Simulation of control processes, stability and stabilization of systems with program constraints

Mukharlyamov, R. G.

doi:10.1134/s1064230715010116

Cited by 19 publications

(6 citation statements)

References 1 publication

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“…A specific nonsmooth form of functional (6) dictates the optimal control in this problem to be of the pulse form; see [16]. This observation limits the potentials of the standard numerical schemes of optimal control [9,12]. Instead, the approach developed in this paper is based on linearization and discretization of the equation and changing the integral in (6) for the sum of absolute values of the sampled control inputs.…”

Section: Optimal Motion Controlmentioning

confidence: 99%

“…Therefore, we arrive at the minimization of function (10) subject to equality-type constraints (12). Use of standard tricks such as changing the absolute value for the difference of nonnegative variables reduces this problem to an LP, and efficient Matlab-based LP-solvers then can be taken as computational tools.…”

Section: Optimal Motion Controlmentioning

confidence: 99%

“…In contrast to the classical numerical methods exploited in optimal control [9][10][11][12], the approach of this current paper accounts for a specific form of the nonsmooth performance functional to be minimized (l 1 -optimization). In the past, similar methods were used to compute minimum fuel-consumption space journeys [13][14][15], but not to stabilization of spacecrafts at equilibria points.…”

Section: Introductionmentioning

confidence: 99%

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Minimum Fuel-Consumption Stabilization of a Spacecraft at the Lagrangian Points

Polyak

Shalby

2019

Autom Remote Control

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We consider the motion of a spacecraft described by the differential equations of the three-body problem in the Earth-Moon system. The goal is to stabilize the spacecraft in the neighborhood of the collinear Lagrangian points (which are know to be unstable equilibria) via use of minimum fuel-consumption control. The adopted approach is based on l 1 -optimization of linearized and discretized equations with terminal conditions being the target Lagrangian point. Therefore, the problem reduces to a linear program, and its solution defines pulse controls for the original three-body equations. Upon reaching the desired neighborhood, the spacecraft performs control-free flight until its deviation from the Lagrangian point exceeds certain prespecified threshold. The correction is then applied repeatedly, so that the spacecraft is kept within a small neighborhood of the unstable equilibrium point.

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Section: Optimal Motion Controlmentioning

confidence: 99%

Section: Optimal Motion Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Minimum Fuel-Consumption Stabilization of a Spacecraft at the Lagrangian Points

Polyak

Shalby

2019

Autom Remote Control

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“…The problem of constructing for systems of ordinary differential equations on a given integral curve was formulated by Yerugin in [1] and there was proposed a method for its solving. Later, this problem was developed by Galiullin, Mukhametzyanov, Mukharlyamov and others [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] to the problem of the construction of systems of differential equations by a given integral manifold, to solving of various inverse problems of dynamics, and to constructing of systems of program motion.The integral manifold is defined as the intersection of hypersurfaces.It should be noted that the construction of stable systems developed into an independent theory. A detailed survey of these works can be found in [2,7,16].…”

mentioning

confidence: 99%

Absolute Stability of a Program Manifold of Non-Autonomous Basic Control Systems

Zhumatov

2018

Physico-Mathematical Series

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In this paper the inverse dynamics problemisstudied: for a given manifold restore a force field, which lies in the tangent subspace to manifold. One of the general inverse problems of dynamics is solved: the corresponding system of differential equations is but as well as the stability is considered. This inverse problem is very important for a variety of mathematical models mechanics.Absolutestability of a program manifold of nonautonomous basic control systems with stationary nonlinearity is investigated.Theproblem of stability of the basic control systems is considered in the neighborhood of a program manifold. Nonlinearitysatisfies to conditions of local quadratic relations. The sufficient conditions of the absolute stability of the program manifold have been obtained relatively to a given vector-function by means of construction of Lyapunov function, in the form "quadratic form plus an integral from nonlinearity". The obtained results are used to solve the problem of the synthesis of high-speed regulators.

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“…Extremal properties of constraints resulting from the dynamic laws that prevail in mechanics make this control method somewhat optimal [15]. Examples of application of this method to robotics problems can be found in [2,17,[20][21][22]36].…”

Section: Introductionmentioning

confidence: 99%

A Study of the Controlled Motion of a Four-wheeled Mecanum Platform

Adamov¹

2018

Nelin. Dinam.

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The object of the study is the mobile platform of the KUKA youBot robot equipped with four Mecanum wheels. The ideal conditions for the point contact of the wheels and the floor are considered. It is assumed that the rollers of each Mecanum wheel move without slipping and the center of the wheel, the center of the roller axis, and the point of contact of the roller with the floor are located on the same straight line. The dynamics of the system is described using Appel's equations and taking into account the linear forces of viscous friction in the joints of the bodies. An algorithm for determination of the control forces is designed. Their structure is the same as that of the reactions of ideal constraints determined by the program motion of the point of the platform. The controlled dynamics of the system is studied using uniform circular motion of the platform point as an example: conditions for the existence and stability of steady rotations are found, conditions for the existence of stable-unstable stationary regimes and rotational motions of the platform are obtained. Within the framework of the theory of singular perturbations, an asymptotic analysis of the rotation of the platform is carried out.

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Simulation of control processes, stability and stabilization of systems with program constraints

Cited by 19 publications

References 1 publication

Minimum Fuel-Consumption Stabilization of a Spacecraft at the Lagrangian Points

Minimum Fuel-Consumption Stabilization of a Spacecraft at the Lagrangian Points

Absolute Stability of a Program Manifold of Non-Autonomous Basic Control Systems

A Study of the Controlled Motion of a Four-wheeled Mecanum Platform

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