A Framework for Continuous Adaptation: Closed Loop Feedback

Abstract

The proposed closed-loop feedback framework is a powerful tool for understanding and controlling complex systems. It can be used to design, analyze, and control a wide range of systems, including engineering systems, product designs, and businesses. The framework is based on the idea that a system can be controlled by continuously measuring its output and adjusting its input accordingly. This feedback loop can help to ensure that the system behaves as desired, even in the face of uncertainty and change.

Gazing at reality

Let's start this piece with a rhetorical question.

How well do we understand reality?

This question has been central to humanity since the dawn of time. We have developed various fields, including philosophy, theology, and science, to examine it from different angles. The better we understand reality and its underlying laws, the better we can manipulate and control it. And yet, because our understanding of reality constantly evolves, there is no straight answer to that question. We are aware that up to a certain degree, the way we see and explain the world around us does not fully match reality. Multiple factors explain this mismatch, such as our limited knowledge of the universe (including ourselves) and cognitive flaws.

Moreover, we have learned to simplify how we think about the material things around us, by looking at them as linear, anthropocentric, ordered, and mechanistic. This reductionist approach seems to be a mechanism that limits our cognitive load and seems to be hard-wired in our brains, see System 1 Thinking. However, the physical world has unexpected behavior and the phenomena we perceive as real and steady could manifest as volatile, uncertain, ambiguous, and complex. Being aware of these ill characteristics forces us to think twice whenever we create solutions to our everyday problems. The effectiveness and accuracy of such solutions (delivered as technological systems) are limited by our know-how, the available technology in our hands and the unknown characteristics of reality.

The best approach to adapt our solutions and systems to the real world is by iteratively, systematically, and incrementally uncovering unknown and complex aspects of reality, and then introducing new knowledge into the design, construction, and control phases of our systems.

What is a complex system?

A system is a collection of multiple entities, elements or components that interact with each other and work together to achieve something, i.e., synergy. In technical terms, the interactions in a system are affected by information, data or energy that flows into and through the system, something known as input. The information, data or energy that flows outside the system is called output.?A system is simple if it can be explained and described using physics and first principles. This means that our understanding of the system dynamics can be expressed with mathematical equations. Take for example a pendulum, where the dynamic interactions between a point of mass, an inextensible string and a fixed support can be expressed through equations. In other words, a pendulum is deterministic and the system state at a given time can be predicted for some initial conditions.

When looking for a system that solves any of our everyday problems, we realize that simple and deterministic systems have limited practical applications. By aggregating simple systems, we end up with more sophisticated and powerful solutions that fulfil our needs. The complexity arises because by adding new elements to any system, one creates unexpected relationships, dependencies and outputs, a phenomenon called emergence. For example, if a second pendulum is added, the new system will experience behavior and properties that cannot be predicted or deduced from the characteristics of individual components alone. Even if the individual components have predictable dynamics.

Nonlinearity is another characteristic of complex systems, which implies that small changes in the input can lead to disproportionately large changes in the output. Nonlinearity contributes to the system's dynamic unpredictability. Even if there is a mathematical model for the complex system, there are no closed expressions to fully describe the system state at a given time for some initial conditions.

The third main characteristic of a complex system is the feedback loop, a process where the current output will modify the next input of the system. The feedback loops can emerge naturally in complex systems due to multiple factors:

• Adaptation: a system modifies its behavior in response to changes in its environment. An ecosystem affected by climate change has this sort of feedback loop.
• Evolution: a population of organisms changes over time given some stimulus in the environment. For example, the changes in DNA that bacteria experience to combat viruses and antibiotics.
• Self-organization: a system spontaneously organizes itself into a more complex state without any external intervention. For example, in a flock of birds, each bird flies not too close and not too far from other birds, constantly adjusting its position about its neighbors.

Building Blocks from Control Theory

In engineering, we use the principle of feedback loops to control and continuously improve the performance of systems. The discipline that studies how to modify the dynamics of a system is called Control Theory. It gives us a mathematical framework to model and design autonomous systems, the characteristics of the inputs that affect the state of the system, and the mechanism to modify the output.

