Control Theory

For the record, as of this writing, we have 2.56 million reported Covid-19 cases globally, as reported by Johns Hopkins.

A Covid-19 Control System

If I were put in charge of defining and setting up the New Normal, being an engineer, I would apply an extended version of control theory. I am not an epidemiologist, maybe they would do exactly that, or better yet their version of it – if they were listened to by the politicians. But I don’t know if epidemiologist even have this kind of systems thinking in their arsenal.

No, I am not proposing a technical automated control system, but a dynamic, organisational framework. Bear with me while I go through a few techie-sounding concepts.

In a nutshell, control theory is about dynamically making, and keeping, a system producing the desired outcomes. That’s the controlled system, a system which is influenced by factors not under our control. In our case here, the controlled system would be the population and the economy. That is, a sociological system, which is even harder to control compared to a technical one, as it cannot easily be modelled and represented by a set of formulae. A system with lots of emergent behaviours. Nonetheless, we need a systematic approach, even if very basic in nature.

The controlled system is controlled by the control system. A control system consists of the following major elements:

  1. A representation of the desired outcomes and results.
  2. A process creating dynamic measures, applied to the controlled system, with the objective to reach the desired outcomes.
  3. A feedback loop, based on measurements of the outcomes, continuously informing the dynamic measures process.

That is, the desired outcomes feed into the dynamic measures process, which influences the controlled system, which produces actual outcomes, which are measured by the feedback loop, which feeds these measurements back into the dynamic measures. Let me depict this with some old-style character-based figure here. Reminds me of my first years in engineering, when a VT-220 terminal was state-of-the-art.

General: One often hears, Well, we don’t know this or that, we don’t have all the information, everything is in change and flow, hence we cannot use a systematic approach. While indeed in our case we do not have the desired level of data, information, and experience, and they also keep changing, it would be a grave mistake to not formalise the control system as well as possible. In engineering and science, missing data or inexact knowledge about behaviour and dependencies is often the starting point. But we can formulate hypotheses, based on clearly identified assumptions, and then test these hypotheses, and adjust as necessary. Without an express, formulated framework, we will not know, first, what the measurements and their data mean, and second, how to correct. Control, or in this case, politics, by the seat of the pants will not be successful, or if it is, only by chance.

Desired outcomes: Here we formulate what we will consider success in our new normal, eg. in terms of new infections over time, number of unemployed people, or patients in hospital care. That is, we want to create a framework for success, with key indicators, and also how to measure them. The desired outcomes will also change with increasing experience, with the availability of a vaccine and viral treatments, and they should change as we go forward and want to expect more of our measures, towards a healthy population and economy.

Dynamic measures process: Measures include lockdowns, in all possible variants and severity, personal protection of different groups of people, contact tracing, economic support for businesses, and so on. We want to formulate how the data from the feedback loop informs the kind, severity, and duration of measures. Again, an express framework is needed, but with the will and the possibility to adapt it continuously. This framework will not be perfect, especially at the start, maybe never, but will serve as the reference for interpreting the data, and for improvements. Here, also time needs to be considered. Firstly, certain measures by their very nature will need more time to show effect, and we need to allow for this time period to pass before we make changes too quickly. Secondly, if the data from the feedback loop suddenly show an alarming situation, immediate emergency measures will be required, which by their very nature might overshoot and not be ideal in hindsight. For nerds, we need a kind of PID1 controller, which has different time constants for different situations and types of measures. Other than with technical control systems, the time constants for this one will not be measured in seconds and milliseconds, but in days or weeks.

Feedback loop: The important aspect here is the measurement of the outcomes, that is, we need to acquire the data to compare the actual to the desired outcomes. Testing for the coronavirus is an obvious measurement, as is testing for anti-bodies. Other relevant data include the number of patients admitted to hospitals or to ICUs, the number of people who have recovered from Covid-19, the number of unemployed workers, plus other economic data about how well businesses are doing. The feedback loop has to provide all key indicators required to assess success, as formulated as desired outcomes.

