Approximate Time-Optimal Control Considering System Bandwidth and Saturation

Time-optimal (TO) control is promising in many fields since it ensures to accomplish a task in minimum time. However, its direct application may cause oscillations or even limit cycles due to the restriction of the sampling period, state measurement accuracy and so on. To solve these problems, a compound proximate time-optimal (PTO) control law is proposed by considering system bandwidth and saturation in this paper. With the help of the phase plane, the switching zone and linear zone of the PTO control law are constructed. When the system state lies outside of both switching and linear zones, the bang-bang optimal scheme is adopted to achieve rapidity. And when the system state enters the switching zone, the bang-bang suboptimal scheme is developed to avoid oscillations or even limit cycles. Proportional-derivative (PD) scheme is applied in the linear zone to obtain local asymptotic stability around the origin. Numerical simulations are carried out to corroborate the advantages of the PTO control law. Copyright (C) 2020 The Authors.