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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)

Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. Reference: Wikipedia.

The method is largely due to the work of Lev Pontryagin and Richard Bellman.

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Hamiltonian in control theory

In the wikipedia article Hamiltonian (control theory), I don't understand why $H(q,u,p,t)$ doesn't depend on $\dot{q}$. Can someone explain this to me?
roi_saumon
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Default LQR cost format

I have widely seen this format for cost $$ J(\boldsymbol{x},\boldsymbol{u}) = \boldsymbol{x}_f^T\boldsymbol{H}\boldsymbol{x}_f + \int_{t_0}^{t_f}{[\boldsymbol{x}^T\boldsymbol{Q}\boldsymbol{x} + \boldsymbol{u}^T\boldsymbol{R}\boldsymbol{u}]}dt $$ But…
griloHBG
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Find optimal control LQR

A system described by $$\frac{dx}{dt} = -x + u$$ is to be controlled to minimise $$J =\int{ 0.5(x^2+u^2)dt}$$ What limits should I use on the integral and how to proceed? $t$ should vary from $0$ to $1$. $P(t)$ should vary from $P(0)$ to $P(1)$.…
ShiS
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optimal control: how to build a good mathematical foundation

I am a PhD student in electrical engineering and need to work on Optimal control theory. Whenever I go through theorems, I see mathematical basics that I don't know (like optimization and theorems about hyper-planes and manifolds). Can you please…
Iman Shafikhani
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Extension of Pontryagin's principle

Is anyone aware of an extension of Pontryagin's principle where the cost (more precisely, the Langrangian) may depend on the derivative of the control? So, instead of $\int_{t_0}^{t_1} L(t,x,u) dt + K(x(t_1))$, the cost would be given by…
Roland
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