Research output: Contribution to journal › Article › peer-review
The Time-consistency problem in nonlinear dynamics. / Petrosjan, L.A.
In: Revista Brasileira de Ciencias Mecanicas/Journal of the Brazilian Society of Mechanical Sciences, No. 2, 1997, p. 291-303.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - The Time-consistency problem in nonlinear dynamics
AU - Petrosjan, L.A.
PY - 1997
Y1 - 1997
N2 - The nonlinear dynamic optimization problem (NDOP) ?(x0,[t0,T]) on the time interval [t0,T] from the initial state x0 is considered. If the NDOP is multicriterial or game-theoretic, there exists a rich variety of optimality principles each one consisting from a set of optimal decisions. Denote one such optimality principle in ?(x0,[t0,T]) by M(x0,[t0,T]). For a given optimal decision m? (x0,[t0,T]) ? M (x0,[t0,T]) let x? (t) be the corresponding optimal trajectory. Consider NDOP subproblems along x? (t)?(x?(t),[t, T]), t?,[t0,T]. Let M(x? (t), [t, T]) be the corresponding optimality principle. Denote by m? (x? (t), [t, T]) the trace of optimal decision m? (x0,[t0,T]) in subproblem ?(x?(t),[t, T]). The optimality principle is called time-consistent if for every m (x0,[t0,T]) ? M (x0,[t0,T]) the trace m? (x? (t), [t, T]) ? M (x? (t),[t,T]) Most of the classical optimality principles in NDOP ?(x0, [t0,T]) (as Shown in (Petrosjan, 1993; Petrosjan and Zenkevich, 1996)) are time inconsistent. The "agreeable solution
AB - The nonlinear dynamic optimization problem (NDOP) ?(x0,[t0,T]) on the time interval [t0,T] from the initial state x0 is considered. If the NDOP is multicriterial or game-theoretic, there exists a rich variety of optimality principles each one consisting from a set of optimal decisions. Denote one such optimality principle in ?(x0,[t0,T]) by M(x0,[t0,T]). For a given optimal decision m? (x0,[t0,T]) ? M (x0,[t0,T]) let x? (t) be the corresponding optimal trajectory. Consider NDOP subproblems along x? (t)?(x?(t),[t, T]), t?,[t0,T]. Let M(x? (t), [t, T]) be the corresponding optimality principle. Denote by m? (x? (t), [t, T]) the trace of optimal decision m? (x0,[t0,T]) in subproblem ?(x?(t),[t, T]). The optimality principle is called time-consistent if for every m (x0,[t0,T]) ? M (x0,[t0,T]) the trace m? (x? (t), [t, T]) ? M (x? (t),[t,T]) Most of the classical optimality principles in NDOP ?(x0, [t0,T]) (as Shown in (Petrosjan, 1993; Petrosjan and Zenkevich, 1996)) are time inconsistent. The "agreeable solution
M3 - Article
SP - 291
EP - 303
JO - Journal of the Brazilian Society of Mechanical Sciences and Engineering
JF - Journal of the Brazilian Society of Mechanical Sciences and Engineering
SN - 1678-5878
IS - 2
ER -
ID: 5027250