Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 354-369 |
| Number of pages | 16 |
| Journal | Communications on Pure and Applied Mathematics |
| Volume | 53 |
| Issue number | 3 |
| State | Published - Mar 2000 |
| Externally published | Yes |
Fingerprint
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
Control of nonlinear underactuated systems. / Auckly, David; Kapitanski, Lev; White, Warren.
In: Communications on Pure and Applied Mathematics, Vol. 53, No. 3, 03.2000, p. 354-369.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Control of nonlinear underactuated systems
AU - Auckly, David
AU - Kapitanski, Lev
AU - White, Warren
PY - 2000/3
Y1 - 2000/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0034387896&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0034387896&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0034387896
VL - 53
SP - 354
EP - 369
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
SN - 0010-3640
IS - 3
ER -