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7:25 AM

WebP Image Test

In an optimal control problem,one adjusts controls in a dynamic system to achieve a goal. The underlying system can have a variety of types of equations such as ordinary differential equations, partial differential equations, discrete equations, stochastic differential equations or integro-difference equations.

We are considering only systems of ordinary differential equations.

In control of a single ordinary differential equation (ODE) we denote u (t) as the control and x (t) as the state. The state function, x (t), satisfies the ODE modeling scenario. The control affects the state ODE by

x’ (t)= g (t, x (t), u (t)),

Where   x’  denote the derivative with respect to time t. Both u (t) and x (t) affect the goal, which is called the objective functional. We seek to find an optimal control and corresponding state that achieve the maximum (or minimum) of our objective functional.
To understand the basic idea of optimal control and the terminology, consider the following example with very simple dynamics.



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4:27 PM

Test Post 7 Bullets, Block qoute & Headings

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4:21 PM

Test Post 6 With Heading Test

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4:12 PM

Test Post 5

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4:08 PM

Test Post 4

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3:51 PM

Test Post 3

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3:19 PM

Test Post 2

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