2 research outputs found
Automated Synthesis of Safe and Robust PID Controllers for Stochastic Hybrid Systems
We present a new method for the automated synthesis of safe and robust
Proportional-Integral-Derivative (PID) controllers for stochastic hybrid
systems. Despite their widespread use in industry, no automated method
currently exists for deriving a PID controller (or any other type of
controller, for that matter) with safety and performance guarantees for such a
general class of systems. In particular, we consider hybrid systems with
nonlinear dynamics (Lipschitz-continuous ordinary differential equations) and
random parameters, and we synthesize PID controllers such that the resulting
closed-loop systems satisfy safety and performance constraints given as
probabilistic bounded reachability properties. Our technique leverages SMT
solvers over the reals and nonlinear differential equations to provide formal
guarantees that the synthesized controllers satisfy such properties. These
controllers are also robust by design since they minimize the probability of
reaching an unsafe state in the presence of random disturbances. We apply our
approach to the problem of insulin regulation for type 1 diabetes, synthesizing
controllers with robust responses to large random meal disturbances, thereby
enabling them to maintain blood glucose levels within healthy, safe ranges.Comment: Extended version of paper accepted at the 13th Haifa Verification
Conferenc
Automated Verification and Synthesis of Stochastic Hybrid Systems: A Survey
Stochastic hybrid systems have received significant attentions as a relevant
modelling framework describing many systems, from engineering to the life
sciences: they enable the study of numerous applications, including
transportation networks, biological systems and chemical reaction networks,
smart energy and power grids, and beyond. Automated verification and policy
synthesis for stochastic hybrid systems can be inherently challenging: this is
due to the heterogeneity of their dynamics (presence of continuous and discrete
components), the presence of uncertainty, and in some applications the large
dimension of state and input sets. Over the past few years, a few hundred
articles have investigated these models, and developed diverse and powerful
approaches to mitigate difficulties encountered in the analysis and synthesis
of such complex stochastic systems. In this survey, we overview the most recent
results in the literature and discuss different approaches, including
(in)finite abstractions, verification and synthesis for temporal logic
specifications, stochastic similarity relations, (control) barrier
certificates, compositional techniques, and a selection of results on
continuous-time stochastic systems; we finally survey recently developed
software tools that implement the discussed approaches. Throughout the
manuscript we discuss a few open topics to be considered as potential future
research directions: we hope that this survey will guide younger researchers
through a comprehensive understanding of the various challenges, tools, and
solutions in this enticing and rich scientific area