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Control of nonlinear underactuated systems
Author(s) -
Auckly David,
Kapitanski Lev,
White Warren
Publication year - 2000
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(200003)53:3<354::aid-cpa3>3.0.co;2-u
Subject(s) - underactuation , control theory (sociology) , nonlinear system , lyapunov function , mathematics , inverted pendulum , control (management) , law , construct (python library) , computer science , artificial intelligence , physics , political science , programming language , quantum mechanics
In this paper we introduce a new method to design control laws for nonlinear, underactuated systems. Our method produces an infinite‐dimensional family of control laws, whereas most control techniques only produce a finite‐dimensional family. These control laws each come with a natural Lyapunov function. The inverted pendulum cart is used as an example. In addition, we construct an abstract system that is open‐loop unstable and cannot be stabilized using any linear control law and demonstrate that our method produces a stabilizing control law. © 2000 John Wiley & Sons, Inc.