Temporal Logic Control of Nonlinear Stochastic Systems with Online Performance Optimization

arXiv (Cornell University)

Abstract

The deployment of autonomous systems in safety-critical environments requires control policies that guarantee satisfaction of complex control specifications. These systems are commonly modeled as nonlinear discrete-time stochastic systems. A~popular approach to computing a policy that provably satisfies a complex control specification is to construct a finite-state abstraction, often represented as a Markov decision process (MDP) with intervals of transition probabilities, i.e., an interval MDP (IMDP). However, existing abstraction techniques compute a \emph{single policy}, thus leaving no room for online cost or performance optimization, e.g., of energy consumption. To overcome this limitation, we propose a novel IMDP abstraction technique that yields a \emph{set of policies}, each of which satisfies the control specification with a certain minimum probability. We can thus use any online control algorithm to search through this set of verified policies while retaining the guaranteed satisfaction probability of the entire policy set. In particular, we employ model predictive control (MPC) to minimize a desired cost function that is independent of the control specification considered in the abstraction. Our experiments demonstrate that our approach yields better control performance than state-of-the-art single-policy abstraction techniques, with a small degradation of the guarantees.

Authors 5

1. Alessandro Riccardi

   Delft University of Technology

   Affiliation as printed

   Delft University of Technology , The Netherlands

2. Thom Badings Aachen

   University of Oxford · RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Germany

   University of Oxford , United Kingdom

3. Luca Laurenti

   Delft University of Technology

   Affiliation as printed

   AI4I , Italy

   Delft University of Technology , The Netherlands

4. Alessandro Abate

   University of Oxford

   Affiliation as printed

   University of Oxford , United Kingdom

5. Bart De Schutter

   Delft University of Technology

   Affiliation as printed

   Delft University of Technology , The Netherlands