Max Cohen got the best ME PhD dissertation award!

... and is now moving to Postdoctoral Position at Caltech. Congratulations Max

New book: Safe Autonomy with Control Barrier Functions

Wei Xiao, Christos G. Cassandras, Calin Belta, Safe Autonomy with Control Barrier Functions, Springer, 2023, DOI:

About the book:

This book presents the concept of Control Barrier Function (CBF), which captures the evolution of safety requirements during the execution of a system and can be used to enforce safety. Safety is formalized using an emerging state-of-the-art approach based on CBFs, and many illustrative examples from autonomous driving, traffic control, and robot control are provided. Safety is central to autonomous systems since they are intended to operate with minimal or no human supervision, and a single failure could result in catastrophic results. The authors discuss how safety can be guaranteed via both theoretical and application perspectives. This presented method is computationally efficient and can be easily implemented in real-time systems that require high-frequency reactive control. In addition, the CBF approach can easily deal with nonlinear models and complex constraints used in a wide spectrum of applications, including autonomous driving, robotics, and traffic control. With the proliferation of autonomous systems, such as self-driving cars, mobile robots, and unmanned air vehicles, safety plays a crucial role in ensuring their widespread adoption. This book considers the integration of safety guarantees into the operation of such systems including typical safety requirements that involve collision avoidance, technological system limitations, and bounds on real-time executions. Adaptive approaches for safety are also proposed for time-varying execution bounds and noisy dynamics.

New book: Adaptive and Learning-Based Control of Safety-Critical Systems

Max Cohen and Calin Belta, Adaptive and Learning-Based Control of Safety-Critical Systems, Springer, 2023, DOI:

About the book:

This book stems from the growing use of learning-based techniques, such as reinforcement learning and adaptive control, in the control of autonomous and safety-critical systems.  Safety is critical to many applications, such as autonomous driving, air traffic control, and robotics.  As these learning-enabled technologies become more prevalent in the control of autonomous systems, it becomes increasingly important to ensure that such systems are safe.  To address these challenges, the authors provide a self-contained treatment of learning-based control techniques with rigorous guarantees of stability and safety.  This book contains recent results on provably correct control techniques from specifications that go beyond safety and stability, such as temporal logic formulas.  The authors bring together control theory, optimization, machine learning, and formal methods and present worked-out examples and extensive simulation examples to complement the mathematical style of presentation.  Prerequisites are minimal, and the underlying ideas are accessible to readers with only a brief background in control-theoretic ideas, such as Lyapunov stability theory.

Machine, meet stem cells: paper in Cell Systems, Nov. 2019

Gladstone Institutes News: “Machine, meet stem cells”, Nov. 20, 2019,

Science: Robotics paper on robots making hot dogs

Also check some media on this publication:

Singularity Hub: “How Two Robots Learned to Grill and Serve the Perfect Hot Dog”, Dec. 19, 2019


Inverse: “This self-aware robot can cook and serve hot dogs”, Dec. 19, 2019,


Boston University Engineering Spotlight Research: “Robot Reinforcement”, Dec. 19, 2019,

Calin is a Distinguished Lecturer of the IEEE Control System Society

The appointment for the Distinguished Lecturer of the IEEE Control System Society starts January 1, 2019 and ends December 31, 2021.

Details about the program can be found here:



Calin teaches an EECI course in Paris, Saclay, Jan 14-18, 2018

The course is titled "Formal Methods in Control Design - from Discrete Synthesis to Continuous Controllers" and is co-taught with Antoine Girard. It is offered as part of the INTERNATIONAL GRADUATE SCHOOL ON CONTROL (IGSC) PROGRAM in the European Embedded Control Institute (EECI).

To register, follow this link:

The schedule is available here:

Summary of the course

In control theory, complex models of continuous physical processes, such as systems of differential or difference equations, are usually checked against simple specifications, such as stability and set invariance. With the development and integration of cyber-physical and safety-critical systems, there is an increasing need for tools to design controllers for richer specifications. The main objective of this course is to present formal methods in control design. The key concept of these approaches is that of discrete abstraction (a.k.a. symbolic model), which is a finite-state dynamical system, obtained by abstracting continuous trajectories over a finite set of symbols. When the abstraction and the continuous dynamics are formally related by some behavioral relationship (e.g. simulation or bisimulation relations), controllers synthesized for the abstraction can be refined to certified controllers for the original continuous system. Moreover, since the abstractions are discrete, controllers can be synthesized automatically, using discrete synthesis techniques, for rich specifications such as languages or formulas of temporal logics. In this course, we will cover all aspects of formal methods in control design from the computation of discrete abstractions, to discrete synthesis and controller refinement.


1. The need for formal methods in control design

2. Systems, behaviors and relations among them

3. Discrete abstractions of continuous systems

3.1 Partition-based approaches

3.2 Lyapunov-based approaches

3.3 Abstraction via feedback

4. Controller synthesis using discrete abstractions

4.1 Finite temporal logic control

4.2 Language-guided control systems

4.3 Optimal temporal logic control

Calin featured in the IEEE CSM

People in Control:


Calin is co-organizing a Dagstuhl Seminar on Formal Synthesis

May 14 – 19 , 2017, Dagstuhl Seminar 17201

Formal Synthesis of Cyber-Physical Systems


Calin A. Belta (Boston University – Brookline, US)
Rupak Majumdar (MPI-SWS – Kaiserslautern, DE)
Majid Zamani (TU München, DE)


Matthias Rungger (TU München, DE)

New book on formal methods for dynamical systems

Our book

Calin Belta, Boyan Yordanov, and Ebru Aydin Gol, Formal Methods for Discrete-Time Dynamical Systems, Springer, 2017 (ISBN: 978-3-319-50762-0) has been published and is available at: