A Remarkable Property of the Dynamic Optimization Extremals∗
نویسنده
چکیده
We give conditions under which a function F (t, x, u, ψ0, ψ) satisfies the relation dF dt = ∂F ∂t + ∂F ∂x · ∂H ∂ψ − ∂F ∂ψ · ∂H ∂x along the Pontryagin extremals (x(·), u(·), ψ0, ψ(·)) of an optimal control problem, where H is the corresponding Hamiltonian. The relation generalizes the well known fact that the equality dH dt = ∂H ∂t holds along the extremals of the problem, and that in the autonomous case H ≡ constant. As applications of the new relation, methods for obtaining conserved quantities along the Pontryagin extremals and for characterizing problems possessing given constants of the motion are obtained.
منابع مشابه
A Note on the Descent Property Theorem for the Hybrid Conjugate Gradient Algorithm CCOMB Proposed by Andrei
In [1] (Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization J. Optimization. Theory Appl. 141 (2009) 249 - 264), an efficient hybrid conjugate gradient algorithm, the CCOMB algorithm is proposed for solving unconstrained optimization problems. However, the proof of Theorem 2.1 in [1] is incorrect due to an erroneous inequality which used to indicate the descent property for the s...
متن کاملOPTIMIZATION OF ENDURANCE TIME ACCELERATION FUNCTIONS FOR SEISMIC ASSESSMENT OF STRUCTURES
Numerical simulation of structural response is a challenging issue in earthquake engineering and there has been remarkable progress in this area in the last decade. Endurance Time (ET) method is a new response history based analysis procedure for seismic assessment and structural design in which structures are subjected to a gradually intensifying dynamic excitation and their seismic performanc...
متن کاملA New Hybrid Conjugate Gradient Method Based on Eigenvalue Analysis for Unconstrained Optimization Problems
In this paper, two extended three-term conjugate gradient methods based on the Liu-Storey ({tt LS}) conjugate gradient method are presented to solve unconstrained optimization problems. A remarkable property of the proposed methods is that the search direction always satisfies the sufficient descent condition independent of line search method, based on eigenvalue analysis. The globa...
متن کاملAutonomous Underwater Vehicles: Singular Extremals and Chattering
In this paper, we consider the time minimal problem for an Autonomous Underwater Vehicle. We investigate, on a simplified model, the existence of singular extremals and discuss their optimality status. Moreover, we prove that singular extremals corresponding to the angular acceleration are of order 2. We produce in this case a semicanonical form of our Hamiltonian system and we can conclude the...
متن کامل