Time-optimal symbolic control of a changeover process based on an approximately bisimilar symbolic model

Many process control problems with complex qualitative specifications cannot be addressed via conventional control design methods. Examples of such specifications include logic specifications expressed in the design of start-up, shut-down, changeover, and emergency shutdown operating procedures. In recent years, it has been shown in the control systems and computer science communities that symbolic models provide convenient and powerful mechanisms to synthesize controllers enforcing such qualitative specifications. The use of symbolic models reduces the synthesis of the controllers to a fixed-point computation problem over a finite-state abstract system. In this paper, after explaining the notion of approximate bisimulation for incrementally globally asymptotically stable (δ-GAS) nonlinear control systems, the construction of approximately bisimilar symbolic models for such systems is presented. Then synthesis of time-optimal symbolic controller for this class of systems is performed based on results from the computer science literature. As a benchmark chemical process control problem, an approximately bisimilar symbolic model is constructed for a safe changeover process. Then a symbolic controller is designed and it is refined to a controller to be applied to the original process. Simulation results show the effectiveness of the symbolic controller. Although the construction of the symbolic model may be complex, the synthesis of the controller in a finite-state space is fast and most importantly the error bounds are adjustable as design parameters.