Approximate supervisory control of nonlinear systems with outputs

Existing results concerning control design of purely continuous or hybrid systems with complex logic-based specifications assume full information of the state, or of its quantization, which may be not available in concrete applications. In this paper we consider the more realistic scenario where the controller cannot access the state of the plant but can only access a quantized measurement of its output. We focus on a control problem where the plant is described by a possibly unstable continuous-time nonlinear system with outputs, the controller is dynamic, digital and quantized, and takes as input a (quantized) measurement of the output of the plant, and the specification is expressed in terms of regular languages. The solution to the control problem is based on the use of formal methods. A finite states system approximating the plant is first derived which is then used to find the solution to the control problem.

[1]  Antoine Girard,et al.  Approximate Bisimulation: A Bridge Between Computer Science and Control Theory , 2011, Eur. J. Control.

[2]  Maria Domenica Di Benedetto,et al.  Integrated Design of Symbolic Controllers for Nonlinear Systems , 2012, IEEE Transactions on Automatic Control.

[3]  George J. Pappas.  LINEAR TIME LOGIC CONTROL OF LINEAR SYSTEMS , 2004 .

[4]  Christos G. Cassandras,et al.  Introduction to Discrete Event Systems , 1999, The Kluwer International Series on Discrete Event Dynamic Systems.

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

[6]  Paulo Tabuada,et al.  Symbolic Models for Nonlinear Control Systems: Alternating Approximate Bisimulations , 2007, SIAM J. Control. Optim..

[7]  Maria Domenica Di Benedetto,et al.  On symbolic control design of discrete-time nonlinear systems with state quantized measurements , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[8]  Paulo Tabuada.  An Approximate Simulation Approach to Symbolic Control , 2008, IEEE Transactions on Automatic Control.

[9]  Calin Belta,et al.  Language-Guided Controller Synthesis for Linear Systems , 2014, IEEE Transactions on Automatic Control.

[10]  Maria Domenica Di Benedetto,et al.  Integrated symbolic design of unstable nonlinear Networked Control Systems , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[11]  Antoine Girard,et al.  Approximation Metrics for Discrete and Continuous Systems , 2006, IEEE Transactions on Automatic Control.

[12]  Antoine Girard,et al.  Low-Complexity Quantized Switching Controllers using Approximate Bisimulation , 2012, ArXiv.

[13]  J. E. Rooda,et al.  Sampled-data control of hybrid systems with discrete inputs and outputs , 2009, ADHS.

[14]  Pierre Wolper,et al.  Memory-efficient algorithms for the verification of temporal properties , 1990, Formal Methods Syst. Des..

[15]  Calin Belta,et al.  Temporal logic control of discrete-time piecewise affine systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

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

[17]  Gunther Reissig,et al.  Feedback refinement relations for symbolic controller synthesis , 2014, 53rd IEEE Conference on Decision and Control.

[18]  Eduardo D. Sontag,et al.  Mathematical control theory: deterministic finite dimensional systems (2nd ed.) , 1998 .

[19]  Maria Domenica Di Benedetto,et al.  Symbolic Control Design of Nonlinear Networked Control Systems , 2014, ArXiv.

[20]  Manuel Mazo,et al.  Symbolic Models for Nonlinear Control Systems Without Stability Assumptions , 2010, IEEE Transactions on Automatic Control.

[21]  Susan H. Rodger,et al.  JFLAP: An Interactive Formal Languages and Automata Package , 2006 .

[22]  Maria Domenica Di Benedetto,et al.  Symbolic Models and Control of Discrete-Time Piecewise Affine Systems: An Approximate Simulation Approach , 2014, IEEE Transactions on Automatic Control.

[23]  Stavros Tripakis,et al.  On-the-Fly Controller Synthesis for Discrete and Dense-Time Systems , 1999, World Congress on Formal Methods.