Guaranteed Control Synthesis for Continuous Systems in Uppaal Tiga

We present a method for synthesising control strategies for continuous dynamical systems. We use Uppaal Tiga for the synthesis in combination with a set-based Euler method for guaranteeing that the synthesis is safe. We present both a general method and a method which provides tighter bounds for monotone systems. As a case-study, we synthesize a guaranteed safe strategy for a simplified adaptive cruise control application. We show that the guaranteed strategy is only slightly more conservative than the strategy generated in the original adaptive cruise control paper which uses a discrete non guaranteed strategy. Also, we show how reinforcement learning may be used to obtain optimal sub-strategies.

[1]  Antoine Girard,et al.  Contract based Design of Symbolic Controllers for Vehicle Platooning , 2018, HSCC.

[2]  Antoine Girard,et al.  Symbolic models for incrementally stable switched systems with aperiodic time sampling , 2018, ADHS.

[3]  Kim G. Larsen,et al.  Verification and Performance Evaluation of Timed Game Strategies , 2014, FORMATS.

[4]  Antoine Girard,et al.  Safety control with performance guarantees of cooperative systems using compositional abstractions , 2015, ADHS.

[5]  Antoine Girard,et al.  Synthesis for Constrained Nonlinear Systems Using Hybridization and Robust Controllers on Simplices , 2012, IEEE Transactions on Automatic Control.

[6]  Sanjit A. Seshia,et al.  Symbolic control design for monotone systems with directed specifications , 2017, Autom..

[7]  Kim G. Larsen,et al.  Safe and Optimal Adaptive Cruise Control , 2015, Correct System Design.

[8]  Antoine Girard,et al.  Controller synthesis for safety and reachability via approximate bisimulation , 2010, Autom..

[9]  David Angeli,et al.  Monotone control systems , 2003, IEEE Trans. Autom. Control..

[10]  Kim G. Larsen,et al.  Online and Compositional Learning of Controllers with Application to Floor Heating , 2016, TACAS.

[11]  J D Pinter,et al.  Global Optimization in Action—Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications , 2010 .

[12]  Antoine Girard,et al.  Robust controlled invariance for monotone systems: Application to ventilation regulation in buildings , 2016, Autom..

[13]  Andrzej Marciniak,et al.  A Survey of Interval Runge-Kutta and Multistep Methods for Solving the Initial Value Problem , 2007, PPAM.

[14]  Nicolas Markey,et al.  Compositional synthesis of state-dependent switching control , 2018, Theor. Comput. Sci..

[15]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results , 2009, IEEE Transactions on Automatic Control.

[16]  Antoine Girard,et al.  On the Composition of Discrete and Continuous-time Assume-Guarantee Contracts for Invariance , 2018, 2018 European Control Conference (ECC).

[17]  Alexandre Chapoutot,et al.  Enclosing Temporal Evolution of Dynamical Systems Using Numerical Methods , 2013, NASA Formal Methods.

[18]  Julien Alexandre Dit Sandretto,et al.  An improved algorithm for the control synthesis of nonlinear sampled switched systems , 2018, Formal Methods Syst. Des..

[19]  Kim G. Larsen,et al.  UPPAAL-Tiga: Time for Playing Games! , 2007, CAV.

[20]  O. Bouissou,et al.  GRKLib: a Guaranteed Runge Kutta Library , 2006, 12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006).

[21]  Kim G. Larsen,et al.  Uppaal Stratego , 2015, TACAS.

[22]  Laurent Fribourg,et al.  Control of Switching Systems by Invariance Analysis: Application to Power Electronics , 2013 .

[23]  Laurent Fribourg,et al.  Control Synthesis of Nonlinear Sampled Switched Systems using Euler's Method , 2017, SNR@ETAPS.

[24]  Nedialko S. Nedialkov,et al.  Validated solutions of initial value problems for ordinary differential equations , 1999, Appl. Math. Comput..

[25]  Kim G. Larsen,et al.  On Time with Minimal Expected Cost! , 2014, ATVA.

[26]  Paulo Tabuada,et al.  Approximately Bisimilar Symbolic Models for Incrementally Stable Switched Systems , 2008, IEEE Transactions on Automatic Control.

[27]  Majid Zamani,et al.  SCOTS: A Tool for the Synthesis of Symbolic Controllers , 2016, HSCC.

[28]  T. Donchev,et al.  Stability and Euler Approximation of One-sided Lipschitz Differential Inclusions , 1998 .

[29]  Adrien Le Coënt,et al.  Guaranteed control synthesis for switched space-time dynamical systems. (Synthèse de contrôle garanti pour des systèmes dynamiques spatio-temporels à commutation) , 2017 .

[30]  Gustaf Söderlind,et al.  On nonlinear difference and differential equations , 1984 .

[31]  Sean Sedwards,et al.  Bounding Errors Due to Switching Delays in Incrementally Stable Switched Systems (Extended Version) , 2018, ADHS.