Elsevier

Automatica

Volume 139, May 2022, 110184
Automatica

Formal synthesis of closed-form sampled-data controllers for nonlinear continuous-time systems under STL specifications

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Abstract

We propose a counterexample-guided inductive synthesis framework for the formal synthesis of closed-form sampled-data controllers for nonlinear systems to meet STL specifications over finite-time trajectories. Rather than stating the STL specification for a single initial condition, we consider an (infinite and bounded) set of initial conditions. Candidate solutions are proposed using genetic programming, which evolves controllers based on a finite number of simulations. Subsequently, the best candidate is verified using reachability analysis; if the candidate solution does not satisfy the specification, an initial condition violating the specification is extracted as a counterexample. Based on this counterexample, candidate solutions are refined until eventually a solution is found (or a user-specified number of iterations is met). The resulting sampled-data controller is expressed as a closed-form expression, enabling both interpretability and the implementation in embedded hardware with limited memory and computation power. The effectiveness of our approach is demonstrated for multiple systems.

Keywords

Achievable controller performance
Optimal controller synthesis for systems with uncertainties
Formal controller synthesis
Temporal logic
Reachability analysis

Cited by (0)

Cees Ferdinand Verdier is a control and dynamics engineer at Hardt Hyperloop. He received his Ph.D. and M.Sc. degrees in Systems and Control in 2020 and 2015 respectively, and a B.Sc. degree in Mechanical Engineering in 2013, all from the Delft University of Technology, the Netherlands. From 2020 to 2021 he was a postdoctoral researcher at the same university. His main interests are hybrid systems, formal methods for control, and computational intelligence.

Niklas Kochdumper received the B.S. degree in Mechanical Engineering in 2015 and the M.S. degree in Robotics, Cognition and Intelligence in 2017, both from the Technical University of Munich, Germany. He is currently pursuing the Ph.D. degree in computer science at the Technical University of Munich, Germany. His research interests include formal verification of continuous and hybrid systems, reachability analysis, computational geometry, controller synthesis, and electrical circuits.

Matthias Althoff is an associate professor in Computer Science at the Technical University of Munich, Germany. He received his diploma engineering degree in Mechanical Engineering in 2005, and his Ph.D. degree in Electrical Engineering in 2010, both from the Technical University of Munich, Germany. From 2010 to 2012 he was a postdoctoral researcher at Carnegie Mellon University, Pittsburgh, USA, and from 2012 to 2013 an assistant professor at Technische Universität Ilmenau, Germany. His research interests include the formal verification of continuous and hybrid systems, reachability analysis, planning algorithms, nonlinear control, automated vehicles, robotics, and power systems.

Manuel Mazo Jr. is an associate professor at the Delft Center for Systems and Control, Delft University of Technology (The Netherlands). He received the Ph.D. and M.Sc. degrees in Electrical Engineering from the University of California, Los Angeles, in 2010 and 2007 respectively. He also holds a Telecommunications Engineering “Ingeniero” degree from the Polytechnic University of Madrid (Spain), and a “Civilingenjör” degree in Electrical Engineering from the Royal Institute of Technology (Sweden), both awarded in 2003. Between 2010 and 2012 he held a joint post-doctoral position at the University of Groningen and the innovation center INCAS3 (The Netherlands). His main research interest is the formal study of problems emerging in modern control system implementations, and in particular the study of networked control systems and the application of formal verification and synthesis techniques to control.

This work is supported by NWO Domain TTW under the CADUSY project #13852, the ERC Starting Grant SENTIENT (755953) and the ERC Consolidator Grant justITSELF (817629). The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Necmiye Ozay under the direction of Editor Daniel Liberzon.