2.4 Online vs. offline identification techniques

System identification techniques are crucial for understanding and controlling dynamic systems. These methods, both online and offline, help estimate system parameters and build accurate models for various applications.

Offline techniques like batch least squares process data in batches, while online methods like Recursive Least Squares update parameters in real-time. Each approach has its strengths, and choosing the right one depends on the specific system and control requirements.

System Identification Techniques

Online vs offline identification techniques

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• Online identification techniques continuously update model parameters in real-time adapting to changing system dynamics (adaptive control)
• Offline identification techniques process collected data in batches performing one-time parameter estimation (system modeling)
• Online techniques track time-varying systems suitable for real-time control applications handling unexpected changes (robotics)
• Offline techniques generally provide more accurate results for time-invariant systems utilizing complex optimization algorithms (chemical process modeling)

Offline methods for parameter estimation

• Batch least squares method minimizes sum of squared errors solving $\hat{\theta} = (X^TX)^{-1}X^Ty$ for parameter estimation
• Data collection process considers experimental design input signal selection (step, PRBS) and sampling rate
• Implementation steps involve data preprocessing regressor matrix construction and model validation
• Extensions include weighted least squares total least squares and regularized least squares (Ridge regression)

Online techniques for real-time estimation

• Recursive Least Squares (RLS) updates parameters with $\hat{\theta}_k = \hat{\theta}_{k-1} + K_k(y_k - x_k^T\hat{\theta}_{k-1})$ using gain and covariance updates
• Kalman filtering estimates parameters using state-space formulation with prediction and update steps
• Implementation considers computational efficiency numerical stability (square root filtering) and handling of missing data

Performance comparison of identification methods

• Performance metrics evaluate parameter estimation accuracy convergence rate and robustness to noise
• Computational requirements assess memory usage processing time and scalability with system complexity
• Scenario analysis compares methods for time-invariant systems time-varying systems and large-scale systems
• Trade-offs balance accuracy vs adaptability computational complexity vs real-time performance
• Hybrid approaches combine online and offline methods for improved performance (periodic offline re-calibration)