DS0704 - Fondements du numérique

Finite Time Control and Estimation for System of Systems – Finite4SoS

Finite4SoS

Finite time control and estimation for Systems of Systems

Context, objectives, partners and positioning

Information technology revolution has become a reality together with its new challenges. Tomorrow we will need to manage Systems of Systems (SoS) with communication facilities, while requiring the best achievable performances: in particular robustness as well as severe time response constraints (for safety reasons, or simply to improve productivity). These technologies will deeply impact society and economy, in particular concerning the following areas:<br />• Service robotics and medical robotics turnover should be multiplied by eight in 2025 (strong inversion of the age pyramid and the increase in life expectancy in advanced countries).<br />• Embedded systems and software (Embedded Systems) that are present in the majority of the daily equipments and are involved in almost all industries (in France mostly within the Aero- nautics, Space, Defense and Automotive sectors: 70% of the embedded systems activity in France).<br />• Multi-modal transportation constitute an on-growing activity that is central in our future cities organization.<br /><br />SoS are composed with connected subsystems of possible different kinds, described by dynamical models and/or logical models. Finite4SoS will focus on dynamical models belonging to ordinary differential equations (ODE, “basic” dynamical motions), differential inclusions (DI, allowing for non-unique dynamics as well as switches or jumps in the dynamics), time delay systems (TDS, taking latencies into account, as in communication networks for example), partial differential equations (PDE, for spatial distribution of the dynamics) and their interconnections.<br /><br />Finite4SoS aims at developing a new promising framework to address control and estimation issues of SoS whose subsystems are described by ODE, DI, TDS, PDE, while achieving robustness and severe time performance constraints.

The project is organized around six tasks. Task 0 concerns the management aspects. Tasks 1 to 5 correspond to the announced objectives (see section 4.1). Let us recall that, in order to achieve our goal, Finite4SoS need to develop:
1. finite-time concepts and their characterization (Task 1),
2. designing tools for finite-time control and estimation (Task 2 for DI (and ODE), Task 3 for TDS, Task 4 for PDE),
3. tools for connecting these subsystems together (Task 5).
For each task, we will describe the partners involved and its timing, we will detail the work program, list the deliverables and discuss the risks and envisioned fall-back solutions.

The goal of Finite4SoS is as follows:
Finite4SoS aims at developing a new promising framework to address control and estimation issues of SoS whose subsystems are described by ODE, DI, TDS, PDE, while achieving robustness and severe time performance constraints.
Thus in order to achieve our goal, Finite4SoS needs to develop: firstly finite-time concepts and their characterization (Objective 1.), then finite-time control and estimation algorithms for each class of systems: ODE (see details of Objective 2.), DI (Objective 2.), TDS (Objective 3.), PDE (Objectives 4.) and lastly, tools to connect these subsystems and analyse the obtained SoS (Objective 5.). This will provide a framework to address control and estimation issues of SoS whose subsystems are described by ODE, DI, TDS and PDE while achieving the desired time performances.
This is the first report of the project: on a general basis the project has started with a good scientific interaction between the project members. However, we are not following exactly the schedule. This is due to two facts:
• The research on finite-time concept and their characterization were expected to be the main research topic during the first year of the project. However, essential difference between finite and infinite dimensional systems requested to change research plan in order to develop a uni- fied approach to development of finite-time concepts. A lot of efforts have been invested in study of finite-time stability and related problems for distributed parameter systems (TDS and PDE), see [4], [13], [12], [11], [14], [1].
• There were several important issues to needed to be solved (as soon as possible) for practical applicability of the theoretical results of the project. For example, the issues of discretization and digital of finite-time algorithms for ODE and DI systems have been studied in [7].
All this temporary shifted our research priorities to Task 5 and some particular issues of Task 2.

The project has started with strong collaborations and with high level results published in top jour- nals and conferences on the finite-toime stability. Some new scientific challenges have appeared such as numerical issue concerning simulation of ODE having this finite-time property.

see report and web site

Systems of Systems (SoS) are composed with interconnected dynamical subsystems with communication facilities, the natures of which lead to different
mathematical models: ordinary differential equations, differential inclusions, time delay systems, partial differential equations ....
Information technology revolution has become a reality together with its new challenges. One of them being the need to manage such SoS with communication facilities, while requiring the best achievable performances: in particular robustness as well as severe time response constraints (for safety reasons, or simply to improve productivity). These technologies will deeply impact society and economy, in particular concerning the following areas: Service robotics, Embedded systems, multi-modal transportation, ...

Finite4SoS aims at developing a new promising framework to address control and estimation issues of SoS subject to this model diversity, while achieving robustness as well as severe time response constraints.

The key ingredients are: finite-time concepts, which will help in managing severe time constraints; homogeneity and time-varying feedback,
which are the main tools for achieving the finite-time property for both convergence and input-to-state stability for each class of system. These concepts will help for both cascade and feedback connections (for example, feedback homogeneization will preserve the finite-time property).

Finite4SoS will develop: firstly finite-time concepts and their characterization (Objective 1.), then finite-time control and estimation algorithms for each class of systems: Oridnary differential equations ODE and Differential Inclusion DI (Objective 2.), Time Delay Systems TDS (Objective 3.), Partial Differential Equations PDE (Objectives 4.) and lastly, tools to connect and analyse these subsystems together (Objective 6.). This will provide a framework to address control and estimation issues of SoS whose subsystems are described by ODE, DI, TDS and PDE while achieving the desired time performances.

Three research groups with the right level of complementary expertise in control, estimation and finite time concepts will collaborate on this project: the NON-A team from Inria Lille (Inria-CNRS-Ecole Centrale de Lille), LJLL from UPMC (in partnership with CNRS) and CAOR from ARMINES (Mines ParisTech).

Project coordination

Wilfrid PERRUQUETTI (ECOLE CENTRALE LILLE)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

Inria Inria Lille - Nord Europe
UPMC Université Pierre et Marie Curie
CRISTAL ECOLE CENTRALE LILLE

Help of the ANR 517,992 euros
Beginning and duration of the scientific project: September 2015 - 48 Months

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