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A Compositional Approach to Stochastic Optimal Control with Co-safe Temporal Logic Specifications
Abstract We introduce an algorithm for the optimal …
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.
fy a complex temporal logic specification.  +
Authors Matanya B. Horowitz, Eric M. Wolff, Richard M. Murray  +
Funding Correct-by-Construction Synthesis of Control Protocols for Aerospace Systems +
ID 2014f  +
Source 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)  +
Tag hwm14-iros  +
Title A Compositional Approach to Stochastic Optimal Control with Co-safe Temporal Logic Specifications +
Type Conference Paper  +
Categories Papers
Modification date
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15 May 2016 06:14:46  +
URL
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http://www.cds.caltech.edu/~murray/preprints/hwm14-iros.pdf  +
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A Compositional Approach to Stochastic Optimal Control with Co-safe Temporal Logic Specifications + Title
 

 

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