Let’s consider a self-driving car as our dynamic system. The figure below illustrates the core processing blocks used by control theory to design an autonomous self-correcting system.

In the planning block, we create a reference for the system to follow. For a self-driving car, the planning block must figure out a path to a destination, considering known obstacles, driving rules, and desired comfort for the passengers. A plan could be stated as a job for the system, "take me from my house to the closest supermarket in less than 10 minutes following all driving rules and assuring smooth driving."

The feedback controller block uses the reference and the current state of the system to produce an adjusted input that will compensate for deviations, external disturbances, noise and unknown system dynamics. The controller's objective is to minimize the difference between the achieved output and the desired output. Feedback loops are quite important because they rule the system's stability by self-reinforcing or self-limiting some aspects of the system. Feedback loops can achieve either a system equilibrium or destroy the system dynamics. Without a correcting input, the system will eventually degrade due to changing internal dynamics, as well as external forces, see entropy. For a self-driving car, the controller will change the next system state by adjusting speed and direction to follow the reference.

The dynamic system block is the set of components that will perform the desired job. Control theory relies on the mathematical model of the system, computed either from physical principles or by fitting a model to available data (i.e., a discipline known as system identification). Models are used for every processing block in the diagram above, i.e., controller design, state estimation, planning and analysis (simulation, testing, as well as stability and performance optimization). For a self-driving car, the system model could represent the speed as a function of the pedal position.

The system is constrained by the environment in which it operates. The disturbance is something that we cannot control or predict, i.e., external inputs that will affect the system dynamics. For a self-driving car, the disturbances are the conditions of the road, moving obstacles, other vehicles on the street, or the weather.

The only way to know the current state of the system is by measuring it. In real systems, measurements are performed with sensors which introduce noise. Furthermore, the full state of a complex system can be decomposed into many attributes, but we only have a finite number of sensors to measure them (besides the fact that sensors are expensive). This means that we partially observe the system state, due to the reduced dimension space used to characterize the system. For a self-driving car, we need to measure the speed, position and near objects to detect potential threads using devices such as radar and lidars.

The state estimation block represents another area of control theory, devoted to mitigating and correcting the measurement noise (e.g., accuracy, dimensionality, scaling) by processing the data and translating it into something useful for the feedback controller.

The self-driving car is a nice example to illustrate the high-level factors involved in its design and operation. The video below multiple sensors and other devices required to enable autonomous driving.

Feedback Loops in Other Disciplines

The feedback loops can be found in many disciplines that go beyond engineering. The core objective of such a structure is to put together a system to produce some result, inspect and understand the output, adapt, and improve some aspects of the system and repeat until a given goal is achieved. The following examples have similarities with the generic feedback loop model presented above.

Product Design

One of the most popular methodologies for product design is called Design Thinking. It is based on an iterative process for collecting users' needs, prototyping solutions and validating assumptions. There are similarities between the processes illustrated in the figure below and the building blocks from control theory. Empathizing with users, articulating their needs and ideating potential solutions can be mapped to the planning block in control theory. The prototype phase is equivalent to the dynamic system, whose job is to satisfy the user's needs or solve a user's problem. The testing phase is like the state estimation block, where the designer validates the effectiveness of the prototype by inspecting the user's feedback. Once some measurements have been collected and insights have been extracted, a new planning phase takes place to refine and adjust the next prototype.

Business Development

The book The Lean Startup presented an iterative process that any company must follow to build a successful business in an environment of high uncertainty, i.e., Build-Measure-Learn:

The fundamental activity of a startup is to turn ideas into products, measure how customers respond, and then learn whether to pivot or persevere. All successful startup processes should be geared to accelerate that feedback loop.

