An inverse control problem is formulated as follows: given a set of trajectories and a control system, find a cost such that these paths are optimal. The first question to ask is the uniqueness of the solution of such a problem. For general classes of costs the problem appears to be very difficult, even with a trivial dynamics. We are therefore interested in this issue for the class of costs which are quadratic in the control, when the dynamics depend linearly in the control (Riemannian and sub-Riemannian case). In this case we can reduce the problem to the question of the existence of geodesically equivalent metrics and the existing results will be described, from the theorem of Levi-Civita (1890) to those we obtained recently with Sofya Maslovskaya and Igor Zelenko.

### Séminaire d'Automatique du Plateau de Saclay : Inverse optimal control: the sub-Riemannian case

**Frédéric Jean (ENSTA)**

### Control of Fuel Cell Hybrid Power Systems

**Prof. Jian Chen, College of Control Science and Engineering, Zhejiang University, Hangzhou, China**

with the environment and energy crisis worsening, fuel cells have shown signiﬁcant potential as an alternative energy conversion device with high efﬁciency and low environmental impact. In particular, Fuel cells are promising for new energy automotive applications. Fuel cell hybrid power systems usually include fuel cells and lithium-Ion batteries. In this presentation, I will talk about control of fuel cell systems, SOC Estimation of Lithium-Ion Batteries, and adaptive control strategies of fuel cell/battery hybrid power systems.

Biography: Jian Chen (M’06-SM’10) received the B.E. and M.E. degrees from Zhejiang University, Hangzhou, China, in 1998 and 2001, respectively, and the Ph.D. degree from Clemson University, South Carolina, USA, in 2005. From 2006 to 2008, he was as a research fellow working on fuel cell modeling and control at the University of Michigan, Ann Arbor, MI, USA. He joined IdaTech LLC, Oregen, USA, working on fuel cell back power systems and Proterra Inc., South Carolina, USA, working on the National Fuel Cell Bus Program, in 2008 and 2012, respectively. In 2013, he joined the Department of Control Science and Engineering, Zhejiang University, Hangzhou, China. Dr. Chen is currently a professor with the College of Control Science and Engineering, Zhejiang University, Hangzhou, China. He has been supported by the Chinese Recruitment Program of Global Youth Experts since 2012 and received the Major Program of National Natural Science Foundation of China on Modeling and Control of Fuel Cell vehicles in 2014. His research interests include fuel cell modeling and control, battery management, visual servo techniques, and nonlinear control.

### Séminaire d'Automatique du Plateau de Saclay: Virtual Inertia Emulation and Placement in Power Grids

**Florian Dörfler (ETH Zurich)**

A major transition in the operation of electric power grids is the replacement of bulk generation based on synchronous machines by distributed generation based on low-inertia power electronic sources. The accompanying "loss of rotational inertia" and the fluctuations by renewable sources jeopardize the system stability, as testified by the ever-growing number of frequency incidents. As a remedy, numerous studies demonstrate how virtual inertia can be emulated through various devices, but few of them address the question of "where" to place this inertia. It is however strongly believed that the placement of virtual inertia hugely impacts system efficiency, as demonstrated by recent case studies. We carry out a comprehensive analysis in an attempt to address the optimal inertia placement problem, considering a linear network-reduced power system model along with an H2 performance metric accounting for the network coherency. The optimal inertia placement problem turns out to be non-convex, yet we provide a set of closed-form global optimality results for particular problem instances as well as a computational approach resulting in locally optimal solutions. We illustrate our results with a three-region power grid case study and compare our locally optimal solution with different placement heuristics in terms of different performance metrics.

### Séminaire d'Automatique du Plateau de Saclay: A modular design of incremental Lyapunov functions for microgrid control

**Claudio De Persis (Groningen University)**

In this talk we propose a Lyapunov based analysis of microgrids. The starting point is an energy function comprising the kinetic energy associated with the elements that emulate the rotating machinery and terms taking into account the reactive power stored in the lines and dissipated on shunt elements. We then shape this energy function with the addition of an adjustable voltage-dependent term, and construct incremental storage functions satisfying suitable dissipation inequalities. The choice of the voltage-dependent term depends on the voltage dynamics/controller under investigation. Several microgrids dynamics that have similarities or coincide with dynamics already considered in the literature are captured in this incremental energy analysis framework. These incremental storage functions allow for a complete analysis of the coupled microgrid obviating the need for simplifying linearization techniques and for the restrictive decoupling assumption in which the frequency dynamics is fully separated from the voltage one.

