# Optimal control of delay systems with differential and algebraic dynamic constraints

Boris S. Mordukhovich; Lianwen Wang

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 11, Issue: 2, page 285-309
- ISSN: 1292-8119

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topMordukhovich, Boris S., and Wang, Lianwen. "Optimal control of delay systems with differential and algebraic dynamic constraints." ESAIM: Control, Optimisation and Calculus of Variations 11.2 (2010): 285-309. <http://eudml.org/doc/90766>.

@article{Mordukhovich2010,

abstract = {
This paper concerns constrained dynamic optimization problems
governed by delay control systems whose dynamic constraints are described by both
delay-differential inclusions and linear algebraic equations. This is a new class of
optimal control systems that, on one hand, may be treated as a specific type of
variational problems for neutral functional-differential inclusions while, on the other
hand, is related to a special class of differential-algebraic systems with a general
delay-differential inclusion and a linear constraint link between “slow” and “fast”
variables. We pursue a twofold goal: to study variational stability for this class of
control systems with respect to discrete approximations and to derive necessary
optimality conditions for both delayed differential-algebraic systems under consideration
and their finite-difference counterparts using modern tools of variational analysis and
generalized differentiation. The authors are not familiar with any results in these
directions for such systems even in the delay-free case. In the first part of the paper
we establish the value convergence of discrete approximations as well as the strong
convergence of optimal arcs in the classical Sobolev space W-1,2. Then using discrete
approximations as a vehicle, we derive necessary optimality conditions for the initial
continuous-time systems in both Euler-Lagrange and Hamiltonian forms via basic
generalized differential constructions of variational analysis.
},

author = {Mordukhovich, Boris S., Wang, Lianwen},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Optimal control; variational analysis; functional-differential inclusions
of neutral type; differential and algebraic dynamic constraints; discrete approximations;
generalized differentiation; necessary optimality conditions.; optimal control; functional-differential inclusions of neutral type; generalized differentiation; necessary optimality conditions},

language = {eng},

month = {3},

number = {2},

pages = {285-309},

publisher = {EDP Sciences},

title = {Optimal control of delay systems with differential and algebraic dynamic constraints},

url = {http://eudml.org/doc/90766},

volume = {11},

year = {2010},

}

TY - JOUR

AU - Mordukhovich, Boris S.

AU - Wang, Lianwen

TI - Optimal control of delay systems with differential and algebraic dynamic constraints

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 11

IS - 2

SP - 285

EP - 309

AB -
This paper concerns constrained dynamic optimization problems
governed by delay control systems whose dynamic constraints are described by both
delay-differential inclusions and linear algebraic equations. This is a new class of
optimal control systems that, on one hand, may be treated as a specific type of
variational problems for neutral functional-differential inclusions while, on the other
hand, is related to a special class of differential-algebraic systems with a general
delay-differential inclusion and a linear constraint link between “slow” and “fast”
variables. We pursue a twofold goal: to study variational stability for this class of
control systems with respect to discrete approximations and to derive necessary
optimality conditions for both delayed differential-algebraic systems under consideration
and their finite-difference counterparts using modern tools of variational analysis and
generalized differentiation. The authors are not familiar with any results in these
directions for such systems even in the delay-free case. In the first part of the paper
we establish the value convergence of discrete approximations as well as the strong
convergence of optimal arcs in the classical Sobolev space W-1,2. Then using discrete
approximations as a vehicle, we derive necessary optimality conditions for the initial
continuous-time systems in both Euler-Lagrange and Hamiltonian forms via basic
generalized differential constructions of variational analysis.

LA - eng

KW - Optimal control; variational analysis; functional-differential inclusions
of neutral type; differential and algebraic dynamic constraints; discrete approximations;
generalized differentiation; necessary optimality conditions.; optimal control; functional-differential inclusions of neutral type; generalized differentiation; necessary optimality conditions

UR - http://eudml.org/doc/90766

ER -

## References

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