System Identification and Adaptive Control - Recursive Least Squares Parameter Estimation for MIMO Systems

System identification and adaptive control represent crucial components in modern control theory. Among these methods, recursive least squares parameter estimation for MIMO systems serves as a widely adopted approach, particularly suitable for systems with two inputs and two outputs. This method enables system parameter estimation through recursive computations, thereby facilitating adaptive control implementation. The program implements the RLS algorithm using matrix operations for efficient parameter updates, featuring a forgetting factor to handle time-varying systems. Key functions include covariance matrix initialization, parameter vector updating, and real-time error calculation. The algorithm maintains a covariance matrix P that gets updated with each new data point, while the parameter vector θ is recursively adjusted to minimize the prediction error. This specialized implementation for 2-input 2-output systems provides convenient parameter estimation and adaptive control capabilities, with the code structure allowing for easy modification of system dimensions and integration with control loops. The implementation includes safeguards against covariance matrix wind-up and numerical stability measures for practical applications.