### Characterization of Photovoltaic systems for Large Scale Solar Power Generation

**Fernando Mancilla-David**

Photovoltaic electric power generation is increasingly attracting the attention of industry and academia mainly motivated by the urgent need to depart from fossil fuel-based electricity generation. As the cost of PV panels production continues to decrease, it is expected that bulk solar power generation will be competitive with other forms of renewable energy, and hence massively deployed. Grid-connected PV power plants are currently generating up to a few megawatts as a single unit, and built through PV arrays containing hundreds of thousands of solar cells. The PV plant is connected to the ac grid via a power electronics-based interphase realized through a voltage source inverter.

The seminar presents research conducted at the University of Colorado Denver on the modeling and control of this type of systems, often referred to as large PV power plants. The modeling of the various elements making up a large PV power plant, namely PV cells, inverter and an equivalent of the ac grid, will be discussed. Furthermore, the seminar addresses the PV array's maximum power point tracking and the regulation of current injection into the ac grid. Considerations regarding the identification of solar irradiance are also to be discussed. The modeling and control techniques presented within the seminar are validated through computer simulations and/or experimentation performed in the University of Colorado Denver campus.

Biography

Fernando Mancilla-David is an Associate Professor at the University of Colorado Denver, where he teaches and directs research in energy and power systems as a faculty member of the Electrical Engineering Department. Prof. Mancilla-David received the B.S. degree in electrical engineering from the Universidad Tecnica Federico Santa Maria, Valparaiso, Chile, in 1999, and the M.S. and Ph.D. degrees in electrical engineering from the University of Wisconsin-Madison, Madison, Wisconsin, United State of America, in 2002 and 2007, respectively. He has been a visiting professor in several universities in Europe and has coauthored more than 60 technical articles, mostly in the area of utility applications of power electronics.

### Pseudorational transfer functions and their spectral properties - an introductory survey

**Yutaka Yamamoto, univ of Kyoto**

This talk gives an overview of the class of pseudorational transfer functions. This class consists of the ratio of entire functions of exponential type that are Laplace transforms of distributions with compact support. It gives rise to a convenient platform for dealing with distributed parameter systems whose state space is determined by bounded-time data. Delay-differential systems, with retarded, neutral or distributed delays, are typical examples. We explore its interesting interplay with the ring of entire functions, and highlight some appealing structures as follows: Starting from a completely general input/output framework, we derive a concrete realization procedure based on the above fractional representation of transfer functions (or impulse responses). It is then also possible to give a complete characterization of spectral properties of such realizations via zeros of the denominator of transfer functions.

Such spectral properties allow us to give a stability criterion and also an appropriate relationship between internal and external stability notions. Based on a concrete representation of the state space, we are led to a concrete characterization of left-shift invariant subspaces of H^2. This result has a direct consequence on H-infinity control theory.

We also give a concise yet comprehensive and unified overview of such results. The talk is concluded with this and also a criterion on the existence of a Bezout identity in this class.

### Dynamics and Control of Inverted Ultra-Flexible Pendulum on Cart System

**Prof. Prasanna S. Gandhi**

Ultra-flexible beams are useful in several flexible mechanisms having applications, for example, in high-precision positioning systems and flexible link robotic systems. They demonstrate interesting dynamics, especially when these systems are in a vertical plane. This talk focuses on a representative of such system: a vertical, large-deformation cantilever with tip mass and actuated at fixed base by a cart. The system is shown to demonstrate multiple equilibria as a function of tip mass using elastica theory. Dynamics of this system is further captured using assumed modes method and imposing length constraint to model potential energy change of tip mass (constrained Langrange formulation). Evolution of chaotic behaviour under harmonic excitation is presented in comparison with experiments. We further develop a nonlinear nested saturations based controller for stabilising the cantilever in central unstable equilibrium with cart also reaching the desired position. Multiple coordinate transformations are performed to obtain a system in feedforward chain of integrators before applying nested saturation based control. Effectiveness of control is established through simulation cases and experimental implementation.

