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Basic discrete control theory mostly studies systems which can be represented as $x_n=A(n)x_{n-1}+B(n)u_n$.

I wonder if optimal control of specific discrete systems of the type $x_n = A(n,u)\cdot x_{n-1}$ have been described in any paper?

Or maybe there is a control theory handbook where different systems and their presumed control are listed?

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If you are willing to consider the special case that $A(n,u)$ is linear in control $u$, then this becomes a bilinear control system (see for example, the book by David Elliott), for which optimal control results have appeared in literature.

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  • $\begingroup$ Thanks, this is the closest to my interest. Do you know any possible references for "bi-nonlinear" control? $\endgroup$ – homocomputeris Apr 15 '16 at 23:47
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    $\begingroup$ I do not know any such references. $\endgroup$ – Abhishek Halder Apr 16 '16 at 5:49

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