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Reporting period: 2022-08-01 to 2023-01-31

The advances in electronic communication and computation have enabled the ubiquity of Cyber-Physical Systems (CPS): digital systems that regulate and control all sorts of physical processes, such as chemical reactors, water distribution and power networks. These systems require the timely communication of sensor measurements and control actions to provide their prescribed functionalities. Event-triggered control (ETC) techniques, which communicate only when needed to enforce performance, have attracted attention as a mean to reduce the communication traffic and save energy on (wireless) networked control systems (NCS). However, despite ETC’s great communication reductions, the scheduling of the aperiodic (and largely unpredictable) traffic that ETC generates remains widely unaddressed – hindering its true potential for energy and bandwidth savings.

To address this problem, in the project SENTIENT we are investigation the following scientific challenges:

- the construction of models for ETC’s communication traffic;
- the design of schedulers based on such models guaranteeing prescribed performance levels.

These challenges are addressed employing methods at the cross-roads between theoretical computer science, control systems and communications engineering.
In particular, we are following a two step approach:

1. modeling as timed-priced-game-automata (TPGA) the timing of communications of event-triggered control systems;
2. solving games over TPGAs to prevent data communication collisions and ensure prescribed performances for the control tasks.

The project's most practical outcome are algorithms (and their software implementations) facilitating the efficient implementation of control loops over shared communication resources, and increasing the energy efficiency of wireless NCS.
The advances will be demonstrated on automotive and wireless water-distribution control applications, showcasing the potential economic impact from the reduction of implementation and maintenance costs on CPSs.
1. A change of paradigm when constructing traffic abstractions has been proposed and developed: instead of partitioning the space and then compute the associated times, reversing the logic and partitioning first time and then compute the associated state-space regions help mitigate in part the curse of dimensionality. This approach has been reflected first on a publication at Necsys 2018 and used in two journal papers (one for linear systems and the other for non-linear systems).
2. The construction of abstractions considering the presence of disturbances has been addressed for linear systems in two forms reflected on the conference paper in Necsys 2018 and on a published paper at the IEEE Transactions on Automatic Control.
3. The work on abstractions for non-linear systems has led to the discovery of some theoretical problems in the paper of Anta, Tabuada (TAC 2011) which served as basis for our research plan. These issues have been solved and a more effective computational approach to construct isochronous manifolds has been proposed. These advances have been published in a journal publication (IEEE TAC, 2020) with an application to self-triggered control (STC).
4. Progress on distributed abstractions has been made to enable our first experiments on wireless control of water distribution systems. These experiments have been performed on a Hardware-in-the-loop setup in collaboration with the University of Trento, illustrating how a low-power wireless communication protocol can be used to implement event-triggered controllers. This has lead to a journal publication (ACM TCPS, 2021)
5. An open-source tool, ETCetera, has been constructed to generate models of the event-triggered control traffic from mathematical models of the plant, controller and event-triggering mechanism. The construction of the abstractions is heavily parallelized for efficiency. The models can be ported to UPPAAL for their analysis and to synthesize schedulers. The tool additionally allows for scheduler design natively in the case of PETC (Periodic Event-Triggered Control) systems, and optimization of sampling mechanisms for average channel use (Self-triggered control). The tool has been announced and described in a publication at HSCC'22.
6. A test-bed for the testing of wireless control in the context of water distribution has been instrumented with a network of wireless sensors and actuators and some experimental evaluations have been performed on it.
7. The study of PETC systems has lead to the discovery of interesting chaotic behavior in the inter-sampling times dynamics, even for simple linear system dynamics, with event-based control updates (IEEE TAC 2023).
8. The models devised for PETC traffic have been exploited to construct more efficient sampling schemes (self-triggered) optimizing the average channel usage.
9. The traffic abstractions work has been extended to cope with stochastic disturbances affecting the dynamics, resulting in models in the form of Interval Markov Decision Processes (IMDPs).
10. Finally, some advances have been made in the construction of abstractions purely from data, without the need of a precise model of the dynamics or event-triggering mechanism.
The expected advances will go beyond the state of the art in several directions:

1. providing models of traffic of ETC systems, which are largely unavailable at this moment.
2. allowing a more methodological evaluation of ETC systems and their expected communication reductions, through automatic analysis of the constructed models
3. enabling the (automated) synthesis of schedulers for ETC systems in a modular and scalable way, by advancing the theory of games over timed-automata.

These advances, together with their implementations as software packages greatly simplify the design and analysis of event-based systems, and in turn of more efficient Cyber-Physical Systems in which networking is central.
Isochronous manifolds of an event-based controlled non-linear system
Trajectories and timing of a self-triggered controlled non-linear system
Wireless Water Irrigation System Testbed