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intro - EE236A(Fall 2007-08 Lecture 1 Introduction and...

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EE236A (Fall 2007-08) Lecture 1 Introduction and overview linear programming example from optimal control example from combinatorial optimization history course topics software 1–1 Linear program (LP) minimize n summationdisplay j =1 c j x j subject to n summationdisplay j =1 a ij x j b i , i = 1 ,...,m n summationdisplay j =1 c ij x j = d i , i = 1 ,...,p variables: x j R problem data: the coefficients c j , a ij , b i , c ij , d i can be solved very efficiently (several 10,000 variables, constraints) widely available high-quality software extensive, useful theory (optimality conditions, sensitivity analysis, . . . ) Introduction and overview 1–2
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Example: open-loop control problem single-input/single-output system (with input u , output y ) y ( t ) = h 0 u ( t ) + h 1 u ( t - 1) + h 2 u ( t - 2) + h 3 u ( t - 3) + · · · output tracking problem: minimize deviation from desired output y des ( t ) max t =0 ,...,N | y ( t ) - y des ( t ) | subject to input amplitude and slew rate constraints: | u ( t ) | ≤ U, | u ( t + 1) - u ( t ) | ≤ S variables: u (0) , . . . , u ( M ) (with u ( t ) = 0 for t < 0 , t > M )
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