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Unformatted text preview: 17 - 1 Continuous-Time LQR S. Lall, Stanford 2009.11.18.01 17. Continuous-Time LQR Continuous-time LQR problem formulation Dynamic programming solution Hamilton-Jacobi equation Riccati differential equation Steady-state regulator Infinite-horizon regulator 17 - 2 Continuous-Time LQR S. Lall, Stanford 2009.11.18.01 The Key Points of This Section LQR problem in continuous-time has an integral cost function solved via dynamic programming solution is Riccati differential equation controller is linear state feedback u ( t ) = K t x ( t ) steady-state/infinite horizon solution gives constant controller 17 - 3 Continuous-Time LQR S. Lall, Stanford 2009.11.18.01 The Continuous-Time LQR Problem continuous-time system x ( t ) = Ax ( t ) + Bu ( t ) x (0) = x problem: choose u : [0 , T ] R m to minimize J = Z T x ( ) T Qx ( ) + u ( ) T Ru ( ) d + x ( T ) T Q f x ( T ) T is the time-horizon Q , Q f , R > are state cost , final state cost and input cost matrices an infinite dimensional problem: trajectory u is the variable 17 - 4 Continuous-Time LQR S. Lall, StanfordS....
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This note was uploaded on 08/23/2010 for the course EE 263 taught by Professor Boyd,s during the Fall '08 term at Stanford.
- Fall '08