This project aims to extend planning to hybrid discrete/continuous systems under exogenous uncertainty, and using this technology for proactive, and therefore more effective, management of cyber-physical systems.

Hybrid system models feature discrete and numeric state variables whose values can be changed by discrete instantaneous actions and continuous durative actions and processes. Hybrid planning shares similarities with the control of switched dynamical systems, where the system can be in different modes, each given by set of differential equations. In planning, the set of possible modes is not fixed a priori and depends on which actions are performed and when.

We have pursued a number of approaches to hybrid planning so far including:

• Discretizing the problem to obtain a numeric sequential planning problem solvable by simpler techniques, such as heuristic search guided by novel heuristics for numeric sequential planning.
• Translating the discretized problem into Satisfiability Modulo Theory, and exploiting its numeric structure to more efficiently reason about the number of times a numeric action needs to be executed in the plan using SMT.
• Employing numerical integration methods within the search to solve differential equations and adaptively discretising the search.

Our planners solve problems compactly described in variants of the PDDL+ language, which feature global constraints rather than events.

We have also investigated applications of hybrid planning, scheduling and control to energy-aware meeting scheduling and HVAC control.