__ Biography: __P.S. Gandhi received the B.Eng. degree in from the University of Bombay, Mumbai in 1994 and the M.Tech degree from the Indian Institute of Technology, Bombay, Mumbai in 1996, both in mechanical engineering. He received the Ph.D. degree in mechanical engineering from the Rice University, Houston in 2001. Since 2001, he has been faculty member, currently Professor, in the Department of Mechanical Engineering at Indian Institute of Technology, Bombay, Mumbai. His research interests are in the areas of MEMS and Microsystems, Mechatronics, and Nonlinear Dynamical Systems and Control. He has been a recipient of 2006 BOYSCAST fellowship of Govt of India, 2007 Best faculty award (ME department) and Prof J.R.Issac fellowship. He has authored several patents and over 85 peer reviewed conference and journal papers. He has coordinated setup of a new laboratory Suman Mashruwala Microengineering Laboratory for research in Microdomain and has successfully developed technologies of Bulk Lithography and Microstereolithography for 3D MEMS fabrication in this laboratory. He has been a qualified teacher of stress relieving, life enhancing techniques of Art of Living foundation by Sri Sri Ravishankar.

### Novel Microstereolithography (MSL) and Bulk Lithography (BL) technologies for polymer/ceramic 3D MEMS

**Prof. Prasanna S. Gandhi**

Polymers are increasingly being used for fabrication of MEMS for their advantages of low cost, easy disposability, high flexibility, and so on. With the area of printable organic electronics developing fast there are enormous possibilities with polymer MEMS, especially 3D. This talk will present two indigenously developed technologies for fabrication of polymer 3D MEMS.

The proposed MSL technology has demonstrated resolution of 6micron and a large overall size of fabricated component at the same time: a feature seldom found in other such systems in the literature. The core opto-mechanical scanner (patent pending) and mechatronic system built around it would be presented. This system is demonstrated to have positioning accuracy within 100 nm. Several cases of micro-component fabrication will be demonstrated. Main drawback of MSL is stair-stepping effects on slanted walls. To overcome this limitation, recently "Bulk Lithography" technology has been proposed by our group. The main principle used here is to impose spatial variation of laser energy dose while scanning. The method gives remarkable accuracy in getting free-form surface features desired for microlenses, tapered micro cantilevers, tapered diaphragm micromirrors and so on, which are otherwise not feasible to fabricate. Finally, ceramic microstereolithography and preliminary fabrication of ceramic microcomponents would be demonstrated. The proposed technologies hold potential for direct prototyping and also mass production of MEMS devices along with packaging.

Biography: P.S. Gandhi received the B.Eng. degree in from the University of Bombay, Mumbai in 1994 and the M.Tech degree from the Indian Institute of Technology, Bombay, Mumbai in 1996, both in mechanical engineering. He received the Ph.D. degree in mechanical engineering from the Rice University, Houston in 2001. Since 2001, he has been faculty member, currently Professor, in the Department of Mechanical Engineering at Indian Institute of Technology, Bombay, Mumbai. His research interests are in the areas of MEMS and Microsystems, Mechatronics, and Nonlinear Dynamical Systems and Control. He has been a recipient of 2006 BOYSCAST fellowship of Govt of India, 2007 Best faculty award (ME department) and Prof J.R.Issac fellowship. He has authored several patents and over 85 peer reviewed conference and journal papers. He has coordinated setup of a new laboratory Suman Mashruwala Microengineering Laboratory for research in Microdomain and has successfully developed technologies of Bulk Lithography and Microstereolithography for 3D MEMS fabrication in this laboratory. He has been a qualified teacher of stress relieving, life enhancing techniques of Art of Living foundation by Sri Sri Ravishankar

### An introduction to neural fields

**Georgios Detorakis, post-doc L2S**

The main objective of the field of Computational Neuroscience is to understand how the brain works through mathematical models (numerical and analytical works). Some of these models are described by neural fields equations. Neural fields are integro-differential equations that describe the spatiotemporal dynamics of the activity of a piece of neocortical tissue. Neural fields equations emerge when one assimilates the high number of neurons of the selected piece of brain tissue in its continuum limit. Neural fields have been studied both analytically and numerically by many researchers. They can model many different and interesting biological phenomena such as attention, working memory, self-organization, or synaptic depression. The seminar consists of two parts. The first part is a brief introduction to neuroscience and the second part is dedicated to neural fields. We will review how neural fields equations can be derived, how the steady-state solution can be computed, and its stability can be insured. Finally, some cognitive models that are based on neural fields will be presented.

