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Unformatted text preview: m is to be solved many times; in each time, the value of u (i.e., a sample) is given, and
then the decision variable x is chosen. The mapping from u into the decision variable x(u) is called
the policy, since it gives the decision variable value for each value of u. When enough time and
computing hardware is available, we can simply solve the LP for each new value of u; this is an
optimal policy, which we denote x⋆ (u).
In some applications, however, the decision x(u) must be made very quickly, so solving the LP is
not an option. Instead we seek a suboptimal policy, which is aﬃne: xaﬀ (u) = x0 + Ku, where x0 is
called the nominal decision and K ∈ Rnp is called the feedback gain matrix. (Roughly speaking,
x0 is our guess of x before the value of u has been revealed; Ku is our modiﬁcation of this guess,
once we know u.) We determine the policy (i.e., suitable values for x0 and K ) ahead of time; we
can then evaluate the policy (that is, ﬁnd xaﬀ (u) given u) very quickly, by matrix multiplication
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.
- Fall '13
- The Aeneid