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Singular Perturbations of a Class of Two Point Boundary Value Problems Arising in Optimal Control

机译：一类两点边值问题的最优控制奇异摄动

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Sufficient conditions are established for the existence of a solution to the system dx/dt = f(x,v,y,w,t,u) x(t sup o) = x sup o, dv/dt = p(x,v,y,w,t,u) v(T) = v sup T, u dy/dt = g(x,v,y,w,t,u) y(t sup o) = y sup o, udw/dt = q(x,v,y,w,t,u) w(T) = w sup T on (t sup o, T), where u is a small positive parameter and x, v, y, and w are vectors possibly of different dimensions, and for convergence of these solutions as u approaches 0 to a known, isolated solution of the degenerate system dx/dt = f(x,v,y,w,t,0) x(t sup o) = x sup o, dv/dt = p(x,v,y,w,t,0) v(T) = v sup T, 0 = g(x,v,y,w,t,0), 0 = q(x,v,y,w,t,0). The behavior of such solutions near the endpoints t sup o and T is examined (boundary layer behavior). An asymptotic expansion technique of Vasileva is extended to this class of problems in a formal way, with a discussion of the computational aspects. Problems of this type are shown to arise in a fixed time free endpoint problem of optimal control, and a design based on the method is carried out for a tension regulator in a strip winding process for a rolling mill plant. (Author)

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