Lev Rapoport

Lev Rapoport
Institute of Control Sciences | IPU · Dynamics of Non-linear control systems

Dr. Sc

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97
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January 1992 - present
Russian Academy of Sciences
Position
  • Principal Investigator

Publications

Publications (97)
Chapter
In precision agriculture, the optimal construction of a complete coverage for an uneven field with parallel paths is often considered. As a rule, a coverage can be defined by some initial path relative to which the whole coverage is constructed. For various purposes, such as minimizing the number of turnarounds, some part of the field boundary can...
Chapter
The problem of motion control of a wheeled robot is considered. The robot is supposed to be moving without lateral slippage along an arbitrary, sufficiently smooth three-dimensional surface. The target path of the robot is defined by a curve with constrained curvature on a given surface. The rear wheels are assumed to be driving while the front whe...
Chapter
Considered is the problem of the attraction domain estimation in the space “distance to the trajectory – orientation” for the problem of the planar motion control of a wheeled robot. This problem has received much attention in connection with precision farming applications [11]. The mathematical model of the robot takes into account kinematic relat...
Article
Convex relaxation methods are commonly used to solve nonconvex mathematical optimization problems. These methods transform the original nonconvex problem in such a way that effective methods of solving convex optimization problems become applicable. Thus, a convex problem giving the approximate solution of the original task can be solved instead of...
Chapter
When processing multiple navigation satellite systems, including GPS, GLONASS, Galileo, Beidou, QZSS, the overall number of the pseudorange and carrier phase signals can exceed several tens. On the other hand, a much smaller number of them is usually sufficient to achieve necessary precision of positioning. Also, some parts of precise positioning a...
Chapter
In this paper we consider the problem of the sign-definiteness of a quadratic form (QF) in the domain defined by quadratic constraints under quadratic constraints. Each constraint is determined by an inequality on a QF. Well known and widely applicable in the control theory approach consists of using so called S–procedure. The semidefinite relaxati...
Article
In this paper, the semidefinite relaxation method is applied to the problem of determining the orientation of a solid body relative to the local horizon using satellite navigation. It is shown how the initial nonconvex quadratic programming problem is immersed in a wider class of convex optimization problems that allow an effective solution. Instea...
Article
Use of the semidefinite relaxation in the problem of sign-definiteness of the quadratic form under quadratic constraints enables one to establish from the duality conditions an S-procedure. However, the S-procedure giving the necessary and sufficient conditions for signdefiniteness of the relaxed problem provides only the sufficient conditions for...
Conference Paper
When processing multiple navigation satellite systems, including GPS, GLONASS, Galileo, Beidou, QZSS, the overall number of the pseudorange and carrier phase signals can exceed several tens. On the other hand, a much smaller number of them is usually sufficient to achieve necessary precision of positioning. Also, some parts of RTK algorithms, like...
Article
Nonlinear single-input affine systems represented in a canonical (normal) form are considered. The control resource is assumed to be constrained. For a closed-loop system obtained by applying a linearizing feedback, the problem of construction of an estimate of the attraction domain of zero solution is studied. A method for constructing an ellipsoi...
Book
GPS Satellite Surveying is the classic text on the subject, providing the most comprehensive coverage of global navigation satellite systems applications for surveying. Fully updated and expanded to reflect the field's latest developments, this new edition contains new information on GNSS antennas, Precise Point Positioning, Real-time Relative Posi...
Chapter
Real-time kinematics (RTK) is a high-precision positioning technique that uses carrier phase and pseudorange measurements in real time. Ultra high frequency (UHF), cellular Global System for Mobile Communications (GSM), Long Term Evolution (LTE), WiFi, or Internet channels can be used for data transmission. The RTK kinematic processing solutions be...
Chapter
In many applications of least-squares adjustments the measurements are taken sequentially at discrete epochs in time. Five arrangements are addressed in this chapter: The first case deals with estimation of static parameters. The second refers to the mixed problem of estimating both static and arbitrary varying parameters. The third case introduces...
