Solution Formulas for Dynamic Linear Optimization Problems |
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Page 32
... x , u T [ ∞x ( t ) + du ( t ) ] at + ¥ dt + Y [ x ( T ) ] ( 2-25 ) s.t. x ( t ) = Ax ( t ) + Bu ( t ) , x ( 0 ) = x , 0 ≤ t≤T ( 2-26 ) Cx ( t ) + Du ( t ) = b ( 2-27 ) x ( t ) ≥0 , u ( t ) ≥ 0 where the dimensions are the ...
... x , u T [ ∞x ( t ) + du ( t ) ] at + ¥ dt + Y [ x ( T ) ] ( 2-25 ) s.t. x ( t ) = Ax ( t ) + Bu ( t ) , x ( 0 ) = x , 0 ≤ t≤T ( 2-26 ) Cx ( t ) + Du ( t ) = b ( 2-27 ) x ( t ) ≥0 , u ( t ) ≥ 0 where the dimensions are the ...
Page 34
Ronald Edward Davis. at each time t and ( t ) is the corresponding price vector on the equality constraints ( 2-37 ) . Since only the objective function changes with t , and optimal ... ( t ) trajectory . If [ x ( T ) ] is not linear 34.
Ronald Edward Davis. at each time t and ( t ) is the corresponding price vector on the equality constraints ( 2-37 ) . Since only the objective function changes with t , and optimal ... ( t ) trajectory . If [ x ( T ) ] is not linear 34.
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Ronald Edward Davis. ΟΝ τ-9 »τ<ι«'ι ΟΤ8Β9 (*.'^χ'*.) ΊΥΛΗ3Ι'ΝΙ Ρ^ε ΟΤ5Β9 ^.'^.'^Χ) ΤνΛΗ3Ι,ΝΙ Ρ"2 ΟΤ5Β9 (2.'Ζ.'τ.) ΊΥΛΗ3Ι'ΝΙ ^31 9β£ΟΓβ άβνβΐορϊησ; £ηβ βχρΐϊοϊί. δοΐυ£χοηδ £ο £ηβ5β βςηιβΐϊοηδ, νβ ηο£β. ΤΤ = (^)Τ.ε+(^) ...
Ronald Edward Davis. ΟΝ τ-9 »τ<ι«'ι ΟΤ8Β9 (*.'^χ'*.) ΊΥΛΗ3Ι'ΝΙ Ρ^ε ΟΤ5Β9 ^.'^.'^Χ) ΤνΛΗ3Ι,ΝΙ Ρ"2 ΟΤ5Β9 (2.'Ζ.'τ.) ΊΥΛΗ3Ι'ΝΙ ^31 9β£ΟΓβ άβνβΐορϊησ; £ηβ βχρΐϊοϊί. δοΐυ£χοηδ £ο £ηβ5β βςηιβΐϊοηδ, νβ ηο£β. ΤΤ = (^)Τ.ε+(^) ...
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actual basis B₁ basic solution basis changes breakpoints Bryson Jr combination of shift continuous time model control variables corresponding d₁ dimension discrete-time dissertation Doctor of Philosophy dual equations dual solutions dual u-interval dynamic linear programming exactly n+m basic formulas iɛQ(j inequality constraints introduced jump values linear control problem linear equations linear programming models matrix multiplier n+m basic variables non-basic non-negative non-singular nonbasic variables number of basic open interval Optimal Control optimal solution optimality conditions optimum p-vector parameters positive price vectors primal and dual primal solution problem LP-P pseudo variables pseudo-basis variables recursively reduced cost reduced gradient shift vectors Simplex Method simultaneous equations square block triangular Staircase Shift Algorithm staircase structured Substituting surplus basic variables surplus period surplus variables system of equations t₁ t₂ terminal condition third interval thrust ti+1 u₁ u₁(t u₂ unbalanced time periods vectors for period x₁ x₁(t x₂ yields Σ Σ