Contract Based Design of Symbolic Controllers for Interconnected Multiperiodic Sampled-Data Systems

Abstract

This paper deals with the synthesis of symbolic controllers for interconnected sampled-data systems where each component has its own sampling period. A compositional approach based on continuous-time assume-guarantee contracts is used. We provide sufficient conditions guaranteeing for a sampled-data system, satisfaction of an assume-guarantee contract and completeness of trajectories. Then, compositional results can be used to reason about interconnection of multiperiodic sampled-data systems. We then show how discrete abstractions and symbolic control techniques can be applied to enforce the satisfaction of contracts and ensure completeness of trajectories. Finally, theoretical results are applied to a vehicle platooning problem on a circular road, which show the effectiveness of our approach.

Controller Synthesis for Nonlinear Systems with Reachability Specifications Using Monotonicity

“…Proof: For this strategy to solve control synthesis problem of reaching the target set X 1 , it is sufficient that the closed-loop system satisfies the conditions of Proposition 1 since X − (T ) = X 1 . This is indeed the case since the conditions (18) and (19) coincide with (8) and (9) respectively written in a matrix form. It then follows that X − is strongly invariant and u enforces the monotonicity of the closed-loop system in graph(X − ).…”

“…One such area is the control of autonomous vehicles. In [19], for instance, an efficient solution to the vehicle platooning problem, which is based on monotonicity of the system, was proposed.…”

A symbolic approach to voltage stability and power sharing in time-varying DC microgrids

“…We are now ready to present the following proposition. The proof, which is the same reported in [18], is here omitted for sake of brevity.…”

“…To ensure that a component satisfies its contract, we can rely on symbolic methods, similarly to [18]. For systems with no control input, as the load subsystem, the same approach can be used to verify whether the contract is naturally satisfied or not.…”

Safety synthesis for incrementally stable switched systems using discretization-free multi-resolution abstractions

“…For systems that consist of interconnected components, compositional techniques have been developed that first compute discrete abstractions of the components that can be composed to compute an abstraction of the full system [32,26,18,28,20,41] or that can be used to synthesize controllers for the components, e.g. using assume-guarantee contracts that enforce a correct behavior at the system level [10,19,33,40]. Other works have explored the efficient encoding of discrete abstractions, e.g.…”