Abstract
This paper delas with the synthesis problems of the minimal time control of n-th order linear, systems, x=Ax+bu, with bounded control amplitude, |u(t)|≤1.
When the initial value of the adjoint vector satisfies φT(0)b=0, it is shown that the reachable subset Ωs, by using the control u(t)=sgn (φT(t)b), constitutes the switching hyper surface. And how to determine the optimal control u*(x) with the usege of Ωs is shown. Applying the GMDH (Group Method of Data Handling), the method of identifying the switching hyper surface is discussed. Also discussed in the paper is the method of reducing the bad effects such as hunting of the state vector arround its equilibrium point or chattering of the manipulated variable caused by an error in the identification.
Several numerical results are shown to demonstrate the possibility of constructing the minimal time feedback control system by using the switching hyper surface.
