Supervisory Control and Regulation of Discrete Dynamical Systems

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Our proposed research lies in the branch of engineering and applied mathematics called automatic control or sometimes cybernetics, namely the science and technology of feedback systems. Such systems are designed to maintain some critical variable(s) within an acceptable range. For instance, an aircraft's automatic pilot corrects for wind disturbances which might otherwise drive the plane off course, perhaps disastrously. Of specific interest to us are systems, such as traffic systems, which must respond to instantaneous events, like the arrival at an intersection of a vehicle; and manufacturing systems, which must respond to a new part order or a machine breakdown. Another example is the pushbutton system in an automobile which, though "randomly" activated by the motorist, should be designed never to fall into a logical error like "hangup" or blocking. Such discrete-event systems and their control call for new and specialized techniques at the interface of control theory and computer science. A major challenge is that these systems can be (logically) very large and complex. For instance, the automobile pushbutton system may potentially enter many millions of different internal states or logical configurations. This may lead to almost overwhelming requirements on the computing power needed for control engineering design. We are developing formal (i.e. systematic and mathematically rigorous) methods of organizing such systems according to effective architectural principles. Such a system architecture could be hierarchical, namely an organization of component groups into logical "layers", analogous to the levels of management in a business or governmental organization. There each level takes orders from the one above, and issues control commands to the one below, but with feedback links by which a given level can report valuable performance data to the level above. Alternatively one might organize the main system components distributively into semi-autonomous smart agents that intercommunicate by networking. In fact many variations and combinations of such vertical and horizontal architectures are employed in practice. The objective of any system architecture is to render a complex system both transparent (i.e. humanly intelligible) and computable (i.e. amenable to control design which guarantees that the system will behave in accordance with specification). Our ultimate goal is to develop laws of architecture to guide the choice of architecture best suited to a given control task. A parallel research goal is extension of the internal model principle (IMP) of control theory, according to which a "good" controller (in a certain technical sense) must be equipped with specific intelligence concerning the dynamical structure of its environment. Of especial interest will be the incorporation of the IMP in the control architectures of discrete-event systems as outlined above.