Quantitative measure of regular languages for supervisory control of engineering applications

by Wang, Xi.

This dissertation formulates a signed real measure of sublanguages of regular languages based on the principle of automata theory and real analysis. The measure allows total ordering of any set of partially ordered sublanguages of a regular language for quantitative evaluation of the controlled behavior of deterministic finite state automata (DFSA) under different supervisors. The computational complexity of the language measure algorithm is polynomial in the number of DFSA states. An online parameter identification procedure is presented for computation of the language measure parameters. A discrete event behavior-based multi-robot system has been designed and constructed to validate the language measure theory and its applications to supervisory control in the discrete-event setting. Each robot is equipped with multiple sensors and multiple actuators. The interactions between the robot(s) and the (possibly) dynamically changing environment are characterized by discrete-event and continuous models, and the design and analysis of the robotic system are presented in both continuous-time and discrete event domains. The robustness and reliability of the controlled behavior is guaranteed in the continuous-time domain. For example, visual servoing is applied to robot navigation during ‘approaching target’ and the vector field historgam (VFH) method is used for robust ‘obstacle avoidance’. The discrete event interactions between behaviors are formulated as a supervisory control theory problem, where multiple supervisors are synthesized and implemented online for robot control under different specifications. The efficacy of the language parameter identification procedure is demonstrated in real-time supervisory control through experiments on the mobile robotic system as well as on a high-fidelity robot simulator. A quantitative performance measure has been used to evaluate various discrete event supervisory (DES) controllers and is validated through experiments. The performance measure is consistent with other heuristic measures in the evaluation of the robotic system performance. An optimal DES controller synthesis procedure based on the language measure theory is presented and applied to the automated design of DES control polices iii for different experimental scenarios of the mobile networked robotic system. The simulation results validate the optimal synthesis procedure. For a hierarchically structured cooperative multi-robot system, it turns out that the language measure theory is also applicable for design and performance analysis of the high level coordination. iv