The technological developments of the past two decades have nurtured a fascinating convergence of computer science and electrical, mechanical and biological engineering. Nowadays, computer scientists work hand in hand with engineers to model, analyze and control complex systems, that exhibit discrete as well as continuous behavior. Examples of such systems include automated highway systems, air traffic management, automotive controllers, robotics and real-time circuits. They also include biological systems, such as immune response, bio-molecular networks, gene- regulatory networks, protein-signaling pathways and metabolic processes.
The more pervasive and more complex these systems become, the more is the infrastructure of our modern society relying on their dependability. Traditionally however, the modeling, analysis and control theory of discrete systems is quite different from the one of continuous systems. The first is based on automata theory, a branch of discrete mathematics, where time is typically abstracted away. The second is based on linear systems theory, of differential (or difference) equations, a branch of continuous mathematics where time is of essence. This course is focused on the principles underlying their combination. By the end of this course the students will be provided with detailed knowledge and substantial experience in the mathematical modeling, analysis and control of hybrid systems.
Hybrid automata as discrete-continuous models of hybrid systems. Executions and traces of hybrid automata. Infinite transition systems as a time-abstract semantics of hybrid automata. Finite abstractions of infinite transition systems. Language inclusion and language equivalence. Simulation and bisimulation. Quotient structures. Approximate notions of inclusion and simulation. State logics, and model checking. Partition-refinement and model checking within mu-calculus. Classes of hybrid automata for which the model-checking problem is decidable. Modern overapproximation techniques for reachability analysis. Simulation-based verification techniques. Controller synthesis problem for exact and approximate quotient structures. Stability, Lyapunov functions and differential invariants. Modern analysis and controller synthesis tools.
Didactic concept: The theoretical knowledge obtained in the lecture will be practiced in several exercises solved in groups.
Familiarity with elementary discrete and continuous mathematics, signals and systems and the control theory. Fluency in devising and writing simple mathematical proofs.
In particular, knowledge about the following topics is highly recommended:
- mathematics: (simulation of) difference/differential equations, approximation, linear algebra, discrete mathematics
- computer science: finite automata theory, logics and boolean algebra, first order logic, temporal logics, abstractions, model checking, formal verification
- control theory: signals and systems, observability, controllability, stability
Courses that cover these topics (additional to computer engineering undergraduate courses like Signals and Systems 1 and 2): Discrete Mathematics, Formal Methods of Computer Science
