AN EIGENVALUE APPROACH TO INFINITE-HORIZON OPTIMAL CONTROL

An Eigenvalue Approach to Infinite-horizon Optimal Control

A method for finding optimal control policies for first order state-constrained, stochastic dynamic systems in continuous time is presented. The method relies on solution of the Hamilton-Jacobi-Bellman equation, which includes a diffusion term related to the stochastic disturbance in the model. A variable transformation is applied that turns the infinite-horizon optimal control problem into a l...

Infinite Horizon Sparse Optimal Control

A class of infinite horizon optimal control problems involving Lp-type cost functionals with 0 < p ≤ 1 is discussed. The existence of optimal controls is studied for both the convex case with p = 1 and the nonconvex case with 0 < p < 1, and the sparsity structure of the optimal controls promoted by the Lp-type penalties is analyzed. A dynamic programming approach is proposed to numerically appr...

Optimal control in infinite horizon problems : a Sobolev space approach

In this paper, we make use of the Sobolev space W 1,1 (R+, Rn) to derive at once the Pontryagin conditions for the standard optimal growth model in continuous time, including a necessary and sufficient transversality condition. An application to the Ramsey model is given. We use an order ideal argument to solve the problem inherent to the fact that L1 spaces have natural positive cones with no ...

An Infinite Horizon Optimal Control Problem for Some Switching Systems

Optimal Control of Nonlinear Uncertain Systems over an Infinite Horizon via Finite-Horizon Approximations

It is well-known that the Hamilton-Jacobi-Isaacs (HJI) equation associated with a nonlinear H-optimal control problem on an infinite-time horizon generally admits nonunique, and in fact infinitely many, viscosity solutions. This makes it difficult to pick the relevant viscosity solution for the problem at hand, particularly when it is computed numerically. For the finitehorizon version of the p...