LimICos is an interdisciplinary project proposal at the frontier of control theory, information theory, and digital communications. The objective of this project is to know to what extent controlled systems are impacted by imperfections due to communication between devices; the main part of the proposal is dedicated to the point-to-point scenario, which typically involves one controller and one plant in communication but the case of networked controlled system is also investigated. One of the main goals of LimICos is to model these imperfections (which imply information constraints on the system under consideration) and take them into account both in the performance analysis and design of controlled systems. Although the literature on control contains some preliminary works into this direction, there is a huge space for innovation and disruptive concepts as advocated by the content of this proposal, which comprises four specific tasks. • Modeling of information constraints. One of our goals here is to model typical communication stages such as the source coder (which typically includes a non-linear quantization stage), the channel coder (including error correction mechanisms and protocols), the communication channel, and the dual stages at the receiver. We want to model the imperfections of these stages and employ new hybrid continuous/discrete formalisms. Additionally, a deepened technical discussion will be conducted on the relevant performance indices to be considered (control theorists and engineers consider performance indices like H2, Hinfinty while communication theorists and engineers consider criteria like distortion or packet error rate). • Analysis of the effect of information constraints on performance. Based on classical control laws for continuous-time systems, one of the key points is to assess the performance of these control or observation schemes subject to information constraints. The focus will be on a point-to-point communication between a controller and a plant but the important case of distributed networks will also be studied by exploiting recent and surprising connections between performance analysis of control dynamic games and network information theory. • Robust control design methods with respect to information constraints. Starting from given features of the network, we aim at developing control and estimation algorithms that are robust with respect to information constraints. In this approach, we suggest to keep in mind these constraints when analyzing the performance, when observing a part of the state, and when designing a control loop. Hence, these new robust strategies should be based on the new indices developed in the first part of the project. An interesting way of study could be to adapt the anti-windup strategy, used classically to alleviate the bad effect due to nonlinearities such as saturations, to mitigate the effect of the phenomena related to limited information. In that case, an additional loop would be incorporated to decrease the potential degradation of the performance due to the introduction of low capacity communication channels. In the case of distributed networks, the goal will be to design control strategies whose performance are reasonably close to the performance limits derived in the second task of the project. • Co-design control and communication schemes. The control design and observation architectures take into account both the control objectives and the design of communication protocols at the same level. The information algorithms adapt themselves in time (adaptive sampling…), in quality and/or quantity (adaptive quantization) with respect to the quality of the network and to the control and observation objectives. In particular, we will also try to design a source coder which compresses control-theoretic quantities such as a system state. This evolution law-driven signal compressor corresponds to a completely new approach of source coding.