The computation of the Linear Quadratic Regulator (LQR) requires solving the algebraic Riccati equation. In theory, one needs to solve the state-dependent Riccati equation (SDRE). The challenge lies in developing an algorithm to solve the SDRE without relying on the built-in lqr() function. In this case, the matrices are state-dependent instead of being constant. There are several tools or solvers available to solve the SDRE, and one of them is the Linear Matrix Inequality (LMI) method.
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