Abstract
We discuss matching control laws for underactuated systems. We previously showed that this class of matching control laws is completely characterized by a linear system of first order partial differential equations for one set of variables (λ) followed by a linear system of first order partial differential equations for the second set of variables (ĝ, V̂). Here we derive a new first order system of partial differential equations that encodes all compatibility conditions for the λ-equations. We give four examples illustrating different features of matching control laws, The last example is a system with two unactuated degrees of freedom that admits only basic solutions to the matching equations. There are systems with many matching control laws where only basic solutions are potentially useful. We introduce a rank condition indicating when this is likely to be the case.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1372-1388 |
| Number of pages | 17 |
| Journal | SIAM Journal on Control and Optimization |
| Volume | 41 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2003 |
| Externally published | Yes |
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Keywords
- λ-equations
- Matching control laws
- Nonlinear control
- Stabilization
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
- Control and Optimization
Cite this
On the λ-equations for matching control laws. / Auckly, David; Kapitanski, Lev.
In: SIAM Journal on Control and Optimization, Vol. 41, No. 5, 2003, p. 1372-1388.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On the λ-equations for matching control laws
AU - Auckly, David
AU - Kapitanski, Lev
PY - 2003
Y1 - 2003
N2 - We discuss matching control laws for underactuated systems. We previously showed that this class of matching control laws is completely characterized by a linear system of first order partial differential equations for one set of variables (λ) followed by a linear system of first order partial differential equations for the second set of variables (ĝ, V̂). Here we derive a new first order system of partial differential equations that encodes all compatibility conditions for the λ-equations. We give four examples illustrating different features of matching control laws, The last example is a system with two unactuated degrees of freedom that admits only basic solutions to the matching equations. There are systems with many matching control laws where only basic solutions are potentially useful. We introduce a rank condition indicating when this is likely to be the case.
AB - We discuss matching control laws for underactuated systems. We previously showed that this class of matching control laws is completely characterized by a linear system of first order partial differential equations for one set of variables (λ) followed by a linear system of first order partial differential equations for the second set of variables (ĝ, V̂). Here we derive a new first order system of partial differential equations that encodes all compatibility conditions for the λ-equations. We give four examples illustrating different features of matching control laws, The last example is a system with two unactuated degrees of freedom that admits only basic solutions to the matching equations. There are systems with many matching control laws where only basic solutions are potentially useful. We introduce a rank condition indicating when this is likely to be the case.
KW - λ-equations
KW - Matching control laws
KW - Nonlinear control
KW - Stabilization
UR - http://www.scopus.com/inward/record.url?scp=0141757433&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0141757433&partnerID=8YFLogxK
U2 - 10.1137/S0363012901393304
DO - 10.1137/S0363012901393304
M3 - Article
AN - SCOPUS:0141757433
VL - 41
SP - 1372
EP - 1388
JO - SIAM Journal on Control and Optimization
JF - SIAM Journal on Control and Optimization
SN - 0363-0129
IS - 5
ER -