The trend towards more and more complex, reliable and secure high performance distributed systems poses great technical challenges. This is due to increasing demands on performance, efficiency, safety and environmental aspects. The research area of cyber-physical systems, i.e~integrations of computation and physical processes, has recently received a lot of attention. The objective is to integrate the dynamics of the physical system with the state of the art in information and communication technology solutions. Advances in (wireless) communications systems and micro-electronics are being key enablers for this rapid development; allowing systems to be efficiently inter-connected in networks, reducing costs and size and paving the way for new sensors and actuators. Model based methods for optimization and control of such systems are crucial to cope with the problem of complexity. Examples abound in areas as diverse as process industry, vehicular systems and mobile communication systems. In particular networked systems pervade many of today’s technologies such as the Internet, power distribution grids and process manufacturing. While this important area is currently receiving ample attention in many research communities, not so much attention has been devoted from a modeling and, especially, a system identification perspective.

Since the key paradigm for systems design, analysis and control is model based, this is a shortcoming that risk to impair the developments in the field. Our research agenda aims at developing system identification methods and theory to overcome these difficulties. It covers the following topics:

*Fundamental limitations.*At the heart of system identification lies the question of what information measured data conveys regarding the system. In particular it is of interest to understand the underlying limitations of various configurations of the system identification problem in terms of the resulting model accuracy. We aim to target identification of nonlinear systems for which not much is known regarding this issue, using a geometric analysis method we recently have developed. This is a key part of the project that also underpins the other sub-projects described below.*Cost of complexity.*Factors such as the performance specifications of the application, the system dynamics, the noise and disturbance characteristics and the used model structure determine what the experimental cost will be for performing an identification experiment that allows a model to be identified that is sufficiently accurate for the intended application. The quantification of this dependence we call the “cost of complexity”. Knowing this quantity allows the user to make informed trade-offs, e.g. between performance specs. and the experimental cost. In particular we will consider the cost of complexity for Model Predictive Control (MPC), the dominating advanced control algorithm, and deconvolution filtering, an essential component in communications systems. Both these applications are MIMO.*Adaptive learning and control using restricted complexity models.*Using our geometric technique (see item 1), we have shown that certain system properties can be identified consistently even in the case of severe under-modeling provided that the input excitation is chosen carefully. While this input is in itself dependent on the true system, we have preliminary results that show that adaptive algorithms based on optimal experiment design are very robust (to under-modeling) and lead to consistent estimates. We intend to investigate to what extent this result can be extended to general system properties. In terms of dual control, these are algorithms tuned entirely towards learning and in direct contrast with certainty equivalence adaptive control. Thus it would be interesting to use our insights from this problem to examine to what extent emphasizing the identification objective would help robustify adaptive control.*Experiment design for nonlinear systems.*The behavior of nonlinear dynamical systems is very dependent on the choice of input signals and the corresponding operating regions. We intend to develop computationally tractable formulations of optimal experiment design problems for nonlinear systems. Further, using our geometric technique (see item I) we have shown that for linear systems there are system properties that can be identified at a cost that is independent of the system complexity, if an optimal input is used. We intend to extend this type of result to nonlinear systems as well as the robustness property discussed under Item 3 above.*Structured systems.*For structured systems there is a range of open and interesting research problems. Models of physical systems are often based on combining and connecting simple blocks/behaviors, resulting in interconnected block structured systems. It is here of interest to investigate how much is lost in modeling accuracy if this structure is ignored. In a past VR project, we have done an investigation together with engineers from ABB about the use of system identification in process industry, where the objective of the model is model predictive control design [BW-B8]. The results highlighted many open research problems. Examples are 1) Automatic tools for preprocessing of data before system identification, 2) Input designs, which take process operating strategies, conditions and constraints into account, and in particular for subspace methods, 3) Structural system identification, e.g. subspace identification and model reduction methods. Input design for identification of structured systems is also a rather open area of research.*Decentralized and networked systems.*For identification of decentralized and networked systems we will build on the first five objectives. We will thus analyze the cost of complexity for this type of systems, we will investigate fundamental limitations, study experiment design and adaptive learning. In particular, we aim to study: i) The differences in model accuracy using decentralized and centralized identification. ii) How to improve decentralized estimates by allowing nodes to transmit information between themselves. Here it is of interest to transmit as little information as possible. iii) How to device identification algorithms of low complexity in order to allow nodes of low complexity.

## Project team

**Division of Decision and Control Systems KTH**

## Project funding and duration

This is a framework project funded by the Swedish Research Council with duration 2010–2013.