On-line identification of language measure parameters for discrete-event supervisory control

The discrete-event dynamic behavior of physical plants is often represented by regular languages that can be realized as deterministic finite state automata (DFSA). The concept and construction of signed real measures of regular languages have been recently reported in literature. Major applications of the language measure are: quantitative evaluation of the discrete-event dynamic behavior of unsupervised and supervised plants; and analysis and synthesis of optimal supervisory control algorithms in the discrete-event setting. This paper formulates and experimentally validates an on-line procedure for identification of the language measure parameters based on a DFSA model of the physical plant. The recursive algorithm of this identification procedure relies on observed simulation and/or experimental data. Efficacy of the parameter identification procedure is demonstrated on the test bed of a mobile robotic system, whose dynamic behavior is modelled as a DFSA for discrete-event supervisory control.