Lecture 2: Controllability of nonlinear systems
Lecture 2: Controllability of nonlinear systems
Lecture 2: Controllability of nonlinear systems
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DISC Systems and Control Theory <strong>of</strong> Nonlinear Systems 4In fact, let the control strategy u = col(u 1 , u 2 ) be defined by⎧(1, 0), t ∈ [0, ε), ε > 0⎪⎨ (0, 1), t ∈ [ε, 2ε)u(t) =(−1, 0), t ∈ [2ε, 3ε)⎪⎩(0, −1), t ∈ [3ε, 4ε),Then the motion <strong>of</strong> the system is described byx(4ε) = x 0 + ε 2 [g 1 , g 2 ](x 0 ) + O(ε 3 ).which indicates controllability, since [g 1 , g 2 ] is everywhereindependent from g 1 , g 2 .This formula holds in general.This is enough for <strong>systems</strong> with two inputs and three statevariables, but what can we do if the dimension <strong>of</strong> the state is > 3?
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