Disturbance Based on Quantum Physics for High-Performance Force Estimation

Quantum fluctuation in affine optimal control systems

Fluctuation in Quantum Mechanics of Affine Optimal Control System

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