Duality-Based Nested Controller Synthesis from STL Specifications for Stochastic Linear Systems

  • Susmit Jha
  • Sunny RajEmail author
  • Sumit Kumar Jha
  • Natarajan Shankar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11022)


We propose an automatic synthesis technique to generate provably correct controllers of stochastic linear dynamical systems for Signal Temporal Logic (STL) specifications. While formal synthesis problems can be directly formulated as exists-forall constraints, the quantifier alternation restricts the scalability of such an approach. We use the duality between a system and its proof of correctness to partially alleviate this challenge. We decompose the controller synthesis into two subproblems, each addressing orthogonal concerns - stabilization with respect to the noise, and meeting the STL specification. The overall controller is a nested controller comprising of the feedback controller for noise cancellation and an open loop controller for STL satisfaction. The correct-by-construction compositional synthesis of this nested controller relies on using the guarantees of the feedback controller instead of the controller itself. We use a linear feedback controller as the stabilizing controller for linear systems with bounded additive noise and over-approximate its ellipsoid stability guarantee with a polytope. We then use this over-approximation to formulate a mixed-integer linear programming (MILP) problem to synthesize an open-loop controller that satisfies STL specifications.



The authors acknowledge support from the National Science Foundation (NSF) Cyber-Physical Systems #1740079 project, NSF Software & Hardware Foundation #1750009 and #1438989 projects, US ARL Cooperative Agreement W911NF-17-2-0196, and DARPA under contract FA8750-16-C-0043.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Susmit Jha
    • 1
  • Sunny Raj
    • 2
    Email author
  • Sumit Kumar Jha
    • 2
  • Natarajan Shankar
    • 1
  1. 1.Computer Science LaboratorySRI InternationalMenlo ParkUSA
  2. 2.Computer Science DepartmentUniversity of Central FloridaOrlandoUSA

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