Control And Data-driven modelling Using Symbolic methods (CADUSY)


Symbolic regression is a novel evolutionary optimization technique that searches for analytical expressions that fit measured numerical data. Symbolic regression has gained much attention recently in the scientific community for its ability to find mathematical laws that explain observed physical phenomena automatically, without human intervention. This has opened the path for the creation of a “robot scientist” where mathematical expressions are manipulated by a machine in a similar way as humans do. Symbolic regression has the potential to change many fields of science, in particular solving many challenges of system identification and control.

System identification, also known as data-driven modeling, aims at extracting low-complexity, but highly accurate, mathematical models of systems directly from measured data. Such models are crucial to synthesize controllers or to predict the response of the system under study. The major handicap of the state-of-the-art of system identification is the selection a priori of an actual model class. This involves imposing assumptions on the structural relationships of the model, which requires vast experience from the user and often leads to costly iterative processes to arrive at valid structural knowledge. For these reasons, system identification remains an arduous and challenging task.

Likewise, the successful synthesis of model-based nonlinear control systems strongly relies on the prior knowledge of the plant and the experience of the control engineer. The lack of general control synthesis algorithms that fulfill any desired control specification for any nonlinear system, results in each control problem being addressed individually. This results in costly (money and time-wise) processes, only attainable by teams of highly specialized control engineers.

Project team members

  • ir. Cees Verdier
  • dr. ir. Ivan Zapreev
  • dr. ir. Manuel Mazo Espinoza
  • <link en organisation departments cognitive-robotics-cor people profdr-r-babuska-robert _blank>prof. dr. ir. Robert Babuska


Learning approaches, correct-by-design controller synthesis, system identification, symbolic regression, genetic programming, cyber-physical systems, data-driven control, plug and play systems.

Sponsored by

This work is supported by NWO Domain TTW, the Netherlands, under the project CADUSY- TTW #13852.


The project is in collaboration with TU/e, ASML, Data Stories, Flanders Make and National Instruments. 

Goal/ objective

The goal of this project is to fully automate the process of system identification and control synthesis. To this end, we will parameterize the different ingredients involved in system identification and control and employ evolutionary symbolic methods to produce succinct and interpretable models and control laws with minimal required human supervision. The symbolic nature of these methods enables the representation and manipulation of models containing continuous dynamical elements alongside with logic expressions, typical of cyber-physical systems. Our main objective is to develop a novel game-changing software tool, which, by employing techniques from artificial intelligence (namely, symbolic regression), enables to automatically manipulate models and/or control laws in order to satisfy complex modeling and/or control objectives dictated by economical, performance and safety specifications. To this end we will expand the scientific knowledge in symbolic regression to new domains, in particular to control synthesis.

Work programme

The project is in callaboration with TU/e. The system identification side of the project is performed by our partners at TU/e and the automatic controller synthesis within DCSC.

For the control synthesis, the project is divided into the following work packages:

  1. Evolutionairy infrastructure
    The core of our proposal is rooted in an evolutionary system with a well-defined genome and the proper interfaces between the genes and the operators.

  2. Symbolic control synthesis
    In this work-package we will address the automatic synthesis of controllers for complex dynamical systems with complex specifications. By directly manipulating (symbolically) analytical expressions, we eliminate the need for direct discretization of the model in space (quantization), and allow expressing the controllers compactly in the form of analytical expressions, thus also facilitating their synthesis and implementation.

  3. Evaluation
    In this work package, we experimentally validate the automated I&C system we propose on two industrial benchmarks:
    1) A high performance motion control system for an ASML wafer stepper;
    2) A non-linear clutch system provided by Flanders Make.

Selected publications

Formal Controller Synthesis via Genetic ProgrammingC.F. Verdier, M. Mazo, Jr., In IFAC-PapersOnLine, Volume 50, Issue 1, 2017, Pages 7205-7210, ISSN 2405-8963.