# System identification - Unleashing the algorithms

Motivation. During the last decades there have been impressive advances in control theory, offering new means for industry to meet the challenges of today’s society. For example, nonlinear and economic MPC together with distributed networked control opens up for large improvements in efficiency and flexibility in process industry. However, technology shifts in this type of industry is notoriously difficult, involving huge investments and training of a wide palette of personell, not to mention the business side. Since long it has been recognized that adequate dynamic process models are necessary to be able benefit from this new technology and that acquiring such models is in general very costly and time-consuming, also requiring highly skilled personnel, thus severely hampering the introduction and maintenance of advanced control. Encouraged by the spectacular success of applying machine learning tools for sequential decision making and control of dynamical systems, the industry is now turning to this area in hope that it will accomodate their needs.

The main paradigm in machine learning for sequential decision making is to combine reinforcement learning with a very flexible function approximator, e.g. a deep learning network, thus requiring huge data sets for the training. While this works well in, e.g., board and video games, where lots of data from a wide variety of scenaria can be obtained almost instantaneously and virtually at no cost, the situation is vastly different in process industry. Here, while huge data bases of historical data are continuously expanding, these data are mainly collected during well controlled operating conditions, offering limited information in regards to process dynamics outside a rather narrow envelope. {\em Highly flexible black-box models trained using this type of data run a large risk of exhibiting unexpected behaviour in operating regimes where advanced control is critical, potentially leading to catastrophic behaviour of the control}. Collecting additional data is very costly and time-consuming. Industry seems to gradually becoming aware of this issue, resulting in a more guarded stance regarding what the new technology can offer.

Aim and significance. The purpose of this project is to tackle the above problem by

developing autonomous learning methods where physical system properties are incorporated in flexible black-box models such as deep learning networks, in a reliable and modularized way.

We believe that by enforcing a model to maintain basic physical relationships such as conservation laws, e.g. mass and energy balances, the model behaviour becomes much more predictable and realistic also in operating regions where training data are scarce. For example, for a paper machine the produced amount of paper should correspond to the material fed into the machine. However, we intend to go one step beyond this notion (that closely relates to classical gray-box modeling), in that algorithms should also be able to automatically detect and infer such fundamental relationships. From a user’s perspective, the interpretability of the model this offers will be important when it comes to building confidence in a model.

At the same time, the strengths of the new types of (machine-learning) black-box algorithms that are emerging should be acknowledged and exploited. Clearly these methods are able to extract complex nonlinear relationships and this ability should be used to model remaining constitutive relationships.

A third important tenet in the research programme we outline below is that such a learning framework should be modular. Physical processes typically consist of interconnected units”, each one equipped with various sensors and actuators, effectively forming an interconnected system. For example, a paper machine can be split into wet-end, press section and drying section. For each unit there are often some well known fundamental physical laws that govern the overall process behaviour but the more precise process characteristics is usually very complicated and not easy to derive from physics. Returning to the paper machine, both the impact of the press- and drying sections on the paper quality are very difficult to model. To benefit from this type of structural and physical knowledge while at the same time allowing model flexibility to account for complex nonlinearities, one is led to a module based modeling framework where each module can be subject to physical laws but with otherwise rich flexibility.

In summary, with such a framework available the resources required for employing advanced control can be significantly reduced. In particular, the autonomy means less demands on high-skilled (read PhDs) personnel and also allows for much easier maintenance. Above we have used process industry as example, but we believe such a framework will be highly beneficial in many industrial applications where model based control is used, e.g. robotics and vehicle technology.

Technical devices integrating physical systems with sensing, actuation, computation and communication, offers fantastic opportunities for society. Challenges in this context are robustness and adaptability. Estimating models of dynamic systems from observed data is known as system identification. The area is highly interdisciplinary, incorporating theory from many areas, and a wide spectrum of applications. The many facets of system identification necessitate expert intervention. This bottleneck threatens the development outlined above. With a team of internationally leading researchers from KTH and LiU, we target two of the core areas of the field from the perspective that algorithms should produce reliable models without human intervention. The overarching aim is thus to “unleash the algorithms”. More specifically we target structured systems and address:

1. Convex algorithms for parameter estimation, based on an idea of how to link iterative, prediction error and subspace methods together such that favorable properties are inherited from all domains.

2. Analysis tools, allowing explicit insights into how sensors and excitation properties influence estimation accuracy.

## Project funding and duration

This project is funded by the Swedish Research Council with duration 2016–2019.