Let's inspect the lean startup model for a software product through the control theory perspective. The ideas phase (planning block) will define what the product should do. The build phase takes the requirements and assumptions collected in the ideation phase and produces a working software (product) ready for testing (this is the dynamic system). Then, the product is presented to the target customers who provide feedback regarding the value of the product. Once the product has been measured in multiple dimensions (e.g., value, reliability, or efficiency), the data collected is used to learn something new about the product, customers, and market. The new insights will be used to refine the product's next iteration (this is the feedback controller block).

It is worth noting that the noise and the disturbances are not explicitly represented in the lean startup model, but they do affect the data and the learning phases. Take for example a customer not willing to invest time giving feedback (noise) or a supplier not paying attention because you are still a small company (disturbance). The measured value of the product will be inaccurate. That is why, the book encourages you to get out of the building, collect as much feedback as possible and guarantee that your measurements are statistically significant. Another source of noise is vanity metrics, which measure irrelevant aspects of the business, but they make you feel great. The state estimation block could be a mentor or company board with enough experience and expertise to help set the right metrics.

The ultimate plan for a startup is to pivot or persevere. Such a decision is the responsibility of the founders (the feedback controller), who oversee high-speed learning, steering the product and targeting the right market.

The Framework

The closed-loop feedback model from control theory can be generalized as a framework to design, analyze, and control many systems, e.g., products, projects, teams and even businesses. The arrows in the canvas show the direction in which the information, data, or energy sinks. The controller is the only block that allows energy to flow towards the previous block, i.e., the planning. This explicit loop is necessary to inspect and adapt the reference defined at the planning block. New information from the system dynamics, the current state and the environment can modify the overall system's job-to-be-done (e.g., pivot or persevere).

Bear in mind that the canvas represents a snapshot in time, and only reflects the current state of the system under some conditions. To have a better understanding of the system dynamics and the efficiency of the controller, it is necessary to assess the closed loop over several iterations.

An example of Business Steering

Let's take as an example the Evidence-Based Management (EBM) framework used by organizations to improve outcomes, reduce risks, and optimize investments. The EBM framework can be mapped as follows:

• Planning: the organization defines objectives for two points in time, present and future. The present planning establishes how the organization operates to keep delivering the current value to customers. The future unrealized value (UV) is assumed to be the gap between the current value and the customers' expectations.
• System: the organization (people, culture, knowledge, and technology) generates a product or service for its customers. The effectiveness of the organization to deliver new capabilities that create value for its customers is called ability-to-innovate (A2I), with the EBM framework.
• Disturbance: the organization and its operations are affected by external factors such as changes in the market, competitors, changes in the business environment and even luck.
• State: the organization produces value for customers, e.g., goods, products, or services, called outcomes within the EBM framework.
• State estimation: the organization measures what the current value (CV) delivered to the customers is. The metrics to quantify the outcomes target customer and employee satisfaction, revenue, and cost.
• Noise: the EBM framework points out that "working more hours (activities) and delivering more features (outputs) does not necessarily lead to improved customer experiences (outcomes)". Therefore, activities and outputs are not part of the current value and must be optimized only if better outcomes are achieved as a result.
• Controller: the organization's leadership inspects internal and external aspects of the system. From the system performance and the current value, the controller identifies unmet needs and market opportunities as well as the effectiveness of the system closing the gap between the outcome and the unrealized value. It also inspects the organization's ability to quickly deliver new capabilities, services, or products, i.e., time-to-market (T2M). Finally, the controller improves the system operation and provides evidence to assess the unrealized value.

Takeaways

The closed-loop feedback framework can serve you as a learning and adapting tool. Few ideas to keep in mind:

• Feedback loops are a common feature of complex systems and can be found in many disciplines, including engineering, product design, and business development.
• By using feedback loops, we can make better decisions about how to design, develop, and operate a complex system.
• By continuously measuring and evaluating our systems through feedback loops, we can identify areas for improvement and make changes accordingly.

Acknowledgements

Part of this work was presented in the Symposium of Physics, Mathematics and Engineering, RGMX Chapter Spain, 2023. I would like to extend my recognition and gratitude to Adela Rendón, PhD for the remarkable results and impact of the symposium over the years.