Chapter
New global navigation satellite system (GNSS) positioning and timing techniques continues to be developed and refined. This chapter first summarizes undifferenced pseudorange and carrier phase functions between a single station and single satellite. It then addresses operational details such as satellite clock corrections, timing group delay, and i...
Chapter
Geodesy is the theoretical and practical framework for utilizing global navigation satellite system (GNSS) vector observations and classical terrestrial observations such as angles and distances. The 3D geodetic model plays a pivotal role in this chapter, followed by the more historical 2D ellipsoidal model, and, last but not least, the popular 3D...
Chapter
The first satellite system presented in this chapter is the Global Positioning System (GPS). Next, the chapter reviews the status of the signal transmissions as of the year 2014, including signal structure and navigation message. Then, the Global'naya Navigatsionnaya Sputnikovaya Sistema (GLONASS) system is discussed with emphasis on the broadcast...
Chapter
Half-Title Page Title Page Copyright Page Table of Contents Preface Acknowledgments Abbreviations
Chapter
This chapter discusses plane and spherical electromagnetic waves of different types of polarization and introduces widely used reference sources of radiation, a Hertzian and a half-wave dipole. It explores antenna directivity and gain. Discussions of antenna phase center, phase center variations, and antenna calibrations are provided. The chapter a...
Chapter
The impact of the atmosphere on Global Navigation Satellite System (GNSS) observations is the focus of this chapter. The chapter begins with a general overview of the troposphere and ionosphere as it relates to GPS satellite surveying, and introduces the general form of the index of refraction. It addresses tropospheric refraction starting with the...
Chapter
The objectivity of least-squares quality control is especially useful in surveying when depositing or exchanging observations or verifying the internal accuracy of a survey. This chapter contains compact but complete derivations of least-squares algorithms. First, the statistical nature of measurements is analyzed, followed by a discussion of stoch...
Conference Paper
Full-text available
In this paper, we present a fast algorithm of time synchronization between User Equipment (UE) and Base Station (BS) which is suitable for Long Term Evolution (LTE) Random Access Channel (RACH). The algorithm reduces the complexity more than 1.5 times. Further, if the SNR is above a threshold, the algorithm allows to extremely reduce the complexity...
Conference Paper
Full-text available
In this paper we establish a connection between the problem of cycle slips detection and isolation and recently developed approach to decoding and error correction via linear programming in the compressive sensing framework, [1,5,6]. New efficient algorithm, based on linear programming or convex optimization is proposed. Experimental results analys...
Patent
Full-text available
The generation of a planar trajectory for use by a vehicle in guiding its position is described. The trajectory is generated by identifying points representing the trajectory, fairing the identified points to generate a set of faired points, and computing a set of polynomial segments from the faired points. The segments form a curve representing th...
Article
This paper studies the following path planning problem for a robot. There is a given path avoiding obstacles. If existing obstacles change their location or new obstacles appear, the preplanned path must be appropriately deformed for all obstacles avoidance. We develop a solution approach based on the component-wise method of smoothing the path cur...
Article
Full-text available
For the problem of stabilizing motion of an n-dimensional nonholonomic wheeled system along a prescribed path, the concept of a canonical representation of the equations of motion is introduced. The latter is defined to be a representation that can easily be reduced to a linear system in stabilizable variables by means of an appropriate nonlinear f...
Conference Paper
Full-text available
In this paper, a new numerical method is pro-posed for fast signal detection in large scale MIMO systems. Semidefnite relaxation (SDR) approach is utilized. The SDR problem is further reduced to the sequential linear programming by adding new form of cutting planes and column generation method. Bit error rate (BER) performance results conclude the...
Conference Paper
Full-text available
BIOGRAPHY Lev Rapoport, received the M.Sc. degree in 1976 from the radio-technical department of the Ural Polytechnic Institute, Sverdlovsk, and the PhD degree in 1982 in automatic control from the Institute of System Analysis of the Russian Academy of Science, Moscow. In 1995 he received the DrSc degree in automatic control from the Institute of C...
