Historically, the intellectual roots of LIDS lie in the field of Systems and Control Theory. The original focus of this field was on the modeling, analysis, and feedback controller design for systems described by linear or nonlinear differential or difference equations, with special emphasis on issues of robustness, a subject in which LIDS played a pioneering role. More recently, numerous challenges have emerged, with the focus shifting towards complex, often distributed and networked, systems. Typical concerns that are driving the field stem from the high-dimensionality of such systems, the simultaneous presence of discrete and continuous dynamics (hybrid systems), the interaction between physical systems with humans or software, and the quantification of appropriate notions of information for the purpose of decision-making.
Some key directions of current and future research include:
- Methodologies for deriving simplified models (model reduction) that on the one hand are well-structured and sufficiently low-dimensional to be tractable, while on the other hand, remain faithful to the actual dynamics and capture the essential features of interest. This activity is driven by either an original high-dimensional model, or by raw data (in the latter case, there is a clear synergy with the field of inference). This methodological research proceeds hand in hand with domain specific work in diverse areas, such as, for example, circuit analysis and design, systems biology, animation, etc.
- The extension of traditional stochastic control methodologies to deal with high-dimensional systems through approximations that rely on a limited but essential set of “features” of the state of the system. LIDS has played a key role in the development of approximate dynamic programming (and its near relative, “reinforcement learning”) but the subject keeps presenting new challenges.
- The development of novel, tractable methodologies to deal with nonlinear or hybrid systems. Particular emphasis is placed here on algorithmic issues, as well as on verification methods that can establish that a given design possesses certain desirable properties.
- Understanding the relation of economic theory (especially game theory and mechanism design) to (i) study incentive systems that can induce socially desirable behavior on the part of the users, (ii) the effects of different pricing mechanisms, and (iii) the effects of different market structures. Such problems arise in the study of congestion control in general transportation systems as well the study of complex social networks.
- The interplay between information networks and control theory. On the one hand, control theory provides insights and tools for the control of networks; on the other hand, there are several challenges in the field of control over networks, whereby feedback controllers operate in the presence of distributed and possibly delayed information that is delivered over a network infrastructure. In fact, the melding of control theory with communications was a key characteristic of the transition from ESL to LIDS; among other successes, it led to a modern (and now firmly established) view of communication networks, in terms of stochastic models and optimization-based approaches to resource allocation.
- Methodologies for dealing with distributed, multi-agent, mobile, systems that achieve desired cooperative behavior through limited information exchange, possibly over an unreliable communication network. This is a subject in which LIDS has had a leading role in the past, and continues to have a very strong presence, in conjunction with various application domains that are driving the field.
- Foundational theory of Cyber-Physical Systems (CPS). This area emphasizes the interaction between the actual physical process and the information and decision network layer on top. Modeling the interface of these two layers will play a critical role in many of the applications mentioned before (e.g., energy systems, Unmanned Vehicles). Research in this area include the development of computationally efficient algorithms for verification of hybrid systems, development of tools for solving combinatorial optimization problems with physical and dynamic constraints, and addressing reconfigurable systems that can deal well with disruptions.