Section: New Results
Communication and control co-design in feedback systems
Differential coding for networked controlled systems
Participants : C. Canudas-de-Wit [ contact person ] , C. Siclet, J. Jaglin.
We have devised several methods for differential modulation in NCS:
gain scheduling 2-bit coding [66] ,
Delta modulation for MIMO systems in
[59] . In
[58] authors have presented a
quantization method based on a one-bit-adaptive 
modulation.
Extensions to Adaptive Delta modulation, and extension to
multi-variable adaptive are also studied. We have introduced a new
adaptive Delta modulation variant called D-ZIZO (Dwell Time Zoom In
Zoom Out). The objective of our work published in
[12] is specifically to treat
aspects related to the energy management, in relation with the
particular code to be used.
In [11] we have investigated the closed loop properties of the differential coding scheme known as Delta Modulation (DM) when used in feedback loops within the context of feedback controlled systems. We propose a new modified scheme of the original form of the DM algorithm which is better suited for applications where the sensed information is used in feedback. A state feedback controller is implemented with the state estimated by a predictor–based differential decoder. Stability of the resulting closed loop systems (controller-coder-decoder) are studied. These properties (stability and performance) depend on the quantization parameter, which is assumed constant in the first part of our work. In a further step, this parameter is made adaptive, by defining an adaptation law exclusively in terms of information available at both the transmitter and receiver side. With this approach both stability and performance are improved.
Current studies addresses new adaptive differential coding algorithms over a limited channel rate. Adaptive coding is preferred over fixed quantizers as these only can reach local practical stability, at its best. The new proposed adaptive algorithm provides global exponential stability for noiseless MIMO system, and Input-to State Stability otherwise. Two of main advantages of the algorithm are that firstly it provides robustness against disturbances, and that secondly it reaches rate theoretical limits. Indeed, the algorithm is coded with the minimum number of possible bits, for both scalar and multi-variable systems. The robustness is achieved thanks to the introduction of a new state namely dwell-time state in addition to the zoom-in and zoom-out ones. The dwell-time mechanism introduces a hysteretic effect that smoothes out the periodic and oscillatory behavior observed in previous ZIZO(Zoom In Zoom Out) quantifiers. Because of this behavior, the algorithm is named dwell-time zoom-in/zoom-out (D-ZIZO).
Energy-aware and entropy coding in NCS
Participants : C. Canudas-de-Wit [ Contact person ] , J. Jaglin, N. Cardoso.
New thesis form Nicolas Cardoso (relation with the FeedNetBack project)
Wireless low-cost sensor networks are an expanded technology in many new and varied areas such as: traffic monitoring and control (urban, highways), undersea monitoring/exploration, environment sensing (forest, farms, etc.), building services, large instruments with distributed sensing and actuators (Tokamak, telescopes), etc.
In this context, future generation of this type of sensors are expected to be packaged together with communication protocols, RF electronics, and energy management systems. Therefore, the development of such integrated sensors will be driven by constraints like: low cost, ease of replacement, low energy consumption, and energy-efficient communication links. In turn, these constraints bring new problems to be considered in the exploitation of this information. For instance, low cost will induce sensors with low resolution (binary sensors, at the extreme) advocating for minimum bit coding strategies, low consumption will impose issues on efficient sensor energy management (sleep and wake-up modes, differentiation of stand-still event), ease of replacement will imply the system ability to keep safe operation in a failure of one or several sensors, and finally communication links and protocols should be designed to account for energy savings, information loss, and varying fading characteristics.
Energy-aware and entropy coding for Networked Controlled Linear Systems has been investigated in [12] . Here we address issues on coding design in the context of control of systems equipped with low-energy sensors networks. We particularly focus on issues concerning minimum bit and energy-aware coding. To this aim, we devise a coding strategy with the ability to quantify and to differentiate stand-still signal events from changes in the source (level crossing detector). Coding is effectuated by defining at least 3-valued alphabet for the minimum bit case, and (2L + 1 )-valued alphabet for a general case with a precision depending on L . Energy saves are studied in two different scenarios; (1) in the word-by-word transmission case, the stand-still signal event is modulated with a low power transmission mechanisms, whereas the changes of levels will be modulated with high-power, (2) in the package-based transmission case, an entropy variable length coding is added to the previous encoding process. Entropy coding assigns some probability distribution to the events, so that the mean transmission energy can be substantially improved for systems where the stand-still events have higher probability to arise (i.e. stable systems). The paper studies the stability properties needed for this type of coding to operate properly, and quantify the energy saves for each of the considered scenarios.
Stabilization under Communication Networks: A Time-Delay Approach
Participants : A. Seuret [ Contact person ] , J.-P. Richard [ LAGIS ] , E. Fridman [ Univ. Tel Aviv ] , J. Gomès Da Silva Jr. [ Univ. Federal do Rio Grande do Sul ] , K.H. Johansson [ KTH ] .
A first contribution consists in developing novel type of tools able to assess stability of time-delay systems. In [22] and [37] , we develop a new type of Lyapunov-Krasovskii functional whose parameters are defined using an arbitrary linear differential equation. In [13] , we propose a method to design a memoryless state feedback control law which stabilizes neutral and delayed systems with saturated input. Concerning the stability of NCS under communication delays, we proposed in [10] , [77] and [21] , to use a time-varying horizon predictor to design a stabilizing control law that sets the poles of the closed loop system. The computation of the horizon of the predictor is investigated and the proposed control law takes into account the average delay dynamics explicitly. The resulting closed loop system robustness with respect to some uncertainties on the delay model is also considered. Tele-operation subject to time-varying delays has been considered in [7] . In [70] and [71] , we also proposed an observer-based controller to ensure the stabilization of networked controlled systems. The main interest of such a controller concerns the potential to take into account the additional dynamics induced by the networks cited above. Further developments will take into account the quantification and the coding of the transmitted data packets.
