A system with dynamics: $x_{k+1} = A_0 x_k + (1-\min(1,|x|)) (A_1F_1(x) + A_2F_2(x) + \dots + A_nF_n(x)) + Bu$.
where $A_0$ are linear dynamics, $(1-\min(1,|x|))$ is a ramp that mixes in whatever arbitrary nonlinear dynamics you want. $F_1(x) \dots F_n(x)$ represent types of nonlinear dynamics with whatever structure you're interested in (e.g. polynomials, etc.). The idea is then that the dimension can be scaled to test performance, vibly can be used to get ground truth (if the dimensions are not too large).
sheim
commented
5 years ago
A system with dynamics: $x_{k+1} = A_0 x_k + (1-\min(1,|x|)) (A_1F_1(x) + A_2F_2(x) + \dots + A_nF_n(x)) + Bu$.
where $A_0$ are linear dynamics, $(1-\min(1,|x|))$ is a ramp that mixes in whatever arbitrary nonlinear dynamics you want. $F_1(x) \dots F_n(x)$ represent types of nonlinear dynamics with whatever structure you're interested in (e.g. polynomials, etc.). The idea is then that the dimension can be scaled to test performance, vibly can be used to get ground truth (if the dimensions are not too large).