Planning in hybrid systems has been gaining research interest in the Artificial Intelligence community in recent years. Hybrid systems allow for a more accurate representation of real world problems, though solving them is very challenging due to complex system dynamics and a large model feature set. We developed DiNo, a new planner designed to tackle problems set in hybrid domains.DiNo is based on the discretise and validate approach and uses the novel Staged Relaxed Planning Graph+ (SRPG+) heuristic.

Hybrid planning with nonlinear continuous change is a significant challenge for existing planners. Prior works limit their scope to linear change or base their formalisms in model checking frameworkswith inherent limitations. We address nonlinear PDDL+ planning with anew encoding in first order logic over real valued functions. Our planner, PluReal, translates PDDL+ to this logical encoding and applies the dReal Satisfiability Modulo Theories (SMT) solver to construct plans. Unlike prior work that uses dReal in the hybrid system model checking tradition, PluReal is based in the planning as satisfiability (SAT) heritage. Adopting the SAT approach helps lift several unnatural restrictions that are imposed by the translation through hybrid systems and leads to improved scalability even without SMT solver variable selection heuristics.

We introduce a modular framework for market making. It combines cost-function based automated market makers with bandit algorithms. We obtain worst-case profits guarantee's relative to the best in hindsight within a class of natural "overround" cost functions . This combination allow us to have distribution-free guarantees on the regret of profits while preserving the bounded worst-case losses and computational tractability over combinatorial spaces of the cost function based approach. We present simulation results to better understand the practical behaviour of market makers from the framework.

The PDDL+ language has been mainly devised to allow modelling of real-world systems, with continuous, time-dependant dynamics. Several interesting case studies with these characteristics have been also proposed, to test the language expressiveness and the capabilities of the support tools. However, most of these case studies have not been completely developed so far. In this paper we focus on the batch chemical plant case study, a very complex hybrid system with nonlinear dynamics that could represent a challenging benchmark problem for planning techniques and tools. We present a complete PDDL+ model for such system, and show an example application where the UPMurphi universal planner is used to generate a set of production policies for the plant.

Systems subject to (continuous) physical effects and controlled by (discrete) digital equipments, are today very common. Thus, many realistic domains where planning is required are represented by hybrid systems , i.e., systems containing both discrete and continuous values, with possibly a nonlinear continuous dynamics. The PDDL+ language allows one to model these domains, however the current tools can generally handle only planning problems on (possibly hybrid) systems with linear dynamics. Therefore, universal planning applied to hybrid systems and, in general, to non-linear systems is completely out of scope for such tools. In this paper, we propose the use of explicit model checking-based techniques to solve universal planning problems on such hardly-approachable domains.