Since linear matrix inequalities can be treated as quadratic optimization problems, I want to apply such an optimization algorithm directly rather than using a toolbox interface.
Doing so I can use matlab mpcActiveSetSolver (https://de.mathworks.com/help/mpc/ref/mpcactivesetsolver.html) which alows code generation for my realtime application.
My first goal will be a linear quadratic regulator using LMI approach (https://de.mathworks.com/help/robust/ug/minimizing-linear-objectives-under-lmi-constraints.html).
Consider a linear state space model and LQR with one state:
A=-1; B=1; Q=1; R=1;
Riccati-Approach is to solve A'X+XA−XBB'X+Q=0 = -1X -1X -X^2+1=0
X=care(A,B,Q,R)
X=0.4142
so good so far. Now I want so solve this using LMI-approach.
schur complement lemma yields the LMI:
[A'X+XA+Q XB]
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