Stochastic optimal control
Stochastic optimal control is a branch of mathematics that deals with finding the best control strategy for a system that is subject to random or probabilistic disturbances. In contrast to deterministic optimal control, the behavior of the system in stochastic optimal control is not fully determined by the initial conditions and the control inputs, but also by the random variations in the system. The term "stochastic" refers to the presence of random or probabilistic elements in the system, which may arise from external factors, measurement errors, or internal fluctuations. The term "optimal" refers to the goal of finding the best control strategy that maximizes or minimizes some performance metric, such as expected value or probability of a certain outcome, in the presence of probabilistic constraints. The process of solving a stochastic optimal control problem involves formulating the problem as a stochastic optimization problem. The solution of this problem provides the optimal control policy that achieves the desired objective, while accounting for the random variations in the system and satisfying the constraints. This solution may be obtained through analytical or numerical methods.