A level-set approach for stochastic optimal control problems under controlled-loss constraints

We study a family of optimal control problems under a set of controlled-loss constraints holding at different deterministic dates. The characterization of the associated value function by a Hamilton-Jacobi-Bellman equation usually calls for additional strong assumptions on the dynamics of the processes involved and the set of constraints. To treat this problem in absence of those assumptions, we first convert it into a state-constrained stochastic target problem and then apply a level-set approach. With this approach, the state constraints can be managed through an exact penalization technique

A Level-Set Approach for Stochastic Optimal Control Problems under Controlled-Loss Constraints

We study a family of optimal control problems under a set of controlled- loss constraints holding at different deterministic dates. The characterization of the associated value function by a Hamilton-Jacobi-Bellman equation usually calls for strong assumptions on the dynamics of the processes involved and the set of constraints. To treat this problem in absence of those assumptions, we first convert it into a state-constrained stochastic target problem and then solve the latter by a level-set approach. With this approach, state constraints are managed through an exact penalization technique

Optimal management of pumped hydroelectric production with state constrained optimal control

We present a novel technique to solve the problem of managing optimally a pumped hydroelectric storage system. This technique relies on representing the system as a stochastic optimal control problem with state constraints, these latter corresponding to the finite volume of the reservoirs. Following the recent level-set approach presented in O. Bokanowski, A. Picarelli, H. Zidani, "State-constrained stochastic optimal control problems via reachability approach", SIAM J. Control and Optim. 54 (5) (2016) , we transform the original constrained problem in an auxiliary unconstrained one in augmented state and control spaces, obtained by introducing an exact penalization of the original state constraints. The latter problem is fully treatable by classical dynamic programming arguments

Multi-aircraft conflict detection and resolution based on probabilistic reach sets

In this brief, a novel scheme to multi-aircraft conflict detection and resolution is introduced. A key feature of the proposed scheme is that uncertainty affecting the aircraft future positions along some look-ahead prediction horizon is accounted for via a probabilistic reachability analysis approach. In particular, ellipsoidal probabilistic reach sets are determined by formulating a chance-constrained optimization problem and solving it via a simulation-based method called scenario approach. Conflict detection is then performed by verifying if the ellipsoidal reach sets of different aircraft intersect. If a conflict is detected, then the aircraft flight plans are redesigned by solving a second-order cone program resting on the approximation of the ellipsoidal reach sets with spheres with constant radius along the look-ahead horizon. A bisection procedure allows one to determine the minimum radius such that the ellipsoidal reach sets of different aircraft along the corresponding new flight plans do not intersect. Some numerical examples are presented to show the efficacy of the proposed scheme