A time-optimal control of steering an unstable rod

Golubev, Yu. F.

doi:10.1134/s1064230708050043

Cited by 4 publications

(8 citation statements)

References 1 publication

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“…1). It was shown in [4] that, for , small deviation angles of the rod from the vertical position, and small velocities of the point B relative to the horizontally moving point A, Eqs. (1.1) imply that (1.2) where and and are the components of the vectors and , respectively.…”

Section: Equations Of Motionmentioning

confidence: 98%

“…As in [4], consider the system consisting of a heavy rod of mass m (Fig. 1) fastened on a hinge to the platform at the point A specified by the radius vector .…”

Section: Equations Of Motionmentioning

confidence: 99%

“…In these algo rithms, the information about the angle of the rod with respect to the support was used for the feedback. Papers [4,5] are devoted to the time optimal problem of steering the point of support at a certain distance under the condition that the rod was initially stabilized in the upper equilibrium position, and it must be put in the upper equilibrium position with the zero velocity at the final point. The present paper is a con tinuation of the study [4].…”

Section: Introductionmentioning

confidence: 99%

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Synthesis of time-optimal control of inverted rod

Golub

Golubev

2011

J. Comput. Syst. Sci. Int.

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The problem of controlling a system consisting of a heavy rod fastened at its lower end on a hinge to a movable support is studied. In the linear statement and under the assumption that the sup port moves without inertia at a bounded velocity, a time optimal motion of the rod from an arbitrary initial state with a nonzero velocity to a vertical unstable equilibrium position with the zero velocity of the rod at this position is found assuming that the point of support must travel a prescribed distance. The domain where a solution exists is found. Formulas for determining the switch times of the support velocity depending on the boundary conditions are obtained. A numerical example illustrating the procedure of choosing the control depending on the initial position of the rod in the absence of distur bances is considered.

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Section: Equations Of Motionmentioning

confidence: 98%

“…As in [4], consider the system consisting of a heavy rod of mass m (Fig. 1) fastened on a hinge to the platform at the point A specified by the radius vector .…”

Section: Equations Of Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Synthesis of time-optimal control of inverted rod

Golub

Golubev

2011

J. Comput. Syst. Sci. Int.

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“…We assume that the vector field F is continuously differentiable and that the Jacobian matrix J(x) at the equilibrium satisfies the same properties as the matrix A in (1).…”

Section: B Nonlinear Systems and Koopman Operatormentioning

confidence: 99%

“…[1], [6], [11]). In this context, it is usually assumed that the control effectively drives the trajectory toward the desired target, however long it takes.…”

Section: Introductionmentioning

confidence: 99%

Converging to and escaping from the global equilibrium: Isostables and optimal control

Mauroy

2014

53rd IEEE Conference on Decision and Control

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Abstract-This paper studies the optimal control of trajectories converging to or escaping from a stable equilibrium. The control duration is assumed to be short. When the control is turned off, the trajectories have not reached the target and they subsequently evolve according to the free motion dynamics. In this context, we show that the problem can be formulated as a finite-horizon optimal control problem which relies on the notion of isostables. For linear and nonlinear systems, we solve this problem using Pontryagin's maximum principle and we study the relationship between the optimal solutions and the geometry of the isostables. Finally, optimal strategies for choosing the magnitude and duration of the control are considered.

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On Quick Action in the Problem of Controlling the Vertical Position of a Pendulum by the Movement of its Base

Lavrovsky

2021

J. Comput. Syst. Sci. Int.

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A time-optimal control of steering an unstable rod

Cited by 4 publications

References 1 publication

Synthesis of time-optimal control of inverted rod

Synthesis of time-optimal control of inverted rod

Converging to and escaping from the global equilibrium: Isostables and optimal control

On Quick Action in the Problem of Controlling the Vertical Position of a Pendulum by the Movement of its Base

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