Plus a Meta-Process

In general, a well-designed control system will stabilise and produce the desired outcomes, while the system under control is impacted by external factors. Now, if these external factors change drastically, ie. beyond as envisioned and defined when designing the control system, the latter might not be able to counteract the external factors, and even become unstable. Then it’s time to rethink and adapt the control system.

With a technical system, such as a production plant, the control system would be reconfigured, or even re-engineered at this point. And put to work again.

With our sociological system towards the new normal, with all the uncertainties in many dimensions, from health factors to medical treatment to economic impact, to name just a few, we need a more dynamic approach. The control system with all its elements must be systematically and continuously put into question, and adapted as needed. We need a control process that controls the control system – a meta-process (not depicted above). The meta-process reviews desired outcomes and their key indicators, and the arsenal of measures with their properties.

Implementation

With a technical system, the above elements of the control system would be implemented by, well, technical means, such as computers, (micro) processors, sensors, and actuators. The computer would make the decisions, based on the coded algorithms and the sensor data. For our Covid-19 control system humans are the “processors”. Of course the responsible people make use of computers to acquire data and reports, to consolidate such data, to compare them. But humans make the decisions. We simply are not in a position to automate our sociological control system, hence human intelligence and common sense is key. Think of groups of experts, using lots of tables and decision trees on paper or computer screens – that’s the core of our control system, the dynamic measures process.

One might wonder, though, don’t we have all this wonderful artificial intelligence available that is being touted so much in recent times? Yes, but also no. Maybe machine learning could help in the longer run to sift through the data and quickly detect dangerous situations and patterns. But for this, we would need to know first what such patterns even look like, and train the algorithms to detect them. In this early stage without firm knowledge about Covid-19, nothing matches human intelligence and reasoning capabilities even closely – if applied within a defined framework.2

Bottom Line

If you think all this sounds complicated and over the top, think again. For starters, we’re looking at a time frame of years here. Until we have a vaccine, the challenge is to finely tune all measures to continuously find and keep a balance between the population’s health, the health systems’ capabilities, and the economy’s health. The record time to develop a vaccine as of now was for mumps, and it took four years. Granted, we have better tools these days, but nonetheless, two to four years to a vaccine that is both effective and can be produced in quantities of billions of shots is not exaggerated.

Also, our control system can start in very, very basic ways. A primitive, but systematic approach is better than running by intuition, gut feeling, partisan squabbles, and personal preferences. And with growing knowledge, data, and experience the primitive system can become more elaborate to achieve the required fine tuning.

It’s crucial to not change too many measures at a time – unless it’s a emergency –, otherwise it will be difficult or even impossible to judge their specific effects on the outcome, which would make learning and stabilising the system very complicated. Or even impossible.

Already making the decision makers, such as politicians and experts,3 writing down, on one piece of paper, what they consider success and how to measure it, would be a good step in itself. Same for a set of all possible measures, listed by priority and how they build upon each other in the direction of increasing severity and impact – both positive and negative, as each measure will have both. And, utterly important as well, same for a list of all assumptions.

So you see, to start, simply a few pages, making things explicit and thus traceable and adjustable. If something is not known yet, as we lack data and experience, formulate hypotheses with corresponding predictions, which can be falsified, or supported by evidence. Be friggin’ scientific. We have known how to successfully do this for decades.

Without a framework of this kind we run the danger to oscillate forever between panicky imposing hard lockdowns and opening them up again. In contrast, a control system brings about balanced stability, predictability, as well as data and knowledge what to change, how to evolve goals and measures going forward.


  1. A PID controller has three parallel control paths: P = proportional, I = integrative, D = derivative. The P part reacts proportionally to the measured changes, the I part “averages” over time for slower reactions, the D part reacts quickly to changes. ↩︎

  2. Also, we could debate if machine learning is even real artificial intelligence. It for sure is not general artificial intelligence. ↩︎

  3. Health professionals, ethics boards, legal scholars, … ↩︎