Exercise 4.2 Consider the double integrator či = 22, 22 = u with u € (-1,1]. Let the initial condition be r(0) = (8), le

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Exercise 4 2 Consider The Double Integrator Ci 22 22 U With U 1 1 Let The Initial Condition Be R 0 8 Le 1 (55.78 KiB) Viewed 19 times

Exercise 4.2 Consider the double integrator či = 22, 22 = u with u € (-1,1]. Let the initial condition be r(0) = (8), let the final state be (1), and let the running cost be L = 1 so that we have a time-optimal control problem. It is easy to check that the control u*(t) = 1, 1 € (0, 2) is optimal. Specialize the main steps of the proof of the maximum principle to this problem and this control. Bring the relevant concepts and conclusions to the level of explicit numerical formulas, and draw figures wherever appropriate.