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 -