Robust mixed time-optimal control for third-order systems with model uncertainty

In this paper, a robust near time-optimal controller for some third-order uncertain systems with constrained input is presented. The response is usually composed of two parts. At first, the states move towards the goal state from arbitrary initial conditions by pure time-optimal control (bang-bang) and then there is sliding along a predetermined surface within an ellipsoid. The sliding surface is chosen in such a way that the integral of the absolute value of the system error is minimized. Using a combined control algorithm, robustness and stability of the system is guaranteed even with parameter uncertainty and disturbance. The error convergence rate is also improved compared with pure time-optimal control. Simulation results demonstrate the advanced performance of the proposed control algorithm.