Steering control of singularly perturbed systems: A composite control approach
For the problem \[ I(u)=\int^{T}_{0}L(x,z,u,\epsilon,t)dt\to \min_{u}, \] \[ \dot x=f(x,z,u,\epsilon,t),\quad x(0)=x^ 0,\quad x\in {\mathbb{R}}^ n,\quad u\in {\mathbb{R}}^{\ell},\quad 0<\epsilon \ll 1, \] \[ \epsilon \dot z=a(x,u,\epsilon,t)+A(x,\epsilon,t)z+B(x,\epsilon,t)u+\epsilon g_ 1(x,z,u,\epsilon,t),\quad z(0)=z^ 0,\quad z\in {\mathbb{R}}^ m \] the authors consider the construction of zero-order composite closed-loop and open-loop controls on the basis of degenerated problem solution and two (left and right) boundary-layer stabilizing controls. The asymptotic validity of the composite controls is established.
zero-order composite closed-loop and open-loop controls
scientific article; zbMATH DE number 4102909
scientific article