## (Closed) PhD Position: Distributed Parameter Systems

Post date: Mar 23, 2015 10:47:56 AM

### Modular Analysis and Control of Interconnected Systems of Conservation Laws: Electric, Hydraulic and Pneumatic Distribution Networks

**Application Deadline: **In order to receive full consideration, the application should be received no later than April 30th, 2015. CLOSED

**Laboratory: **Ampère, UMR CNRS 5005

**Main Scientific Domain: ***Control Systems*

**Secondary Scientific Domains: **Applied mathematics, energy distribution networks

**Keywords: **Control and Observation of infinite-dimensional systems, interconnected systems, networked systems, conservation laws, hyperbolic PDEs, distribution networks.

**Candidate profile**: Control Systems, Applied Mathematics, some electrical/mechanical engineering knowledge is desirable.

**Subject description:**

Networks of balance laws are defined by the interconnection (mainly through boundary conditions) of subsystems individually characterized by the conservation of certain quantities (mass/charge/etc.). These systems are often encountered when modeling distribution networks (for energy, water, fuel, etc.). As these systems adopt more complicated topologies and decentralized structures (aiming to increase the resilience of the network with respect to localized failures), new challenges are introduced. In this PhD, the candidate will study some of the problems linked to the large-scale interconnection of infinite-dimensional (distributed parameter) systems. Two motivating examples are the control of high-voltage direct current (HVDC) networks and the problem of leak detection and localization in pipelines.

The general objective of this PhD is the development of modular tools and methods for the study of networks of conservation laws. Guided by recent developments in the domain of control systems concerning both infinite-dimensional systems and networked systems, we propose to address the following points:

*Modeling:*generic elementary modules (components) for the network (electric/hydraulic/pneumatic); interconnection conditions between modules (active or passive); generic network formulation (components, inputs/outputs and interconnections).*Analysis:*stability, controllability (stabilizability) and observability (detectability) conditions under actuation/sensing/communication constraints (local or global control/information), definition of performance criteria.*Synthesis and Optimization:*Estimation and control laws under actuation/sensing/information constraints and optimization of performance criteria.

One of the main originalities of this work consists on taking into account the infinite-dimensional dynamics of the distribution lines, which is particularly important when studying transient regimes. Using reduced- order models (e.g., quasi-static models or fixed-frequency models) can force the adoption of a certain level of conservatism in order to avoid problems linked to unmodeled dynamics. This conservatism is, in general, not well characterized. Another key aspect is the modularity of the tools developed (in order to maximize the domain of application) and accounting for computational constraints (both real-time and offline).

**See full description and contact information in the attached ****PDF file****.**