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Circular constraint matrices in a Model Predictive Control application

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MC
MC 2017-5-21
关闭： John D'Errico 2017-5-21
Hello I need some help constructing the Q,l and r matrices for a circular constraint using cplexqcp in an MPC application. I'm using cplexqcp with a Matlab interface to solve this, where the constraint is to be given as: z'*Q*z + l'*z <= r. And z=[x(k+1) x(k+2) .. x(k+N+1) u(k) u(k+1) .. u(k+N) e(k) e(k+1) .. e(k+N)]'. Whre x is the state vector x=[x1 x2 x3 x4 x5 x6 x7]', u is the input vector u=[u1 u2 u3 u4]' and e a scalar slack variable.
The constraint is: (x-x_ref)^2 + (y-y_ref)^2 <= w, where w is the radius of the circle. The system has 7 states, 4 inputs and a slack variable and a prediction horizon of 30, thus the decision variable has (7+4+1)*30 = 360 variables. Since the reference is changing at each step in the horizon I should get 30 constraints, of the form given above (just a slightly different value for the ref's at each step). I just can't seem to construct the matrices correctly, r becoms 30x1, l 30x360 but Q becomes 360x360 which cplexqcp deems to be wrong (which it probably is). Anyone can help me out a little bit?
Best regards MC

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