OPTIMAL MULTI-MODES SWITCHING PROBLEM IN INFINITE HORIZON

Optimal Multi-Modes Switching Problem in Infinite Horizon

This paper studies the problem of the deterministic version of the Verification Theorem for the optimal m-states switching in infinite horizon under Markovian framework with arbitrary switching cost functions. The problem is formulated as an extended impulse control problem and solved by means of probabilistic tools such as the Snell envelop of processes and reflected backward stochastic differ...

An Infinite Horizon Optimal Control Problem for Some Switching Systems

A Finite Horizon Optimal Multiple Switching Problem

We consider the problem of optimal multiple switching in finite horizon, when the state of the system, including the switching costs, is a general adapted stochastic process. The problem is formulated as an extended impulse control problem and completely solved using probabilistic tools such as the Snell envelop of processes and reflected backward stochastic differential equations. Finally, whe...

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...

Stochastic Optimal Multi-Modes Switching with a Viscosity Solution Approach

We consider the problem of optimal multi-modes switching in finite horizon, when the state of the system, including the switching cost functions are arbitrary (gij(t, x) ≥ 0). We show existence of the optimal strategy, and give when the optimal strategy is finite via a verification theorem. Finally, when the state of the system is a markov process, we show that the vector of value functions of ...