Optimal control on an infinite domain

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...

An Infinite Horizon Optimal Control Problem for Some Switching Systems

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...

On the Infinite-Horizon Optimal Control of Age-Structured Systems

The paper presents necessary optimality conditions of Pontryagin’s type for infinite-horizon optimal control problems for age-structured systems with stateand control-dependent boundary conditions. Despite the numerous applications of such problems in population dynamics and economics, a “complete” set of optimality conditions is missing in the existing literature, because it is problematic to ...

On Existence Results for Infinite Horizon Optimal Control Problems

Still at the beginning of the previous century the optimal control problems with infinite horizon became very important with regards to applications in economics and biology, where an infinite horizon seems to be a very natural phenomenon, (5), (3), (10). Since then these problems were treated by many authors and various necessary, sufficient as well as transversality conditions were obtained, ...