# Adaptive system

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(Redirected fromAn **adaptive system** is a system that is able to adapt its behavior according to changes in its environment or in parts of the system itself.

Adaptive systems are self-modifying mathematical models that act as intelligent agents that can find complex patterns in data, make accurate predictions and learn from mistakes. In an age when the quantity of data is growing exponentially adaptive systems are a revolution in the way we handle and understand information. With adaptive systems we can do better, faster and more sustainable than what could have been imagined only a few years ago.

Adaptive systems in engineering are an interdisciplinary field that deals with distributed, nonlinear systems. They complement present engineering design principles and are suitable to interface directly with the real world with little or no preprocessing. When applied correctly, such systems can considerably outperform more traditional methods.

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## Applications

*Main article: Applications of adaptive systems*

**Adaptive systems** can be applied in many important engineering applications, such as function modeling, pattern recognition, clustering, feature extraction, anomaly detection, system identification, prediction, optimization and control. Adaptive systems are today commonly used in finance, industry, consumer products, medicine, science and software detection.

## Characteristics and benefits

The main characteristic of adaptive systems is their ability to dynamically construct a model. Instead of being built a priori from a pre-existing model, adaptive systems use external data to automatically set their parameters. In doing so their generic parametric structure becomes not only a computational model but also a model for the physical system.

Before the dawn of adaptive systems you had the choice of either trying to describe your data with equations or try to use regression to make a function fit to the data. In many real world problems it is difficult to know if and how different variables are connected and describing it with an exact equation or differential equation can be outright impossible. Regression methods(fitting a simple function to data) work with simple static data with one or two parameters but they don't survive contact with real world data for long. Adaptive systems on the hand dynamically build a model - you don't have to figure out the equations - and they can capture very complex relationships in the data.

There are different ways of adapting the structure parameters to data. One common type of system has a recurrent connection from a cost function applied to the system output supplying performance feedback. This feedback is then used to change the parameters through algorithmic procedures called learning or training rules.

The benefits of such systems are manifold. The system designer has to define a system topology and select an adaptive algorithm. Unlike the traditional approach of physical modeling, the designer does not have to have a full understanding of the underlying problem. As long as the data captures the fundamental characteristics of the problem, the adaptive system will form itself to best fit that data. Therefore the designer can work with a nearly ideal black-box model. The non-linear nature of adaptive systems such as neural networks gives the system designer the power of modeling very complex phenomena. It can be shown that neural networks are universal function approximators. In theory they can with an arbitrary accuracy approximate any function. Furthermore adaptive systems have strong generalization capabilities.

The parameters of an adaptive system can be set to adapt continuously during operation and therefore such systems are well suited to model dynamic phenomena or phenomena occurring in changing environments.

Adaptive systems are a developing technology and new advances are made every year. Despite its young age it already supplies some very useful engineering tools. This is because we have knowledge of useful topologies that work as universal function mappers as well as the algorithms to train them. We also have, to some extent, an understanding of how to get them to generalize beyond the data used to train them. Therefore we are in a position to design effective adaptive solutions to moderately difficult real-world problems.

## Commanding complexity

Engineering is a discipline that builds practical physical systems based on recurring phenomena in the physical world around us. It is founded on the applications of the laws of physics and the scientific method has been highly successful in the field of Engineering. As technology is continuously growing in importance so are the requirements on engineering design. Different subsystems are needed to interact and interaction with the real world is more common. Engineering design requires a mathematical/physical model for each system. When the number of systems increases the number of interactions among them increases exponentially. Fundamental research provides an inflow of new physical and mathematical principles, but these deal for the most part with the world in a reductionist manner. Problems arise when very large numbers of subsystems are expected to work together. Complex effects emerge that cannot be described as a combination of the effects from the individual interacting subsystems. Mathematical chaos theory gives us some very vague qualitative insights, but today we do in fact not have a clear approach of how to handle complex systems.

Physicists have already faced this problem for centuries. Nature is a complex system where the number of interactions within and between physical subsystems is enormous. The solution has always been to make approximate models that gave a required accuracy within certain boundary conditions. In some situations it has so far proven unfeasible to construct models with the required accuracy and there are a number of fields in physics where the (classical, approximate) models cannot adequately predict the behavior of natural physical phenomena. A good example of such a field is the mechanics of fluids where statistical models are used to capture some of the global characteristics of the system while there is no quantitative model of the local interactions within the system.

Traditionally humans have handled the interaction between engineering systems and the external world. Since the introduction of the computer, there has been a trend of removing the humans from the loop and letting the machines interface directly with the external world. This brings the complexity of the real world into the engineering systems and through that into the physical models that are not well-suited for it. This creates performance, precision and stability problems. Through the interaction of many subsystems even small approximation errors can be fatal to the model.

## Nature: The mother of adaptation

A category of systems that do not seem to have a problem of dealing with complexity and that interact directly with nature are biological systems. Adaptive systems are very much linked to the study of biological systems and have drawn much inspiration from them.

The study of biological entities and their interaction with nature from an engineering perspective has given us many valuable insights. Through millions of years of evolution, biological systems have found a set of inductive principles that work extremely well with a complex and unpredictable environment. While we far from fully understand them, we still have some knowledge of them on both qualitative as well as quantitative levels. These principles involve extracting data from sensors, finding invariant patterns, efficient learning and decision making with very vague conditions and a large uncertainty in the parameters. In mimicking these principles we have to build systems that construct and fit models to data collected from external environments. These models have to be stored and the system must choose which should be applied under which circumstances as well as estimate the likelihood of completing the task successfully. Optimization is an emerging quality since the goal of the system is generally to achieve the best performance with available information.

Biological systems use adaptation to build optimal systems for survival (in a broader evolutionary sense). In effect it means that nature builds optimal systems to meet the challenges an animal or plant face in life. Many of these challenges are general in nature and we can use the biological solution to approach a variety of problems. On a general level the biological hardware of the animal is defined on a long term by the environment, through evolution. In the short term, the individual animal develops a custom system (connections in the brain) to process real time information that is required for it to survive. The knowledge of the detailed workings of the nervous system is still limited but we do know some fundamentals. It is well accepted by the scientific community that interaction with the environment influences the creation and modification of connections between neurons in the brain.