Tracking Control of an Unknown Linear System for a Fragment of Signal Temporal Logic Task

In this paper, we study the problem of tracking control for an unknown linear system, to achieve complicated, high-level, long-term objectives that are assigned to the system. We consider that the task specification of the system takes a form of a signal temporal logic (STL) formula, due to its ability to deal with some sophisticated tasks. A reference signal is produced by an STL specification, and we develop a control law to make the system track the reference signal. The majority of existing approaches for tracking control problem result in large computational burdens. In order to reduce the computational complexity, a continuous-time feedback control law generated by the approach of prescribed performance control (PPC) is used to guarantee satisfaction of STL specifications. Meanwhile, both quick response and arbitrary small steady-state error are taken into account. The efficacy of the proposed method is demonstrated by numerical examples.