Suppose we have a nonlinear system:

x_dot=A x + B u(t-T) + phi(x) + d(t)

y=Cx

where x:state, u:control input, d:exogenous disturbance (bounded), phi(x): nonlinear vector (satisfy local Lipschitz), A: system matrix (with uncertain parameters), T:time delay, y;

output.

Assumptions:

i. Exogenous disturbance bounded.

ii. Parameter uncertainty bounded

iii. Nonlinear function satisfies locally Lipschitz condition

Constraints:

i. control , u>=0, for all time,t >0 and u=0, for all time t>0

Q/ How to design a robust MPC that will account for the input time-delay uncertain nonlinear system?

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