**Bio:**

Georgios Detorakis has studied Applied Mathematics and Neuroscience. He did his PhD on cortical plasticity, self-organization and neural fields. During his PhD, he studied the formation of topographic maps in area 3b of the primary somatosensory cortex and the multimodal problem of “Touch and the body”. He is now a postdoc fellow at L2S working with Antoine Chaillet on Parkinson’s disease in the ANR project "SynchNeuro". He uses delayed neural fields in order to model some brain areas that play a crucial role in Parkinson’s disease motor symptoms.

### Stability theory, as told by its developers

**Antonio Loria, Elena Panteley (L2S)**

We present a brief but detailed historical review on the development of stability theory, from its early starts out of the minds of Lagrangia and Dirichlet. The survey carries on to focus on Lyapunov stability. Through exact citations from the works of the developers of stability, including many Soviet texts from the 20th century, we revise the fundamental definitions and theorems; making emphasis on several misfortunate translations which have led to wrong interpretations and ambiguous statements. We favour depth and sacrifice generality: on technical grounds, we focus on the most elementary (yet not so) well-known forms of Lyapunov stability and common but crucial qualifiers that go with it: uniform, asymptotic, global. We revise the origin of the wrongly known invariance principle ...

### FREEDM Concept: Power Distribution System Modernization with Solid State Electronics and Integrated Renewables

**Prof. Iqbal Husain**

This FREEDM concept provides an architecture for a future electric power distribution system that is suitable for plug-and-play of distributed renewable energy and distributed energy storage devices. Motivated by the success of the (information) Internet, the FREEDM concept envisions the “Energy Internet,” a system that enables flexible energy sharing for consumers in a residential distribution system. One of the core technologies for the FREEDM system is the solid-state transformer (SST) which is a power electronic device, but makes use of high frequency transformer for isolated AC-AC power conversion. The SST not only dramatically decreases the volume and weight compared with the conventional power transformer, but also behave like a smart transformer with the advantage of power flow control, reactive power compensation capability, and potential fault current limitation. Besides, the regulated low voltage DC/AC bus of SST could be used as an interface to distributed renewable resources and storage devices such as wind, solar, charging stations, and DC micro-grid. The SST is an "Energy Router" proposed to provide such a compatible and flexible interface for energy routing. In addition to the role of a traditional ac transformer, the SST can also provide a low voltage (LV) DC bus. The bi-directional power flow capability of the SST provides possibilities to feed locally generated power back to the grid. Islanding can also be achieved when the HV side is disconnected from grid. The SST has been designed and built based on 13kV SiC MOSFET and JBS diode and is to be connected to medium voltage (MV) distribution network up to 7.2kV and output both a 380V low voltage (LV) dc and 120/240V ac.

This talk will present the hardware research activities and results aimed at demonstrating the FREEDM concept followed by the power electronic controls for the SST. The experimental results of the developed DC/AC hybrid microgrid built to demonstrate the SST's ability to integrate different renewable energy sources and to improve grid quality will also be discussed.

**Biography:**

**Dr. Iqbal Husain** is the Director of the Future Renewable Electric Energy Delivery and Management (FREEDM) Engineering Research Center and the ABB Distinguished Professor at North Carolina State University where he joined in Fall 2011. Prior to coming to NC State he was serving as a faculty member at the University of Akron, Ohio for seventeen years. He was a visiting Professor at Oregon State University in 2001, and also lectured at Texas A&M University. Prof. Husain also serves as the Director of the Advanced Transportation Energy Center (ATEC).He received the B.Sc. degree from Bangladesh University of Engineering and Technology, Bangladesh, and the M.S. and Ph.D. degrees from Texas A&M University, College Station, Texas.

