Robust optimal control of regular languages and engineering applications

Complex human-engineered systems (e.g., aircraft, power plants, networked robotic systems) require Discrete Event Supervisory (DES) decision and control for enhanced reliability, improved performance, and augmented operating range. From these perspectives, the dynamics of plant operation is usually captured by Finite State Automaton (FSA) models that are equivalent to regular languages. This dissertation focuses on robust optimal decision and control of regular languages based on a real signed language measure that has been recently reported in literature. The proposed approach for analysis and synthesis of DES decision and control laws is quantitative. Both theoretical formulation and experimental validation of the concept are presented.; Unconstrained optimal control of regular languages allows synthesis of a supervisor that restricts the behavior of the unsupervised plant to a sublanguage having the maximal signed real language measure with maximal permissiveness. The theory of unconstrained optimal control is further enhanced by including additional cost of (controllable) event disabling. This is achieved by compensating the characteristic vector of the language measure for optimal trade-off between maximizing the language measure of the supervised plant and minimizing the incurred disabling cost. The synthesis of robust optimal control of regular languages addresses the issue of uncertain event cost parameters to ensure that the sublanguage of the supervised plant has the highest minimal language measure over the specified uncertainty range of the event cost parameters.; One of the major objectives of the research, presented in this dissertation, is to develop a systematic methodology to integrate the DES decision and control laws with complex continuously varying dynamic systems (CVDS). This dissertation has shed light on how to build an interface between these heterogeneous systems and how to assure reliable information exchange. This novel concept of DES decision and control as well as the methodology of interconnecting DES control with CVDS has been validated by extensive simulation experiments on a model of a commercial-scale aircraft turbo-fan jet engine. Additional function blocks, such as event generators and action generators, are designed to convert continuous information into discrete information and vice versa. The language model parameters are identified for synthesis and analysis of optimal supervisors. The experimental results on both simulation test bed and networked robotic test bed, strongly suggest that the optimal DES decision and control is potentially very useful not only for performance and operating range enhancement of complex human-engineered systems but also for reliability improvement by life extension of critical plant components.