Computational Issues in Linear Least-Squares Estimation and Control
STANFORD UNIV CA STANFORD ELECTRONICS LABS
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The dissertation focuses on the steady-state solution to the linear estimation and control problems. Following a pertinent review of linear algebra and computation fundamentals, various approaches to solving the matrix Riccati equation are examined. After reviewing eigenvector decomposition and various iterative algorithms, square root doubling algorithms are motivated. Scattering theory is used to initiate an algebraic derivation of these algorithms, and is then extended to provide a pure derivation of several square root algorithms. A set of criteria for choosing among these algorithms is presented and examined with empirical evaluations. Differentiating criteria include sensitivity to repeated closed-loop eigenvalues, the impact of singular model parameters, computational accuracy, and rate of convergence. Sensitivity to parameter uncertainty in discrete-time systems is considered using a quadratic minimization of a generalized cost function. This same algorithm is used to design arbitrary-order compensation using complete system information. Algorithm implementation is then considered in terms of both present and future hardware.
- Statistics and Probability