# Questions tagged [optimal-control]

Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. (Def: http://en.m.wikipedia.org/wiki/Optimal_control)

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### How to solve these nonlinear ODEs numerically without enough boundary conditions? [closed]

\begin{aligned} x_1'(t) &= x_2(t)\\ x_2'(t) &= -0.1 \left(100\ \text{sgn}(p_2(t))-10 x_1(t) x_4(t)^2+50 x_2(t)+98 \sin (x_3(t))\right)\\ x_3'(t) &= x_4(t)\\ x_4'(t) &= -\frac{0.1 (1000\...
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### Is there any difference in result between quadratic programming VS linear programming?

Assume that we want to solve this equation: $$Ax \leq b$$ So we can either use Quadratic Programming: $$J_{max}: x^TQx + c^Tx$$ $$Ax \leq b$$ $$x \geq 0$$ Or Linear Programming: $$J_{max}: c^Tx$$ ...
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### Can optimal control be used to obtain a desired result?

I am pretty new to the theory and application of optimal control. However, I am curious as it is not mentioned in the textbook that I use. Is it possible to optimize $u(t)$ such that we can obtain a ...
115 views

### trade-off on control performance for system with imaginary conjugate poles

I'm writing a feedback controller for the following SIMO system, where I want to give as input reference position and velocity $r_{ref}$, $v_{ref}$. The errors on position and velocity will be ...
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### The error size of discrete approximation to a optimal control problem

I'm considering an optimal control problem of form $$M=\underset{p(k)\in [0,V]}{\max}\int_{k\in K} p(k)h(k)\ dk,$$ where $h(k)$ is a given function and $p(k)$ must be (weakly) decreasing. I know that ...