Lygeros John, Tomlin Claire, Sastry Shankar. Hybrid Systems Modeling: Analysis and Control

New York, 2008. — 168 p.While rapid progress in embedded hardware and software makes plausible ever more ambitious multi-layer, multi-objective, adaptive, nonlinear control systems, adequate design methodologies and design support lag far behind. Consequently, today most of the cost in control system development is spent on ad-hoc, prohibitively expensive systems integration, and validation techniques that rely almost exclusively on exhaustively testing more or less complete versions of complex nonlinear control systems. The newest research direction in control addresses this bottleneck by focusing on predictive and systematic hierarchical design methodologies for building an analytical foundation based on hybrid systems and a practical set of software design tools which support the construction, integration, safety and performance analysis, on-line adaptation and off-line functional evolution of multi-agent hierarchical control systems. Hybrid systems refer to the distinguishing fundamental characteristics of software-based control systems, namely, the tight coupling and interaction of discrete with continuous phenomena. Hybridness is characteristic of all embedded control systems because it arises from several sources. First, the high-level, abstract protocol layers of hierarchical control designs are discrete as to make it easier to manage system complexity and to accommodate linguistic and qualitative information; the low-level, concrete control laws are naturally continuous. Second, while individual feedback control scenarios are naturally modeled as interconnections of modules characterized by their continuous input/output behavior, multi-modal control naturally suggests a state-based view, with states representing discrete control modes; software-based control systems typically encompass an integrated mixture of both types. Third, every digital hardware/software implementation of a control design is ultimately a discrete approximation that interacts through sensors and actuators with a continuous physical environment. The mathematical treatment of hybrid systems is interesting in that it builds on the preceding framework of nonlinear control, but its mathematics is qualitatively distinct from the mathematics of purely discrete or purely continuous phenomena. Over the past several years, we have begun to build basic formal models (hybrid automata) for hybrid systems and to develop methods for hybrid control law design, simulation, and verification. Hybrid automata, in particular, integrate diverse models such as differential equations and state machines in a single formalism with a uniform mathematical semantics and novel algorithms for multi-modal control synthesis and for safety and real-time performance analysis.