Parametrizations in Control Estimation and Filtering Problems: Accuracy Aspects

1 Introduction. - 1. 1 Motivation and general statement of objectives. - 1. 2 A historical view and some motivating examples. - 1. 3 Outline of the book. - 2 Finite Word Length errors and computations. - 2. 1 Introduction. - 2. 2 Representations of binary numbers. - 2. 3 Overflow and quantization errors. - 2. 4 Arithmetic computations and roundoff errors. - 2. 5 Dynamic range and scaling. - 2. 6 Conclusions. - 3 Parametrizations in digital system design. - 3. 1 Introduction. - 3. 2 State space realization set. - 3. 3 Sensitivity measure of a state space realization. - 3. 4 Optimal realizations with respect to a sensitivity measure. - 3. 5 Roundoff noise gain of state space realizations. - 3. 6 Minimal roundoff noise gain realizations. - 3. 7 Relationship between sensitivity measure and roundoff noise gain. - 3. 8 Examples and simulations. - 3. 9 Alternative approaches. - 3. 10 Conclusions. - Appendix 3: Proof of Theorem 3. 2. - 4 Frequency weighted optimal design. - 4. 1 Introduction. - 4. 2 Minimization of a frequency weighted sensitivity measure. - 4. 3 Computation of the optimal realization set. - 4. 4 Numerical example. - 4. 5 Conclusions. - Appendix 4. A: Proof of existence of a minimum. - Appendix 4. B: Computation of weighted Gramians. - 5 A new transfer function sensitivity measure. - 5. 1 Introduction. - 5. 2 Minimization of an L2 sensitivity measure. - 5. 3 Relationship between L1/L2 and L2 sensitivity measures. - 5. 4 An example. - 5. 5 Conclusions. - 6 Pole and zero sensitivity minimization. - 6. 1 Introduction. - 6. 2 A pole-zero sensitivity measure. - 6. 3 The eigenvalue sensitivity problem. - 6. 4 Pole sensitivity minimization and normal matrices. - 6. 5 Zero sensitivity measure. - 6. 6 Pole-zero sensitivity coordinate dependence. - 6. 7 Optimal realizations for pole-zero sensitivity minimization. - 6. 8 Numerical example. - 6. 9 Conclusions. - 7 A synthetic sensitivity roundoff design. - 7. 1 Introduction. - 7. 2 A synthetic FWL noise gain. - 7. 3 Optimizing the Total Noise Gain. - 7. 4 A numerical example. - 7. 5 Conclusions. - Appendix 7: Existence of a constrained minimum. - 8 Sparse optimal and suboptimal realizations. - 8. 1 Introduction. - 8. 2 Sparse optimal realizations. - 8. 2. 3 Sparse block-balanced realizations. - 8. 3 Theoretical versus actual sensitivity measure. - 8. 4 Sparse quasi-optimal realizations. - 8. 5 Sparse suboptimal realizations. - 8. 6 Conclusion. - 9 Parametrizations in control problems. - 9. 1 Introduction. - 9. 2 Implementation of a pole placement controller. - 9. 3 FWL LQG controller design. - 9. 4 Conclusions. - Appendix 9: Sensitivity functions of closed loop system. - 10 Synthetic FWL compensator design. - 10. 1 Introduction. - 10. 2 State space description of a compensator. - 10. 3 Analysis of FWL effects of a compensator. - 10. 4 Optimal FWL compensator realizations. - 10. 5 A design example. - 10. 6 Conclusion. - 11 Parametrizations in the Delta operator. - 11. 1 Introduction and motivation. - 11. 2 Delta operator parametrizations. - 11. 3 Sensitivity of delta parametrizations. - 11. 4 Roundoff noise analysis. - 11. 5 Conclusions. - Appendix 11: Proof of Theorem 11. 5. - 12 Generalized transfer function parametrizations for adaptive estimation. - 12. 1 Introduction. - 12. 2 Parameter estimation and the information matrix. - 12. 3 Connection between parametrization and data filtering. - 12. 4 Optimal and suboptimal design choices. - 12. 5 ?-operator parametrizations. - 12. 6 Applications in estimation and adaptive filtering. - 12. 7 Conclusions. - References. Language: English