Structurally Time Optimal Control for Linear Systems with Bounded Control and Bias Disturbance

We consider the development of structurally optimal algorithms in the minimum time optimal control setting. That is, we develop control laws capable of producing bang-bang and bang-intermediate control. Of interest are systems that are linear in the state and decoupled from the scalar, bounded control; the presence of an unknown, bias disturbance in the state equations is assumed. The developed algorithms utilize Lyapunov optimizing control and trajectory following minimization techniques to preserve optimal structure while creating sub-optimal, closed-loop controls. The derivation considers target stability in the presence of the unknown disturbance and chatter due to actuator saturation.