NDLI: Periodic solution of the selector-linear differential inclusion and estimation of invariant regions in the wheeled robot control problem

Content Provider	IEEE Xplore Digital Library
Author	Rapoport, L.B.
Copyright Year	2010
Description	Author affiliation: Institute of Control Sciences RAS and Javad GNSS, Moscow, Russia (Rapoport, L.B.)
Abstract	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 to drive the target point of the robot plaform to the specified trajectory and to stabilize the motion along it. The trajectory consists of line segments and circular arcs. The current curvature of the trajectory of the target point is taken as control. The control must satisfy two-sided constraints. Given control law, the attraction domain estimation problem is considered. The attraction domain must be inscribed into the certain parallelepiped of the 'distance to the trajectory-orientation' phase space. Time-varying curvature of the target trajectory is considered as arbitrary varying function which takes values from the specified interval. The feedback linearization scheme is used for synthesis of the control low. The 'saturation function' is then used to take into account control constraints. The closed loop system takes form of the nonlinear system with parametric disturbances. The absolute stability approach is explored for stability analysis. Some nonlinearities take values from the interval. Other nonlinearities satisfy sector constraints. Along with the nonlinear time-varying system the uncertain linear time varying system is considered. Every solution of the nonlinear system is also solution of the time varying system for certain set of time-varying disturbances. To estimate the attraction domain of the nonlinear closed loop system, the Lyapunov function for SLDI is constructed. A convex invariant function is known to exist at the boundary of the absolute stability of SLDI. The extremum trajectory, corresponding to the boundary of the absolute stability in the second order case belongs to the level set of the invariant function and is the periodic solution. The periodic solution has finite number of switches on the period. It circumscribes the boundary of the attraction domain estimate. The illustrative example is given.
Starting Page	000055
Ending Page	000059
File Size	268055
Page Count	5
File Format	PDF
ISBN	9781424486816
e-ISBN	9781424486823
DOI	10.1109/EEEI.2010.5661948
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-11-17
Publisher Place	Israel
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Trajectory Stability analysis Numerical stability Motion segmentation Time varying systems Asymptotic stability Lyapunov method
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Control design method for time-delay linear differential inclusion systems

Necessary and sufficient numerical conditions for asymptotic stability of linear time-varying systems

Finite-time partial stability theory and fractional Lyapunov differential inequalities

Local approximations and stability: a trajectory-based approach

Semi-global Practical Stability of Periodic Time-Varying Systems via Averaging: A Lyapunov Approach

Stability and stabilization of discrete-time linear systems with nearly-periodic impulses

Current-estimation-based iterative algorithms for solving periodic Lyapunov matrix equations

UGAS of nonlinear time-varying systems: A /spl delta/-persistency of excitation approach

Stability and stabilization for discrete systems with time-varying delays based on the average dwell-time method

Periodic solution of the selector-linear differential inclusion and estimation of invariant regions in the wheeled robot control problem

Similar Documents

Control design method for time-delay linear differential inclusion systems

Necessary and sufficient numerical conditions for asymptotic stability of linear time-varying systems

Finite-time partial stability theory and fractional Lyapunov differential inequalities

Local approximations and stability: a trajectory-based approach

Semi-global Practical Stability of Periodic Time-Varying Systems via Averaging: A Lyapunov Approach

Stability and stabilization of discrete-time linear systems with nearly-periodic impulses

Current-estimation-based iterative algorithms for solving periodic Lyapunov matrix equations

UGAS of nonlinear time-varying systems: A /spl delta/-persistency of excitation approach

Stability and stabilization for discrete systems with time-varying delays based on the average dwell-time method

Periodic solution of the selector-linear differential inclusion and estimation of invariant regions in the wheeled robot control problem