Partially observed optimal control of local and remote controllers

The article investigates a networked optimal control problem with one remote controller and N$$ N $$ local controllers, where each local controller partially observes the local state and sends the observed information to remote controller through an unreliable channel and yet the channels from remote controller to local controllers are perfect. The objective of all the controllers is to cooperate to minimize a common cost function. In order to overcome the difficulties caused by partial observation of state, sufficient statistic of historical data is firstly investigated for a nonlinear non-Gaussian partial observation model, which takes the same role as that of state in the full observation model. Then, a dynamic programming framework is given for solving the optimal control problem based on the sufficient statistic and common information approach. Furthermore, the explicit closed-form solution is obtained for a linear-quadratic-Gaussian optimal control problem. Finally, a numerical example is given to show the effectiveness of the obtained results of this article.