Tracking Control of Join-Free Timed Continuous Petri Net Systems under Infinite Servers Semantics

A new low-and-high gain algorithm is presented for tracking control of a subclass of timed continuous Petri Net (contPN) systems working under infinite servers semantics. The inherent properties of timed contPN determine that the control signals must be non-negative and upper bounded by functions of system states. In the proposed control approach, LQ theory is first used to design a low-gain controller such that the control signals satisfy the input constraints. Based on the low-gain controller, a high-gain term is further added to fully employ available control energy, and control performance can be improved consequently. In order to guarantee global tracking convergence and smoothness on the tracking target, a mixed trajectory (state step and ramp) is used instead of a pure step reference signal. The new tracking target is designed to ensure the existence of the low-gain controller and possible fast system response concurrently. Rigorous proof based on Lyapunov function is provided to guarantee that for a conservative and strongly connected Join-Free (JF) timed contPN system, the proposed algorithm can ensure the global asymptotical convergence of both system states and control signals.