assn6 - MIT OpenCourseWare http:/ocw.mit.edu 16.323...

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MIT OpenCourseWare http://ocw.mit.edu 16.323 Principles of Optimal Control Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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± ² ³ ´ ³ ´ ³ ´ 16.323 Handout #6 Prof. J. P. How April 25, 2008 Due: May 8, 2008 16.323 Homework Assignment #6 1. Finish 4(b) and 4(c) of Homework #5. 2. (total 15pts) Find the control input u ( t ) sequence that minimizes the cost functional J = y ( t f ) subject to the state constraints y ˙( t ) = y ( t ) u ( t ) y ( t ) u 2 ( t ) for an initial condition y (0) = 2 and ±nal time t f = 5. Give both the control, the state response, and the costate. 3. Given the plant dynamics, x ˙ 1 ( t ) = x 2 ( t ) x ˙ 2 ( t ) = x 1 ( t ) + u ( t ) + w ( t ) y ( t ) = x 2 ( t ) + v ( t ) and cost function, 1 t f J = E (3 x 1 2 ( t ) + 3 x 2 2 ( t ) + u 2 ( t )) dt 2 0 where w ( t ) ∼ N (0 , 4) and v ( t ) ∼ N (0 , 0 . 5) are Gaussian, white noises and t f = 15. (a) Numerically integrate the Riccati equations for LQR and the LQE to ±nd the time-varying regulator and estimator gains. (b)
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This note was uploaded on 11/07/2011 for the course AERO 16.323 taught by Professor Jonathanhow during the Spring '08 term at MIT.

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assn6 - MIT OpenCourseWare http:/ocw.mit.edu 16.323...

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