Friday 21 March 2025
A new approach to state estimation, a fundamental problem in control theory, has been developed by researchers. State estimation is the process of inferring the current state of a system based on noisy and incomplete measurements. This is a crucial task in many fields, including robotics, finance, and healthcare.
The traditional method for state estimation is the Kalman filter, which works well for linear systems. However, many real-world systems are nonlinear, making it difficult to apply the Kalman filter directly. To address this issue, researchers have turned to machine learning techniques, specifically neural networks. These networks can learn complex relationships between inputs and outputs, allowing them to be used as state estimators.
One type of neural network, called a Jordan recurrent network (JRN), has been shown to be particularly effective for state estimation. This is because JRNs are able to capture the nonlinear dynamics of the system being estimated. In contrast, traditional neural networks are limited by their inability to model the underlying dynamics of the system.
The researchers used a combination of theoretical and experimental methods to develop their approach. They first developed an ISS (Input-to-State Stable) Lyapunov function for the error dynamics of the JRN. This function ensures that the error between the estimated state and the true state converges to zero over time.
To test their approach, the researchers applied it to three different systems: a mass-spring-damper system, a down pendulum, and a reversed Van der Pol oscillator. These systems are nonlinear and have been widely used as benchmarks for state estimation algorithms.
The results were impressive. The JRN-based state estimator was able to accurately estimate the states of all three systems, even in the presence of noise. In fact, the accuracy of the estimates was comparable to that of traditional methods, such as the Kalman filter.
One of the key advantages of the JRN-based approach is its ability to handle nonlinear systems. This is because JRNs are able to learn complex relationships between inputs and outputs, allowing them to capture the underlying dynamics of the system. In contrast, traditional neural networks are limited by their inability to model these dynamics.
The researchers believe that their approach has the potential to be widely used in a variety of fields. For example, it could be applied to robotic systems to improve their ability to navigate and track objects. It could also be used in finance to estimate the state of complex financial systems.
Cite this article: “Machine Learning-Based State Estimation for Nonlinear Systems”, The Science Archive, 2025.
State Estimation, Neural Networks, Jordan Recurrent Network, Kalman Filter, Nonlinear Systems, Machine Learning, Robotics, Finance, Healthcare, Control Theory
