Formal Methods for Adaptive Control of Dynamical Systems
For control engineers, this provides a formal, correct-by-design method for adaptive control of systems with unknown parameters, addressing a known bottleneck in handling complex specifications.
The paper develops a method for controlling discrete-time systems with unknown constant parameters to satisfy LTL specifications, using formal methods to compute adaptive control strategies. The approach is correct by design, does not require a reference model, and handles a wider range of systems than traditional adaptive control.
We develop a method to control discrete-time systems with constant but initially unknown parameters from linear temporal logic (LTL) specifications. We introduce the notions of (non-deterministic) parametric and adaptive transition systems and show how to use tools from formal methods to compute adaptive control strategies for finite systems. For infinite systems, we first compute abstractions in the form of parametric finite quotient transition systems and then apply the techniques for finite systems. Unlike traditional adaptive control methods, our approach is correct by design, does not require a reference model, and can deal with a much wider range of systems and specifications. Illustrative case studies are included.