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Published September 2014 | public
Book Section - Chapter

A Compositional Approach to Stochastic Optimal Control with Co-safe Temporal Logic Specifications

Abstract

We introduce an algorithm for the optimal control of stochastic nonlinear systems subject to temporal logic constraints on their behavior. We compute directly on the state space of the system, avoiding the expensive pre-computation of a discrete abstraction. An automaton that corresponds to the temporal logic specification guides the computation of a control policy that maximizes the probability that the system satisfies the specification. This reduces controller synthesis to solving a sequence of stochastic constrained reachability problems. Each individual reachability problem is solved via the Hamilton-Jacobi-Bellman (HJB) partial differential equation of stochastic optimal control theory. To increase the efficiency of our approach, we exploit a class of systems where the HJB equation is linear due to structural assumptions on the noise. The linearity of the partial differential equation allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to conservatively satisfy a complex temporal logic specification.

Additional Information

© 2014 IEEE. The authors thank the anonymous reviewers for their helpful comments. The first and second authors were supported by NSF GRFP and NDSEG fellowships, respectively. Additional support was provided by the Boeing Corporation.

Additional details

Created:
August 20, 2023
Modified:
October 23, 2023