for linear control systems x_dot=Ax+Bu the reachability set can be calculated using the Image of the controllability matrix, i.e
R=([B AB A^2B,....,]) and reachability set=Im(R)
when rank(R)=n, and we do not have any control constraint the reachibilaty set of linear system is R^n (n is the dimension of states)
if we have a non-linear affine-control system
x_dot=f(x)+g(x)*u
R can be calculated using Lie algebra
R=[g1,g2,[f,g1],[f,g2],...]
my question is, in this case reachability set is again Im(R)?
and if reachability set=Im(R), how can we compute the rachability set, because here R will be a matrix with function arrays (function of states)
Dear Ali,
I suggest you to see links and attached file on topic.
-Approximate Bisimulations for Nonlinear Dynamical Systems
https://www.georgejpappas.org/papers/CDC05-Nonlinear.pdf
-Computing the Projected Reachable Set of Stochastic ... - dei.unipd
www.dei.unipd.it/~meme/MEV/.../TAC_PariseValcherLygeros.pdf
-Validating a Hamilton-Jacobi Approximation to Hybrid System ...
https://web.stanford.edu/class/aa278a/References/mbt01_lncs.pdf
Best regards
Dear Ali
May be interested to linearze the system and use the technique linear systems in finite and for infinite use the approach of semi-group in distributed parameter systems
Best regards
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