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 -