Henzinger henzinger describes a digital controller of an analogue plant as a paradigmatic example of a mixed discrete-continuous system. The discrete states (control modes) and dynamics (control switches) of the controller are modelled by the vertices and edges of a graph. The continuous states and dynamics of the plant are modelled by vectors of real numbers and differential equations. The behaviour of the plant depends on the state of the controller, and vice versa: when the controller switches between modes it can update the variables that describe the continuous behaviour of the plant and hence bring about discrete changes to the state of the plant. A continuous change in the state of the plant can affect invariant conditions on the control mode of the controller and result in a control switch.
In a similar way, PDDL+ distinguishes processes, responsible for continuous change, from events and actions, responsible for discrete change. Further, the constraint in PDDL+, that numeric values only appear as the values of functions whose arguments are drawn from finite domains, corresponds to the requirement made in hybrid automata that the dimension of the automaton be finite.
An important contribution of our work is to demonstrate that PDDL+ can support succinct encodings of deterministic hybrid automata for use in planning. We expect that both the formal (semantics and formal properties) and practical (model-checking techniques) results in Hybrid Automata theory will be able to be exploited by the planning community in addressing the problem of planning for discrete-continuous planning domains. Indeed, some cross-fertilisation is already beginning [DierksDierks2005,Rasmussen, Larsen, SubramaniRasmussen et al.2004,EdelkampEdelkamp2003].
Derek Long 2006-10-09