Prof. Husain’s research interests are in the areas of control and modeling of electrical drives, design of electric machines, development of power conditioning circuits, microinverters for distributed power generation, inverter controls for grid synchronization, and modeling and control of electric and hybrid vehicle systems. The primary application of Prof. Husain’s work is in the transportation, automotive, aerospace, power system and renewable energy industries.

Prof. Husain was the General Co-Chair for Energy Conversion Congress & Expo (ECCE) 2012 in Raleigh, NC, the chairman of the IEEE-IAS Transportation Systems Committee, and the chairman of the IEEE-IAS Electric Machines Committee. Prof. Husain received the 2006 SAE Vincent Bendix Automotive Electronics Engineering Award, the 2004 College of Engineering Outstanding Researcher Award, the 2000 IEEE Third Millennium Medal, the 1998 IEEE-IAS Outstanding Young Member award, and several IEEE-IAS prize paper awards. He was elected to be an IEEE Fellow in 2009.

### Online adaptive optimal control of a hybrid electric vehicle

**Catalin Stefan Teodorescu**

Par Doctor Catalin Stefan Teodorescu Project engineer, Flanders' Mechatronics Technology Centre (FMTC), www.fmtc.be A division of Flanders Make, www.flandersmake.be In general, the hybrid driveline concept consists of using simultaneously 2 power sources: the internal combustion engine (ICE) on the one hand, and an electric power source, e.g., a supercapacitor (SC), on the other hand. In the above figure, the red arrows represent power flow of the two illustrated power sources: specifically, it can be generative or regenerative. The latter translates the ability of the SC to store some energy, which can potentially be used in order to achieve significant fuel consumption reduction: e.g. by avoiding wasting energy when the driver pushes the break pedal and instead storing it. In this presentation we will investigate the following problem. In order to be able to cope with the actual demand of the driver expressed in terms of demanded power load (see the above figure), we have an infinite number of choices/combinations concerning the power split ICE versus SC. However, only one (or a few) of these trajectories are optimal in terms of fuel consumption and this is what is being investigated. Two control solutions are presented: Dynamic Programming, mainly used for benchmarking purpose and Equivalent Consumption Minimization Strategy. Results show the latter to be a strong candidate towards online, real-time implementation.

### Five generations of sliding mode controllers: stages of evolution

**Prof. Leonid Fridman from Universidad Nacional Autónoma de México (UNAM)**

The history and evolution of sliding control will be discussed. The reason for the crisis of the first order sliding modes will be explained. The second order sliding mode control algorithms and their specific features will be presented. The control chattering of the continuous second order super-twisting control algorithm will be discussed. The precision of the arbitrary order sliding mode controllers will be shown. The continuous arbitrary order sliding mode controllers will be presented and discussed. Videos with the experimental illustration of the properties of the main sliding mode algorithms will be presented. **Short biography:** Leonid M. Fridman received an M.S. degree in mathematics from Kuibyshev (Samara) State University, Samara, Russia, in 1976, a Ph.D. degree in applied mathematics from the Institute of Control Science, Moscow, Russia, in 1988, and a Dr. Sc. degree in control science from Moscow State University of Mathematics and Electronics, Moscow, Russia, in 1998. From 1976 to 1999, he was with the Department of Mathematics, Samara State Architecture and Civil Engineering University. From 2000 to 2002, he was with the Department of Postgraduate Study and Investigations at the Chihuahua Institute of Technology, Chihuahua, Mexico. In 2002, he joined the Department of Control Engineering and Robotics, Division of Electrical Engineering of Engineering Faculty at National Autonomous University of Mexico (UNAM), Mexico. His research interests are variable structure systems. He is currently a Chair of TC on Variable Structure Systems and Sliding mode control of IEEE Control Systems Society. Prof. Fridman is an Associated Editor of the Journal of Franklin Institute, Nonlinear Analysis: Hybrid Systems, and the Conference Editorial Board of IEEE Control Systems Society. He is an author and editor of seven books and 12 special issues and author of more than 350 technical papers on sliding mode control. He is a winner of Scopus prize for the best cited Mexican Scientists in Mathematics and Engineering 2010. He was working as an invited professor in 19 universities and research centers of Argentina, Australia, France, China, Germany, Italy, Israel, and Spain. **Web page:** verona.fi-p.unam.mx/~lfridman/