Do check out the examples for more detailed explanations of various functionalities of the toolbox.

List of functions in SReachTools

In MATLAB, you can use:

  • help FUNCTION_NAME to understand the details of a function
  • methods(CLASS_NAME) to understand the details of a class
  • <Ctrl+F1> to get function hints for a given function

Click on any of the SReachTools functions listed below to learn more about it. This information is obtained from their docstrings.

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Features of SReachTools

The following table1 summarizes the features in SReachTools.

Function method-str Utility Notes
SReachPoint   Approximation of the maximal reach probability for a target tube from a given initial state 2 Synthesize open-loop or affine disturbance feedback controllers
  chance-open Guaranteed underapproximation 3, 4 Open-loop
  genzps-open Approximate up to \( \epsilon_\mathrm{genz}\), a user-specified quadrature error tolerance 5 Open-loop
  particle-open Approximate with quality proportional to the number of particles used 3 Open-loop
  voronoi-open Probabilistically enforced upper bound on overapproximation error 6 Open-loop
  chance-affine-uni Guaranteed underapproximation 7 Affine disturbance-feedback (decoupled risk allocation and controller synthesis)
  chance-affine Guaranteed underapproximation 4 Affine disturbance-feedback (coupled risk allocation and controller synthesis)
SReachSet   Polytopic approximation of the stochastic reach sets for the stochastic reachabilty of a target tube problem2,8 Synthesize open-loop controllers in some cases
  chance-open Guaranteed underapproximation 2 Optimal open-loop controllers at vertices
  genzps-open Approximation up to \( \epsilon_\mathrm{genz}\), a user-specified quadrature error tolerance 2,8 Optimal open-loop controllers at vertices
  lag-under Guaranteed underapproximation 9 Set-based feedback controller for all points within the set
  lag-over Guaranteed overapproximation 9  
SReachFwd   Forward stochastic reachability analysis of an uncontrolled LTI/LTV system from a given initial state 10,11  
  state-stoch Stochasticity of the state at a future time  
  concat-stoch Stochasticity of the concatenated state vector up to a specified future time  
  state-prob Probability that the concatenated state vector (trajectory) up to a future time will lie in a given target tube set 11  
  concat-prob Probability that the state at a future time will lie in a given target set 11  
SReachDyn   Dynamic programming approximation of the maximal reach probability and the reach set Analyze 2D and 3D LTI/LTV systems

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  1. This table was generated using https://www.tablesgenerator.com/markdown_tables# ↩

  2. A. Vinod and M. Oishi, “Stochastic reachability of a target tube: Theory and computation”, submitted to IEEE Transactions of Automatic Control, 2018 (submitted). ↩ ↩2 ↩3 ↩4

  3. K. Lesser, M. Oishi, and R. S. Erwin, “Stochastic reachability for control of spacecraft relative motion,” in Proceedings of the IEEE Conference on Decision and Control, pp. 4705-4712, 2013. ↩ ↩2

  4. A. Vinod and M. Oishi, “Affine controller synthesis for stochastic reachability via difference of convex programming”, in Proceedings of Conference on Decision and Control, 2019 (submitted). ↩ ↩2

  5. A. Vinod and M. Oishi, “Scalable Underapproximation for Stochastic Reach-Avoid Problem for High-Dimensional LTI Systems using Fourier Transforms”, in IEEE Control Systems Letters (CSS-L), pp. 316–321, 2017. ↩

  6. H. Sartipizadeh, A. Vinod, B. Acikmese, and M. Oishi, “Voronoi Partition-based Scenario Reduction for Fast Sampling-based Stochastic Reachability Computation of LTI Systems”, In Proceedings of American Control Conference, 2019 (accepted). ↩

  7. M. Vitus and C. Tomlin, “On feedback design and risk allocation in chance constrained control”, in Proceedings of Conference on Decision and Control, 2011. ↩

  8. A. Vinod and M. Oishi, “Scalable Underapproximative Verification of Stochastic LTI Systems using Convexity and Compactness”, in Proceedings of Hybrid Systems: Computation and Control, pp. 1–10, 2018. ↩ ↩2

  9. J. Gleason, A. Vinod, and M. Oishi, “Underapproximation of Reach-Avoid Sets for Discrete-Time Stochastic Systems via Lagrangian Methods,” in Proceedings of the IEEE Conference on Decision and Control, pp. 4283-4290, 2017. ↩ ↩2

  10. A. Vinod, B. HomChaudhuri, and M. Oishi, “Forward Stochastic Reachability Analysis for Uncontrolled Linear Systems using Fourier Transforms”, in Proceedings of the 20th International Conference on Hybrid Systems: Computation and Control (HSCC), pp. 35-44, 2017. ↩

  11. A. Genz, “Quadrature of a multivariate normal distribution over a region specified by linear inequalities: QSCMVNV”, 2014. ↩ ↩2 ↩3