Collaborative behavior of a fleet of AUVs
Participants : A. Seuret, C. Canudas-de-Wit [ contact person ] , L. Briñón-Arranz, B. Moore.
An effort has been devoted to the problem of controlling a set of agents, cooperating under communication constraints. Formation control of multi-agent systems is also considered and we focus on the translation control and uniform distribution of the agents in a moving circle.
In [25] we propose a control algorithm to stabilize a circular formation of AUVs tracking a circle with a time-varying center and a time varying radius [54] . We also consider the problem of uniform distribution of all the agents along the circle from two approaches: all-to-all and limited communication. We tackle this communication constraint using a cooperative control which includes the Laplacian matrix of the communication graph (fixed or distance-dependent). Based on those preliminary results, we developed a gradient search algorithm The objective for this agent to reach a circular formation whose center is located a the maximum of a potential function.
A version of decentralized formation control for multiple mobile agents was analyzed based on a concept of alignment error and the optimization thereof. This resulted in the development of a type of consensus algorithm for which the total alignment error of the formation is monotonically decreasing [35] . Current research is focused on source seeking behavior for a fleet of AUVs. One part focuses on centralized continuous time outer-loop control for steering a circular formation of AUVs and another on discrete time decentralized control with information delays.
Consensus algorithm under communication delay
Participants : A. Seuret[Contact person], G. Rodrigues de Campos, D.V. Dimarogonas [ MIT ] , K.H. Johansson [ KTH ] .
Another effort has
been devoted to the problem of controlling a set of agents
cooperating under communication constraints. It is well-known that
introducing a delay generally leads to a reduce of the performance
or to instability. Thus, investigating the impact of time-delays in
the consensus problem is an important issue. In our research, we
assume that each agent receives instantaneously its own output
information but receives the information from its neighbors after a
constant delay 
. The setup we considered leads to study the
following equation 
, where 
>0
and A is the classical adjacency matrix. These corresponds to a
more realistic setup than the one usually considered in the
literature [68] . More especially, in
[9] ,
[20] , we investigate the influence of
the communication on the location of the agreement point and on the
convergence rate, which is not straightforward when delays appear in
the network. First, we proved that whatever the delay and whatever
the graph, the set of agents will reach a consensus. The consensus
equilibrium depends on the delay and on the initial conditions taken
in an interval given by:
where U2 is a vector depending on the communication graph. Then, based on Lyapunov-Krasovskii techniques and LMI representation, an estimate of the convergence rate is provided. Figure 7 shows the examples of four communications graphs and Figure 8 shows the corresponding convergence rate.
|
It can be seen that the convergence rate strongly depends on the connection. Note that an interesting phenomena concerning the full connected network is pointed out. It is now well known that for some systems, delays could improve the performance and even lead to stability [16] . It thus appears that a set of full connected agents is one of those systems.
AUVs formation control using relative position information
Participants : M. Alamir [ contact person ] , J. Zikmund.
In this work, a novel observer-based relative positioning method is proposed. It makes it possible to maintain a "solid" and predefined configuration between a leader and a set of followers in a fleet of AUVs. The scheme is based on dynamic observer in which the leader sends its level as well as the module of its own velocity to the followers. Each of the latter dynamically deduces the state of the leader in its own reference frame. This makes it possible for each follower to regulate its own position in a pre-defined formation structure. A particular feature in the proposed solution is that the success of the estimation algorithm does depend on the control being applied. The control and the observation algorithm are intimately linked and need to cooperate towards the success of the overall task.
Adaptive Observer Design under Low Data Rate Transmission with Applications to Oil Well Drill-string
Participants : C. Canudas-de-Wit [ Contact person ] , R. Barreto Jijón, S.-I. Niculescu [ LSS ] .
In oil well drilling operations, one of the important problem to deal with is represented by the necessity of suppressing harmful stick-slip oscillations. A control law named D-OSKIL mechanism uses the weight-on-the-bit force as a control variable to extinguish limit cycles. It uses the value of the bit angular velocity that is found through an unknown parameter observer by means of the measure of the table rotary angular speed.
Since the physics effects occurring downhole have no strong influence at surface due to the attenuation along the drill string, the measurement does not effectively reflect them. This means that the signal to noise ratio is small and it affects the quality of estimation. We are to improve the observer's behavior, using some coarse information of the bit angular velocity coming from the drilling toll equipped with a new embedded sensor. There are mainly two types of sensor technologies : telemetry signals send along the drilling fluid often referred to as mud-pressure pulses, and acoustic waves send along the drillstring. These technological constraints induce the presence of a transmission delay . The work in [52] concerns linear-time varying systems with a delayed output feedback. It extends the works done by Q. Zhang, on Adaptive observer for MIMO linear time varying systems, to linear time-varying systems.
Tele-operated system
Participants : C. Canudas de Wit [ Contact person ] , O. Sename, W. Jiang, J. Dumon.
NecsCar is an electrical vehicle (scale 1/3) to be used as an experimental platform to study improvement of new control architectures. The vehicle is designed to be remotely tele-operated from our active steering wheel platform, ant it is equipped of a 3D vision system to provide the operator with stereo vision capabilities. Bilateral teleoperation can be performed using wheel contact torque measurements, feedback for force deflection. Wireless connection will allow us to test coding algorithms, resource sharing, and robustness against transmission delays. The vehicle was redesigned this year to lower the center of gravity. New experiments were conducted this summer and a demo is available at http://necs.inrialpes.fr/pages/setups-software/setups.php .
