Infinite Horizon Optimal Control

First results of optimal control of average biogas production for the chemostat over an infinite horizon

“…As the cost is unbounded on a infinite horizon, we have to choose a concept of optimality (Carlson et al (1991)). The limiting averaged value appears to us the most natural choice in the present context of biotechnology where the process is expected to be operated on a very long duration and the performance expected from the practitioners is to maintain a high average value over time.…”

On the Existence of a Classical Optimal Solution and of an Almost Strongly Optimal Solution for an Infinite-Horizon Control Problem

“…Such conditions are restrictive and not always satisfied in real-life applications; cf. Gale's cake eating problem in [3] and [4]. It, therefore, seems reasonable (necessary) to consider another notion of optimality.…”

“…Here we use the method presented in [3]. It is based on the concept of the modified Lagrangian, and on a suitable version of the lower closure theorem for multifunctions defined over an unbounded domain.…”

“…We prove some versions of this theoremTheorem 6.1 and Theorem 6.2-for multifunctions in a general form, defined on the interval [0, ∞[. Such a theorem, with slightly different assumptions, has been stated in [3] without proof. The proofs of our lower closure theorems are based on some extensions of the classical Olech's theorem on the lower semicontinuity of an integral functional to the case of functions defined on an unbounded domain; see [7].…”

Allee Effect and Control of Lake System Invasion

“…General solution of this optimal control problem is complicated. However, it is known that for infinite horizon problems the solution must end at a steady state [12], which often is a fixed point [4]; that is for t → ∞ du/dt → 0, dµ/dt → 0, and hence u → u * , x → x * , s → s * . The controls x i and s i also tend to some constant values.…”