Article
Path planning problem arises in many practically important fields for different robots, including wheeled and space ones. The following motion planning problem for a robot is considered. Suppose that there is a precomputed collision-free path, but, in the course of time, there may appear new obstacles (or old ones may change their positions) that p...
Conference Paper
Full-text available
In this paper the extremum periodic trajectory of the two-dimensional selector-linear differential inclusion (SLDI) is used to estimate boundary of the invariant set of the nonlinear time-varying system arising in the stability analysis of the wheeled robot control. The motion is supposed to be planar without a lateral slippage. The control goal is...
Article
For the problem of control of the plane motion of a wheeled robot the estimate of the attraction domain is set up, which ensures the prescribed exponential speed of asymptotic stability and the absence of overcontrol. This statement of the problem is the generalization of the problems “on the attraction domain,” “on overcontrol,” and “on monotone d...
Conference Paper
Extremum properties of the two-dimensional linear time-varying (LTV) system are used in this paper to estimate boundary of the attraction domain in the problem of the wheeled robot control. The motion is supposed to be planar without a lateral slippage. The control goal is to drive the target point of the robot platform to the specified trajectory...
Article
Full-text available
A control synthesis problem for a wheeled robot moving on uneven terrain is studied. The terrain is assumed to be described by a sufficiently smooth function that does not vary too much at distances of the order of the platform size, which makes it possible to employ a planar robot model. The terrain model is not a priori known, and the information...
Article
Two systems are described in this work. The first system is based on four dual-band GNSS (L1+L2, GPS/GLONASS) receiver boards. The second system consists of a single dual-band GNSS receiver and an INS block. Application of the integrated system in control of wheeled robots is considered. The control is the turning angle of the front wheels. The con...
Article
Full-text available
The synthesis control problem for the plane motion of a wheeled robot is studied. The goal of the control is to bring the robot to an assigned curvilinear trajectory and to stabilize its motion along it in the presence of phase and control constraints. For a synthesized control law, invariant ellipsoids—quadratic approximations of the attraction do...
Conference Paper
Full-text available
A stabilization problem for a wheeled robot following a curvilinear target path is studied. In [1], a method for constructing invariant ellipsoids—quadratic approximations of the attraction domains for the target trajectory under a given control law—was developed. A basic result of that study is a theorem by means of which construction of the invar...
Article
Full-text available
A control synthesis problem for planar motion of a wheeled robot with regard to the steering gear dynamics is considered. The control goal is to bring the robot to a given curvilinear path and to stabilize its motion along the path. The trajectory is assumed to be an arbitrary parameterized smooth curve satisfying some additional curvature constrai...
Conference Paper
ABSTRACT: Considered is the control synthesis problem for planar motion of a wheeled robot. The mathematical model of the robot is based on kinematic relationships between the velocity of a given point of a robot platform, referred to as the target point, orientation of the platform, and control. It is supposed that all four wheels move without a l...
Article
Consideration was given to the problem of controlling the planar motion of a wheeled robot with the driving rear wheels and forewheels intended for chassis rotation. The aim of control is to drive the goal point to the prescribed trajectory and stabilize the motion along it. The trajectory consists of segments of straight lines and circles. The for...
Article
Full-text available
A path planning problem for a wheeled robot is considered. The problem consists in constructing a trajectory that approximates a given ordered sequence of points on the plane and satisfies certain smoothness requirements and curvature constraints. Such a problem arises, for example, when it is required to follow in an automated mode a path stored a...
Article
The problem of controlling the wheeled robot was considered. In the robot model used, the current curvature of the trajectory of the objective point which is related by simple algebraic expressions with the angle of rotation of the front wheels was taken as the control parameter. Boundedness of the angle of rotation of the robot front wheels impose...
Article
The problem of synthesizing a law for the control of the plane motion of a wheeled robot is investigated. The rear wheels are the drive wheels and the front wheels are responsible for the turning of the platform. The aim of the control is to steer a target point to a specified trajectory and to stabilize the motion along it. The trajectory is assum...
