Choice of a control input to minimize an objective subject to differential equations for a state and constraints on the control, state or terminal time. Necessary conditions such as the Pontryagin maximum principle require regularity hypotheses and do not by themselves prove global optimality.
Optimal control refers to a mathematical and engineering discipline that deals with finding a control policy for a dynamic system to optimize a certain performance criterion. The goal is to determine the control inputs that will minimize (or maximize) a particular objective, which often involves the system's state over time. ### Key Concepts of Optimal Control: 1. **Dynamic Systems**: These are systems that evolve over time according to specific rules, often governed by differential or difference equations.
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