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This is a Deliverable Report for the FeedNetBack project (www.feednetback.eu). Networked Control Systems (NCS) are systems in which the sensors or/and the actuators communicate with the controller through a network. Energy saving and robustness to unreliable channels are major challenges in networked control, notably in wireless scenarios. Energy efficiency and in particular asynchronous design methodologies are studied in this deliverable. The presence of a channel between the sensors measuring the plant and the controller generating the control inputs implies that the measurements should be quantized. As a preliminary step, the problem of finding a stabilizing policy with quantized measurements and bounded control inputs is considered. It is common to assume that the different nodes of a Network Control System use a periodic synchronized clock, this simplifies the model which may take into account some transmission delays. However, this assumption is strong and energy consuming. Indeed, the periodic sampling time is often chosen to ensure given performance in the worst case scenario, wasting energy when the system is running around its working point. To relax the assumption of synchronized nodes, the rest of the deliverable introduces two asynchronous design methodologies, event-based and self-triggered methodologies. The former consists in limiting the transmissions between the nodes when a given condition holds, or, in other words, when an event occurs. Not only this approach relaxes the assumption of synchronized nodes, but it also limits the transmissions which save energy. In the following, event-based approach is applied to a feedback control case and an estimation case. However, by its nature, event-based approach forces the communicating node to watch for the occurrence of the triggering event. This is relaxed in self-triggered approach where each node decides, at the end of an action (e.g. measuring, transmitting, controlling), when the next action will take place. In between these times, the node usually goes to down mode to save energy. In the last part of this deliverable, this approach is applied to a variable sample rate control and to the case of IEEE 802.15.4 protocol.

This report is an overview of the research activities regarding WP06 (C4E co-design) of the FeedNetBack project. The objective of WP6 of Feed- NetBack is to propose a co-design framework, which allows the integration of control-estimation, communication, computation, complexity, and energy considerations in networked control systems. In this report we outline gen- eral guidelines for co-design and illustrate their applicability to the following case studies: (i) surveillance systems using a network of smart cameras and (ii) eets of Autonomous Underwater Vehicles (AUVs). 2

In this report some methodologies for control and scheduling co-design are reviewed. Although control and real-time computing co-exist since several decades, control and computer scientists and engineers traditionally work in a cascaded way under separation of concerns : this approach leads to misunderstand many constraints and requirements concerning the implementation of control loops on real-time and distributed architectures. A very common misconception considers that control systems are "hard real-time", i.e. that they cannot suffer timing disturbance such as jitter or missing data. Indeed closed-loop systems are, to some extend, inherently robust to uncertainties, including implementation induced timing deviations : this property could be further enhanced to design controllers to be weakly timing sensitive and to accommodate for specified timing uncertainties. Relaxing the usual fixed sample rate and delays assumptions also allows for closed-loop scheduling control where the controller scheduling parameters are on-line adapted w.r.t. the measured computer activity while keeping the system stability. Thus variable sampling or asynchronous control can be used to automatically constrain the CPU or network bandwidth inside specified bounds under weakly known operating conditions. Considering the variety of plant models, computing architectures and associated constraints found across case studies, a large part of the current control tool-box can be adapted and reused for this purpose. On the other hand some other more extreme methods, such as event based control, can be designed to better cope with the asynchronous and timely sporadic nature of real-life systems. Indeed beyond the design of timely robust control laws on one hand, and the implementation of control aware feedback schedulers on the other hand, the problem in the large can be stated as "optimizing a control performance under implementation constraints" : up to now this problem only has partial answers based on case studies and particular configurations. Due the complexity and uncertainty of real life control systems, finding such general solutions is out of the scope of the project. Hence the ongoing research in FeedNetBack WP4 will focus on two promising directions : Variable sampling based on LPV/H1 control, as described in section 5.2, provides a way of preserving the stability and requested performance level of linear systems whatever are the variations of the control period inside prescribed bounds. The method based on polytopic models has a low complexity, allowing an easy implementation on a real-time target. However it is up to now limited to the case where the sampling rate is the only variable parameter in the plant model. Other LPV based robust control methods, such as gridding and LFT, will be investigated to handle both timing and plant model parameters variations. However the current method provides a safe platform to build state-based scheduling control loops as depicted in section 6.2. The properties and timing related performance of such variable sampling control laws deserve to be further studied, so that they can be further combined with an appropriate outer scheduling controller, to ensure both the stability of the controlled process and the efficiency of the execution resources sharing. The previous methods only provide a limited way for handling non-linearities. On the other hand Model Predictive Control, as described in section 5.3, naturally deals with non-linear plants and controllers. However it usually suffers from an high computational complexity which is not compliant with limited computation power and restrict its use for slow dynamic systems. In particular co-designing control and computing over distributed architecture, using MPC design, up to now received poor attention. The way in which MPC can be applied to the Control and Computing Co-Design problem will be investigated. The research will include topics such as how to implement MPC in a distributed manner taking into account the computation capability of the nodes. Techniques such as multi parametric MPC in a distributed context, approximations and the necessary MPC robustification will be studied. Current methods for distributed MPC have relied on the use of input-to-state stability coupled with a generalized small-gain condition as a way of designing robust controllers for distributed, networked systems. However, these methods suffer from conservativeness. We shall investigate the possibility of alleviating this conservativeness through the use of iterative redesign schemes and scheduled communication among the subsystems. As part of WP4 of the FEEDNETBACK project we shall also investigate approximate explicit MPC methods (based for example on wavelet theory), which require less storage and on-line searching, but provide stability and performance guarantees comparable to those of the exact explicit MPC schemes.