Formal Synthesis of Analytic Controllers for Sampled-Data Systems via Genetic Programming

This paper presents an automatic formal controller synthesis method for nonlinear sampled-data systems with safety and reachability specifications. Fundamentally, the presented method is not restricted to polynomial systems and controllers. We consider a periodically switched controllers based on a Control Lyapunov Barrier-like function. The proposed method utilizes genetic programming to synthesize these function in analytic form, as well as the controller modes. Correctness of the controller are subsequently verified by means of a Satisfiability Modulo Theories solver. Effectiveness of the proposed methodology is demonstrated on multiple systems.

[1]  S. Sankaranarayanan,et al.  Counterexample Guided Synthesis of Switched Controllers for Reach-While-Stay Properties , 2015, ArXiv.

[2]  Sriram Sankaranarayanan,et al.  Robust controller synthesis of switched systems using counterexample guided framework , 2016, 2016 International Conference on Embedded Software (EMSOFT).

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

[4]  A. Packard,et al.  Searching for Control Lyapunov Functions using Sums of Squares Programming , 2022 .

[5]  Antoine Girard,et al.  CoSyMA: a tool for controller synthesis using multi-scale abstractions , 2013, HSCC '13.

[6]  Z. Artstein.  Stabilization with relaxed controls , 1983 .

[7]  Raymond Ros,et al.  A Simple Modification in CMA-ES Achieving Linear Time and Space Complexity , 2008, PPSN.

[8]  Bayu Jayawardhana,et al.  Stabilization with guaranteed safety using Control Lyapunov-Barrier Function , 2016, Autom..

[9]  Edmund M. Clarke,et al.  dReal: An SMT Solver for Nonlinear Theories over the Reals , 2013, CADE.

[10]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[11]  Friedrich L. Bauer,et al.  Revised report on the algorithm language ALGOL 60 , 1963, CACM.

[12]  Miroslav Krstic,et al.  A globally asymptotically stable polynomial vector field with no polynomial Lyapunov function , 2011, IEEE Conference on Decision and Control and European Control Conference.

[13]  Paulo Tabuada,et al.  Control Barrier Function Based Quadratic Programs for Safety Critical Systems , 2016, IEEE Transactions on Automatic Control.

[14]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[15]  Antonis Papachristodoulou,et al.  Generalised absolute stability and Sum of Squares , 2011, Proceedings of the 2011 American Control Conference.

[16]  Manuel Mazo,et al.  Formal Controller Synthesis via Genetic Programming , 2017 .

[17]  Peter A. Whigham,et al.  Grammatically-based Genetic Programming , 1995 .

[18]  Paulo Tabuada,et al.  Verification and Control of Hybrid Systems - A Symbolic Approach , 2009 .

[19]  A. Papachristodoulou,et al.  On the construction of Lyapunov functions using the sum of squares decomposition , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[20]  Cesare Tinelli,et al.  Satisfiability Modulo Theories , 2021, Handbook of Satisfiability.

[21]  Manuel Mazo,et al.  PESSOA: A Tool for Embedded Controller Synthesis , 2010, CAV.

[22]  Frank Allgöwer,et al.  CONSTRUCTIVE SAFETY USING CONTROL BARRIER FUNCTIONS , 2007 .