Dieky Adzkiya

Muhammad Syifa'ul Mufid, Dieky Adzkiya, Alessndro Abate

This paper describes the development of finite abstractions of Max-Plus-Linear (MPL) systems using tropical operations. The idea of tropical abstraction is inspired by the fact that an MPL system is a discrete-event model updating its state with operations in the tropical algebra. The abstract model is a finite-state transition system: we show that the abstract states can be generated by operations on the tropical algebra, and that the generation of transitions can be established by tropical multiplications of matrices. The complexity of the algorithms based on tropical algebra is discussed and their performance is tested on a numerical benchmark against an existing alternative abstraction approach.

Dieky Adzkiya, Manuel Mazo

We discuss the scheduling of a set of networked control systems implemented over a shared communication network. Each control loop is described by a linear-time-invariant (LTI) system with an event-triggered implementation. We assume the network can be used by at most one control loop at any time instant and after each controller update, a pre-defined channel occupancy time elapses before the network is available. In our framework we offer the scheduler two options to avoid conflicts: using the event-triggering mechanism, where the scheduler can choose the triggering coefficient; or forcing controller updates at an earlier pre-defined time. Our objective is avoiding communication conflict while guaranteeing stability of all control loops. We formulate the original scheduling problem as a control synthesis problem over a network of timed game automata (NTGA) with a safety objective. The NTGA is obtained by taking the parallel composition of the timed game automata (TGA) associated with the network and with all control loops. The construction of TGA associated with control loops leverages recent results on the abstraction of timing models of event-triggered LTI systems. In our problem, the safety objective is to avoid that update requests from a control loop happen while the network is in use by another task. We showcase the results in some examples.