Conference Paper
Full-text available
The paper is concerned with path planning for mobile robots. Specifically, the discussion is related to the following problem: Given an ordered sequence of points on the plane, construct a path that fits these points and satisfies certain smoothness requirements. These requirements may be different in different problems and imply basically that the...
Conference Paper
Full-text available
BIOGRAPHY Lev B. Rapoport received an MSEE degree from the radiotechnical department of the Ural Polytechnic Institute, Sverdlovsk, in 1976, a PhD degree in Automatic Control from the Institute of System Analysis, Moscow, in 1982, and a DrSc degree in Automatic Control from the Institute of Control Sciences, Moscow, in 1995, where he serves as a he...
Article
Considered is the control design problem for planar motion of a wheeled robot. The mathematical model of the robot accounts for kinematic relationships between the velocity of a given point of chassis referred to as the reference point, orientation of the chassis, and control. Among the kinematic relations is the requirement that each of the four w...
Conference Paper
Full-text available
is positive denite. Well known is that if m 2 then S-procedure gives only sucien t conditions for positive deniteness of the quadratic form q(x) under constraints pi(x) 0; i = 1; : : : ; m. Necessity takes place only for m = 1. This property is called "lossness" of the S-procedure for several constraints. Using only sucien t conditions leads to add...
Article
Consideration was given to a generalization of the so-called S-procedure in the problem of sign-definiteness of the quadratic form under quadratic constraints. Application of the algebraic criterion obtained to analysis of the multidimensional control system was discussed. The results were formulated in terms of solvability of the linear matrix ine...
Article
Consideration was given to a generalization of the so-called S-procedure in the problem of sign-definiteness of the quadratic form under quadratic constraints. Application of the algebraic criterion obtained to analysis of the multidimensional control system was discussed. The results were formulated in terms of solvability of the linear matrix ine...
Conference Paper
Full-text available
The real time kinematic system for precise attitude determination on the based on carrier phases from four dual band GPS Half-Eurocard GD receivers [1] is considered in the paper. The system is based on the general purpose real time kinematic engine [2] and on the attitude determination engine. The last one estimates the rotation matrix using...
Conference Paper
Full-text available
The real time kinematic system for precise attitude determination on the based on carrier phases from four dual band GPS Half-Eurocard GD receivers is considered in the paper. The system is based on the general purpose real time kinematic engine. It includes carrier phase differential ambiguity filter, on-the-fly ambiguity resolution, position...
Conference Paper
Full-text available
For multivariable Lur'e systems which are not stable “in whole” the problem of estimating of the attraction domain is considered. This problem has received much attention in the literature. The state variable method as well as the frequency domain method were used. In the both cases the problem has been treated by Lur'e-Postnikov Lyapunov functions...
Conference Paper
Full-text available
The real time kinematic system for precise positioning and attitude determination is described in the paper. Architecture, numerical scheme, and experimental results are described.
Article
Full-text available
A parametric class of quadratic Lyapunov functions is proposed for robust stability problem. The right hand side matrix is supposed to belong to the matrix polytope. New sufficient conditions are proposed which are less conservative then those, obtained by using so-called S-procedure.
Conference Paper
Full-text available
The paper deals with the problem of precise carrier phase processing and ambiguity resolution for combined GPS / GLONASS satellite constellation
Article
For analyzing Lur'e systems consisting of linear time-invariant SISO plant and sector-bounded time-invariant nonlinear feedback the Popov criterion is traditionally used (M.A. and F.R., 1964). The multivariable extensions of Popov criterion use so called S-procedure (V.A., 1977; S. et al., 1964) to obtain (only) sufficient conditions of sign defini...
Article
Full-text available
New constructive criteria of asymptotic stability of selector-linear differential inclusions are established. The well-known absolute stability problem is also considered as a particular case of the above problem. Asymptotically stable inclusions are very similar in properties to linear stable time-invariant systems. This similarity concerns the wi...
Conference Paper
Full-text available
The problem under consideration is a robust stability of uncertain time-varying systems. There are various approaches to this problem. Most of them lead to sufficient conditions only. This paper contains some results concerning necessary and sufficient conditions. The main idea is the relation between the stability property and an existence (absenc...
