Details
| Original language | English |
|---|---|
| Pages (from-to) | 440-467 |
| Number of pages | 28 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 19 |
| Issue number | 2 |
| Publication status | Published - Mar 1998 |
| Externally published | Yes |
Abstract
This paper presents a new approach to the numerical solution of boundary value problems for higher-index differential-algebraic equations (DAEs). Invariants known for the original DAE as well as invariants of the reduced index 1 formulation are exploited to stabilize initial value problem (IVP) integration, derivative generation, and nonlinear and linear systems solution of an enhanced multiple shooting method. Extensions to collocation are given. Applications are presented for two important problem classes: parameter estimation in multibody systems given in descriptor form, and singular and state-constrained optimal control problems. In particular, generalizations of the "internal numerical differentiation" technique to DAE with invariants and a new multistage least squares decomposition technique for DAE boundary value problems are developed, which are implemented in the multiple shooting code PARFIT and in the collocation code COLFIT. Further, a method is described which minimizes the number of necessary directional derivatives in the presence of multipoint conditions and invariants. As numerical applications, a parameter identification problem for a slider crank mechanism and a periodic cruise optimal control problem for a motor glider aircraft are treated.
Keywords
- Boundary value problems, Descriptor form for multibody systems, Higher-index differential-algebraic equations, Invariants, Optimal control, Parameter identification, Singular control, State constraints
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: SIAM Journal on Scientific Computing, Vol. 19, No. 2, 03.1998, p. 440-467.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Exploiting invariants in the numerical solution of multipoint boundary value problems for DAEs
AU - Schulz, Volker H.
AU - Bock, Hans Georg
AU - Steinbach, Marc C.
PY - 1998/3
Y1 - 1998/3
N2 - This paper presents a new approach to the numerical solution of boundary value problems for higher-index differential-algebraic equations (DAEs). Invariants known for the original DAE as well as invariants of the reduced index 1 formulation are exploited to stabilize initial value problem (IVP) integration, derivative generation, and nonlinear and linear systems solution of an enhanced multiple shooting method. Extensions to collocation are given. Applications are presented for two important problem classes: parameter estimation in multibody systems given in descriptor form, and singular and state-constrained optimal control problems. In particular, generalizations of the "internal numerical differentiation" technique to DAE with invariants and a new multistage least squares decomposition technique for DAE boundary value problems are developed, which are implemented in the multiple shooting code PARFIT and in the collocation code COLFIT. Further, a method is described which minimizes the number of necessary directional derivatives in the presence of multipoint conditions and invariants. As numerical applications, a parameter identification problem for a slider crank mechanism and a periodic cruise optimal control problem for a motor glider aircraft are treated.
AB - This paper presents a new approach to the numerical solution of boundary value problems for higher-index differential-algebraic equations (DAEs). Invariants known for the original DAE as well as invariants of the reduced index 1 formulation are exploited to stabilize initial value problem (IVP) integration, derivative generation, and nonlinear and linear systems solution of an enhanced multiple shooting method. Extensions to collocation are given. Applications are presented for two important problem classes: parameter estimation in multibody systems given in descriptor form, and singular and state-constrained optimal control problems. In particular, generalizations of the "internal numerical differentiation" technique to DAE with invariants and a new multistage least squares decomposition technique for DAE boundary value problems are developed, which are implemented in the multiple shooting code PARFIT and in the collocation code COLFIT. Further, a method is described which minimizes the number of necessary directional derivatives in the presence of multipoint conditions and invariants. As numerical applications, a parameter identification problem for a slider crank mechanism and a periodic cruise optimal control problem for a motor glider aircraft are treated.
KW - Boundary value problems
KW - Descriptor form for multibody systems
KW - Higher-index differential-algebraic equations
KW - Invariants
KW - Optimal control
KW - Parameter identification
KW - Singular control
KW - State constraints
UR - http://www.scopus.com/inward/record.url?scp=9144254129&partnerID=8YFLogxK
U2 - 10.1137/S1064827594261917
DO - 10.1137/S1064827594261917
M3 - Article
AN - SCOPUS:9144254129
VL - 19
SP - 440
EP - 467
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
SN - 1064-8275
IS - 2
ER -