Peter Caines - A COCOLOG logic for systems and control theory

The COCOLOG (Conditional Observer and Controller Logic) system [Caines and Wang, SIAM J. Cont Opt., 1995] is a framework for the design and implementation in first order logic of controllers for finite deterministic input-state-output machines. A COCOLOGcontrol system consists of a partially ordered family of first order logical theories expressed in the typed first order languages describing and enabling the controlled evolution of the state of a given partially observered finite machine . The machine theories, , depend upon the observed input-output trajectories, where new data constitutes new axioms . The combination of these new axioms with the previous COCOLOG axioms generates a set of axioms for the new theory, denoted . Next, the extra-logical conditional control rules CCR(L_k) gives (mutually exclusive and exhaustive) formulas each of which triggers a distinct control action. So as to increase the efficiency of COCOLOG, a class of restricted versions is introduced called (the systems of) Markovian fragments [Wei and Caines, SIAM J. Cont Opt., 1996]. Further, since the expression of relatively simple control specifications may become extremely complicated, a theory and methodology has been introduced (see [Martínez-Mascarúa and Caines, Proc. WODES'96) for the introduction of new together with their definitional formulas. The resulting Macro ( COCOLOG) Languages are integrated with the system of so-called Macro ( COCOLOG) Actions. Finally, the dynamical consistency notion of state aggregation for hierarchical control [Caines and Wei, Systems and Control Letters, 1995] permits the construction of hierarchically layered COCOLOG controllers.