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Unformatted text preview: 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 Example: open-loop control problem single-input/single-output system (with input u , output y ) y ( t ) = h 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:...
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This note was uploaded on 09/26/2009 for the course CAAM 236 taught by Professor Dr.vandenber during the Spring '07 term at Monmouth IL.
- Spring '07