The American Association for Artificial Intelligence Spring Symposium on Hybrid Systems and AI was held at Stanford University from 22--24 March, 1999. The symposium attracted 54 researchers, from both the hybrid systems communities in electrical engineering and computer science, and from the AI community.

The use of digital computers to control complex continuous, dynamical processes has contributed to the development of a new field of research that focuses on techniques for analyzing, synthesizing, and controlling dynamical systems whose behavior is modeled by hybrid (discrete + continuous) models. Hybrid system models include intervals of piecewise continuous behavior interleaved with discrete transitions. Each interval of continuous behavior represents a so-called mode of system operation; transitions between modes are discrete and may cause discontinuous changes in the system configuration and variables. Examples of hybrid systems include robots, air traffic control systems, chemical plants, autonomous spacecraft control, smart buildings and automated multi-vehicle highway systems.

The hybrid systems community is a cross-disciplinary community that combines modeling and analysis techniques from discrete event systems, continuous dynamic systems, and control theory. The growing field of hybrid systems has seen a great deal of activity over the last few years often focusing on synthesis, verification and stability analysis of controllers for hybrid systems. Interestingly, a number of the problems addressed by this community are shared by AI researchers studying robotics, online time-critical computation, planning, simulation, verification, execution monitoring, decision analysis, reasoning about action, diagnosis, modeling and analysis of physical systems, and perception. The {\it Hybrid Systems and AI Spring Symposium brought together these different communities to explore opportunities for exploiting AI representation and reasoning techniques for hybrid system modeling and analysis, and for integrating techniques from hybrid systems into current AI research.

To accommodate the diverse background of workshop participants, the symposium included four invited talks by researchers from the two communities. Alan Mackworth (who also graciously agreed to be our plenary speaker.) presented The Dynamics of Intelligence: Constraint-Satisfying Hybrid Systems for Perceptual Agents in which he described the Constraint-Net model, a unitary framework for building hybrid intelligent systems as situated agents. His team has applied this framework to several applications including soccer playing robots. Shankar Sastry's talk on Algorithms for the Design of Networks of Unmanned Aerial Vehicles linked problems in non linear control to formal verification methods employed in Computer Science and Game Theory. He discussed applications in Intelligent Vehicle Highway Systems (IVHS), Unmanned Aerial Vehicles (UAVs) and Air Traffic Management Systems (ATMS). Tom Henzinger's talk on Hybrid Games presented a classification of verification problems based on varying models of hybrid automata. He extended this classification to two-player structures (plant vs. controller) to similarly classify control problems. The presentation, in particular, provided a number of interesting results for polyhedral automata. Brian Williams' talk on Model-Based Programming of Reactive Systems: The Journey of Deep Space One (DS1) presented the concept of model-directed autonomous systems, and his group's experiences in developing the Remote Agent (RA) autonomous control system. RA is soon to be demonstrated as a technology experiment on the DS1 mission.

There were five theme sessions coordinated by session chairs, each of whom provided an overview of their session area and facilitated discussion. The first session of the symposium, Behavioral Programming (Chair: Michael Branicky) discussed a body of techniques for predictably composing lower-level behaviors into solutions that satisfy higher-level goals. Typically, the lower-level behaviors are given by sensorimotor loops or controllers, operating in a continuous domain, while higher-level goals are encoded symbolically. Papers covered a range of topics related to the general problem of procedural learning in domains including walking robots, artificial fish and cooperating robots for manufacturing. The session on Formal Methods (Chair: Howard Wong-Toi) examined the use of logic to model and analyze hybrid systems. Several papers discussed expressive logic-based theories of action and how to extend them to represent and reason about hybrid systems. Another paper discussed situated multi-agent architectures and the mapping of logic-based theories of action to these architectures. A final paper discussed the modal $\mu$-calculus, demonstrating that it, and various extensions, provide an expressively rich yet highly usable logical framework for formal analysis of hybrid systems. There were two sessions on Synthesis and Control (Chairs: Feng Zhao and Claire Tomlin) which discussed theory and tools for analyzing, synthesizing, and verifying multi-modal hybrid systems. A number of papers went beyond analytic approaches and exploited geometric structure in the phase space to achieve computational efficiency. Other papers used game-theoretic approaches to verify and synthesize controller function. The last session on Applications (Chair: Dan Clancy) included papers that discussed computational issues, such as the tracking of piecewise continuous behaviors and the enhancing of discrete event simulation by including continuous system models. The symposium also included a poster session for all authors to discuss their work in detail.

The symposium was a success, and plans are underway for including sessions with AI themes at the next International Hybrid Systems Workshop (HS'00) to be held at Carnegie-Mellon University in March 2000. For further information about the Spring Symposium please see http://www.ksl.stanford.edu/springsymp99. Information on HS'00 will be available at http://www.ece.cmu.edu/hs00 after May 1, 1999.