stoch_lqr

stoch_lqr - EE363 Winter 2008-09 Lecture 5 Linear Quadratic...

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Unformatted text preview: EE363 Winter 2008-09 Lecture 5 Linear Quadratic Stochastic Control linear-quadratic stochastic control problem solution via dynamic programming 51 Linear stochastic system linear dynamical system, over finite time horizon: x t +1 = Ax t + Bu t + w t , t = 0 ,...,N- 1 w t is the process noise or disturbance at time t w t are IID with E w t = 0 , E w t w T t = W x is independent of w t , with E x = 0 , E x x T = X Linear Quadratic Stochastic Control 52 Control policies state-feedback control: u t = t ( x t ) , t = 0 ,...,N- 1 t : R n R m called the control policy at time t roughly speaking: we choose input after knowing the current state, but before knowing the disturbance closed-loop system is x t +1 = Ax t + B t ( x t ) + w t , t = 0 ,...,N- 1 x ,...,x N , u ,...,u N- 1 are random Linear Quadratic Stochastic Control 53 Stochastic control problem objective: J = E parenleftBigg N- 1 summationdisplay t =0 ( x T t Qx t + u T t Ru t ) + x T N Q f x N parenrightBigg with Q , Q f , R > J depends (in complex way) on control policies ,..., N- 1 linear-quadratic stochastic control problem : choose control policies ,..., N- 1 to minimize J (linear refers to the state dynamics; quadratic to the objective) an infinite dimensional problem: variables are...
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This note was uploaded on 02/04/2012 for the course ECE 222 taught by Professor Goengi during the Spring '11 term at Maryland.

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stoch_lqr - EE363 Winter 2008-09 Lecture 5 Linear Quadratic...

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