Deterministic optimal control
Deterministic optimal control is a branch of mathematics that deals with finding the best control strategy for a system described by a set of differential equations subject to constraints. In other words, it involves determining the control inputs that will optimize the behavior of a system, given a set of objectives and constraints. The term "deterministic" refers to the fact that the system's behavior is fully determined by the initial conditions and the control inputs, with no random or probabilistic elements. The term "optimal" refers to the goal of finding the best control strategy, which is typically defined in terms of minimizing or maximizing some performance metric, such as energy consumption, time to reach a desired state, or cost. The process of solving a deterministic optimal control problem involves formulating the problem as a mathematical optimization problem, typically in the form of a nonlinear programming problem. The solution of this problem provides the optimal control inputs that achieve the desired objective while satisfying the given constraints. This solution may be obtained through analytical or numerical methods.