What is the theory of optimal control?
The theory of optimal control is largely used in science and engineering. It is a technique of mathematical optimization, which is commonly used in creating control policies. The Lion Pontryagin, along with his team in the former Soviet Union and American Richard Bellman, are mostly responsible for optimal control theory. The general aim of the theory is to use different methods of analysis to determine the parameters of the system by performing processes of trial and error.
The theory of optimal control is useful when trying to solve problems with optimizing continuous time. The theory solves the problem by determining the control law for the hypothetical system to achieve the level of optimality. Optimal control consists of a set of different equations that describe the paths of variables that increase the cost function to a minimum. Function costs are essentially a function of variables related to the state and control. The theory of optimal control uses maximum at pontryaginnciple that generally states that one can solve the Optim problemAlization P using the Hamilton function H for one period, which is a necessary condition. The theory can also be derived from the Hamilton-Jacobi-Bellman equation.
In order to help one understand the optimal control theory, the example of "driving through a car through hilly roads" is commonly used. Imagine traveling in a car on a rough road in a straight line. The theory can determine how one should speed up to minimize the absolute time of travel. In this case, the "system" consists of a vehicle and a rocky road and the optimality criteria is to minimize travel time. It is known that these problems include restrictions (eg fuel limits, speed limits). Another question may be to find a way to optimize its fuel consumption while it is obliged to complete the Cekurz Rtain within a given time limit.
Another example of the use of optimal management theory is price solutioncost or shadow. It consists of the limit value of the expansion of the state variable. After solving it, the optimum control value may be a differential equation conditional on the state. It is common for this strategy to solve for regions that describe optimal control and separate the actual choice values over time.