Fuel-Optimal Control of a Double Integral Plant With Response Time Constraints

Given the double integral plant ÿ(t)=u(t), |u(t)|≤1, the control u(t) is determined which, in the time interval [0, T], forces the state of the plant to zero, minimizes the fuel consumed, as measured by ∫
₀
^T
|u(t)|dt, and results in a response time T which does not exceed a prespecified multiple of the minimum time. A design of the nonlinear controller necessary is included.