2024 | Rapisarda, P.; van Waarde, H. J.; Camlibel, M. K.
The paper "Orthogonal Polynomial Bases for Data-Driven Analysis and Control of Continuous-Time Systems" by Rapisarda, van Waarde, and Camlibel explores the use of polynomial orthogonal bases (POBs) to perform data-driven analysis and control of linear, continuous-time invariant systems. The authors transform continuous-time input and state trajectories into discrete sequences of coefficients using POBs, demonstrating that the dynamics of these transformed signals are described by the same system matrices as the original continuous-time system. They investigate informativity, quadratic stabilization, and \(\mathcal{H}_2\)-performance problems for continuous-time systems. The key contributions include:
1. **Direct Computation of State Derivatives**: The state derivative trajectory can be computed directly from the state trajectory using POBs, with machine-precision accuracy if the state trajectory is sufficiently regular.
2. **Equivalence of System Matrices**: The transformed input and state trajectories satisfy equations involving the same system matrices as the original continuous-time system, allowing for direct analysis and control design.
3. **Informativity for System Properties**: The paper develops an informativity perspective for continuous-time systems, enabling the assessment of system properties such as controllability and stabilizability directly from data.
4. **Stabilization under Approximation Errors**: The authors leverage the matrix \(S\)-lemma to solve quadratic stabilization and \(\mathcal{H}_2\)-performance problems when the approximation error is nonnegligible, without requiring prior knowledge of system dynamics.
The paper provides a comprehensive framework for data-driven control of continuous-time systems, emphasizing the numerical accuracy and computational efficiency of POBs, and their ability to handle noisy data and approximate derivatives accurately.The paper "Orthogonal Polynomial Bases for Data-Driven Analysis and Control of Continuous-Time Systems" by Rapisarda, van Waarde, and Camlibel explores the use of polynomial orthogonal bases (POBs) to perform data-driven analysis and control of linear, continuous-time invariant systems. The authors transform continuous-time input and state trajectories into discrete sequences of coefficients using POBs, demonstrating that the dynamics of these transformed signals are described by the same system matrices as the original continuous-time system. They investigate informativity, quadratic stabilization, and \(\mathcal{H}_2\)-performance problems for continuous-time systems. The key contributions include:
1. **Direct Computation of State Derivatives**: The state derivative trajectory can be computed directly from the state trajectory using POBs, with machine-precision accuracy if the state trajectory is sufficiently regular.
2. **Equivalence of System Matrices**: The transformed input and state trajectories satisfy equations involving the same system matrices as the original continuous-time system, allowing for direct analysis and control design.
3. **Informativity for System Properties**: The paper develops an informativity perspective for continuous-time systems, enabling the assessment of system properties such as controllability and stabilizability directly from data.
4. **Stabilization under Approximation Errors**: The authors leverage the matrix \(S\)-lemma to solve quadratic stabilization and \(\mathcal{H}_2\)-performance problems when the approximation error is nonnegligible, without requiring prior knowledge of system dynamics.
The paper provides a comprehensive framework for data-driven control of continuous-time systems, emphasizing the numerical accuracy and computational efficiency of POBs, and their ability to handle noisy data and approximate derivatives accurately.