LQR with variable matrices

Good morning, hope someone can answer this question: I'm dealing with an LQR with A and B matrices that are dependant on one of the variables of the state; how can I resolve the LQR with such matrices?

Answer 1

[Sam Chak]

Hi @Matteo Cazzetta

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.

Also read:

https://dcsl.gatech.edu/papers/aiaa10a.pdf