Contract-Based Design of Symbolic Controllers for Safety in Distributed Multiperiodic Sampled-Data Systems

Abstract

This paper presents a symbolic control approach to the design of distributed safety controllers for a class of continuous-time nonlinear systems. More precisely, we consider systems made of components where each component is equipped with a sampled-data controller with its own sampling period, resulting globally in a distributed multiperiodic sampled-data system. Moreover, controllers receive partial information on the state of the other components. We propose a component-based approach to controller synthesis, which relies on the use of abstractions and continuous-time assume-guarantee contracts. The abstractions describe the dynamics of the system from the point of view of each component based on the information structure, while assume-guarantee contracts specify guarantees that a component must satisfy if assumptions on the other components are met. We show that our approach makes it possible to decompose a global safety control problem into local ones that can be solved independently. We then show how symbolic control techniques can be used to synthesize controllers that enforce the local control objectives. Illustrative applications in building automation and vehicle platooning are shown.

Compositional Synthesis of Symbolic Controllers for Attractivity Specifications

“…We presented an algorithm for systems with finite state and input spaces and we have shown, using an example, how our approach can also be used to design controllers for systems with infinite state and input spaces using symbolic abstractions. Future work will focus on extending the approach to other types of specifications and to other types of interconnected systems such as systems with overlapping components as in [11], [14].…”

“…With that respect, assume-guarantee contracts offer an appealing theoretical framework [4] where a global system specification is decomposed in contracts specifying the obligations of a component under assumptions on the behavior of other components. Several approaches for compositional synthesis of symbolic controllers make use of such contracts [8], [10], [6], [14]. Some other approaches are based on generalizations of the celebrated small-gain theorem [5], [12], [1], [2].…”

Compositional safety rules for inter-triggering hybrid automata

“…Our self-safety and responsibility rules utilize this structure to provide sufficient conditions for global safety. In comparison, existing compositional frameworks, such as [5,9,14,17,19,22,23,25], that give sufficient conditions for global safety allow agents' dynamics to be coupled but do not allow for triggering actions. • We note that our approach can be extended to guarantee safety for settings in which individual systems may have communication delays or sensor noise by leveraging recent advances in invariant set computation [10,12,15,29] for systems with these imperfections.…”

“…On the other extreme, one can analyze agents individually, assuming all of the remaining agents act adversarially, in which case safety is hard to attain, if at all possible. Several frameworks have been developed between these two extremes to capture various notions of coordination, collaboration, or contracts [5,6,9,14,17,23,25,28].…”

Approximately symbolic models for a class of continuous-time nonlinear systems

“…Although continuous-time systems are extensively studied and various abstraction techniques are proposed in the existing literature, most techniques for the construc-tion of symbolic models require time-space discretization of the continuous-time system, which constitute property satisfaction non-trivial since closeness of the observed behaviors between the concrete system and its abstraction is not guaranteed within neighboring discrete time instants. Recently, different approaches have been proposed in the literature to deal with this [20,22,29]. In [22], a disturbance simulation relation is introduced for incrementally input-to-state stable nonlinear systems.…”