Smooth optimal synthesis for infinite horizon variational problems

Smooth Optimal Synthesis for Infinite Horizon Variational Problems

We study Hamiltonian systems which generate extremal flows of regular variational problems on smooth manifolds and demonstrate that negativity of the generalized curvature of such a system implies the existence of a global smooth optimal synthesis for the infinite horizon problem. We also show that in the Euclidean case negativity of the generalized curvature is a consequence of the convexity o...

Well-posed Infinite Horizon Variational Problems

We give an effective sufficient condition for a variational problem with infinite horizon on a Riemannian manifold M to admit a smooth optimal synthesis, i. e. a smooth dynamical system on M whose positive semi-trajectories are solutions to the problem. To realize the synthesis we construct a well-projected to M invariant Lagrange submanifold of the extremals’ flow in the cotangent bundle T ∗M ...

General necessary conditions for infinite horizon fractional variational problems

We consider infinite horizon fractional variational problems, where the fractional derivative is defined in the sense of Caputo. Necessary optimality conditions for higher-order variational problems and optimal control problems are obtained. Transversality conditions are obtained in the case state functions are free at the initial time.

One dimensional infinite-horizon variational problems arising in viscoelasticity

Gauss Pseudospectral Method for Solving Infinite-Horizon Optimal Control Problems

The previously developed Gauss pseudospectral method is extended to the case of nonlinear infinite-horizon optimal control problems. First, the semi-infinite domain t ∈ [0,+∞) is transformed to the domain τ = [−1,+1). The first-order optimality conditions of NLP obtained from the pseudospectral discretization are then presented. These optimality conditions are related to the KKT multipliers of ...