Memorised quasi-time-fuel-optimal feedback control of perturbed double integrator

Quasi-time-fuel-optimal feedback control of the perturbed double integrator ẍ = f(ẋ,x,t) + g(ẋ,x,t)u is studied. A feedback control strategy is presented to overcome overshoot by introducing two compensation factors into time-fuel-optimal switching curves of the ideal double integrator. Robust convergence of the closed-loop system is proved. The control strategy presented has memory of past on-off commutation which eliminates chattering of the system and makes the system converge to the origin in a boundary layer, rather than slide to the origin along the switching curves. A simulation example is given to illustrate feasibility of the control strategy.