LQR control design with un certainty

M

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Mfatima

LQR controller is simple to design with matlab. BUT what if the state matrices of the LQR contain unknown terms. How can we separate those unknown terms from the state space form and design the controller the usual way.<pre>
The state space form is as follows
Xdot=[0 1.132+sin(d1) 0 -1 ]x
0 -0.0538+cos(d2) -0.1732+d3 0 0.0705+d4
0 0 1 0
0 0.0485+d5 -0-856+d6 -d7

+ [0 0 0 ]u
0.012+d11 1+d12 0


x=x1, x2, x3, x4
u= u1, u2</pre>
all the d terms are uncertainty and are unknowns.
with them in the matrices, we cannot use the usual LQR command in matlab to design the controller.
If any one can help, i''ll be grateful
 
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