Article
Full-text available
The problem of absolute stability of nonlinear nonstationary control systems is considered under sector constraints on nonlinearity. The size of the sector of absolute stability is assumed to be less than that of Hurwitz stability sector. It is proved that the convex invariant function that exists on the boundary of the sector of absolute stability...
Article
Existence of non-smooth Lyapunov functions is proved. They appear on the boundary of the absolute stability region
Article
It is established that in third-order systems, for a boundary value of the parameter k, defining the variation sector of the nonlinear characteristic in the absolute stability problem, there occurs antiperiodic motions having two switchings of the control over a half- period. A similar result has been established in 1971 for second-order systems On...
Article
The problem of the stability of the equilibrium of a mechanical system constrained by single-sided constraints is considered. It is assumed that in the equilibrium state the constraints are realized, but there are no reactions. It is shown that the conditions for the equilibrium of such systems to be stable can be obtained by an analysis of the sig...
Article
The analysis of stability of nonlinear nonstationary systems with arbitrary order is given. The authors establish that near the boundary value of the parameter which defines the domain of varying of nonlinearity in the problem of absolute stability in the system with arbitrary order and invariant cone the periodic motions are existed. The existence...
Article
It is established that periodic motions occur for a boundary value of the parameter k determining a sector of change of nonlinearity in the problem of absolute stability in third order systems. An analogous result was established in 1971 for second order systems. Its extension is based on an existence theorem for an invariant function of the second...
Article
The first author [ibid. 1971, 1-11 (1971; Zbl 0228.93017)] and the second author [ibid. 51, No. 10,1368-1375 (1990; Zbl 0735.93039)] established that periodic motions occur for a boundary value of the parameter k which defines a sector of change of nonlinearities in the problem of absolute stability in second and third order systems. The use of the...
Article
Convex invariant functions exist on the boundary of the absolute stability region
Article
A technology has been developed for processing wastes from the grinding of alloy steels so as to permit their subsequent refining. The technology includes concentration of the wastes and their thermal briquetting. To remove oil from sludge wastes, a process was developed involving vacuum drying at temperatures not exceeding the degradation point of...
Article
New frequency criterion for absolute stability was obtained. It generalizes the Popov criterion for multidimensional case
Article
The problem of sign definiteness of a quadratic form under quadratic constraints is considered. Necessary and sufficient conditions for this algebraic problems are obtained for a particular cases. Results are applied to the absolute stability problem.
Article
Necessary and sufficient conditions of existence of Lurie-Postnikov Lyapunov Functions were obtained. Only sufficient conditions were known prior this work
Article
The use of the second Lyapunov method in many problems in the theory of stability of motion leads to the problem of sign definiteness of a quadratic form whose variables are defined in a convex polyhedral cone C ⊂Rn. A method of obtaining the necessary and sufficient conditions is given for this problem. The conditions imposed on the elements of th...
Article
Full-text available
JPS where he researches in the area of signal processing for receivers of direct spread spectrum signals. Alexander Khvalkov is currently a Software Ingineer at JPS where he works on satellite navigation problem. Lev Rapoport received his DrSc degree in Automatic Control in 1995 from the Institute of Control Sciences, where he served as a leading r...

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Projects (2)
Project
The project goal is to formalize the situation of stability loss and diagnose it at an early stage of autonomous operation. While ongoing changes in the environment can bring the wheeled robot out of stable movement, it is necessary to construct of attraction domains and maintain predictable robot behavior.
Archived project
The Permanent Scientific Seminar (Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, ISC RAS, Moscow, Russia), - last prolongation (April 2020) - URL: [ https://www.ipu.ru/en/node/57010 ] // - and old (archival) - URL: [ http://www.ipu.ru/smart (in Russian) ] /// The discussion continues (in the framework of a new thematic area) - URL: [ https://www.researchgate.net/project/Workshop-Maturity-of-artificial-intelligence-system-integration-and-management-problems-Moscow-Russia ]. Lab: collaboration in Virtual Lab's