A survey is given on the state of the art in theory and numerical solution of general autonomous linear quadratic optimal control problems (continuous and discrete) with differential algebraic equation constraints. It incorporates the newest developments on differential algebraic equations, Riccati equations and invariant subspace problems. In particular, it gives a decision chart of numerical methods, that can be used to determine the right numerical method according to special properties of the problem. The book closes a gap between mathematical theory, numerical solution and engineering application. The mathematical tools are kept as basic as possible in order to address the different groups of readers, mathematicians and engineers.Content: Front Matter....Pages -Introduction....Pages 1-8Notation and definitions....Pages 9-14Existence of solutions....Pages 15-26Uniqueness and stability of feedback solutions....Pages 27-38Algebraic Riccati equations and deflating subspaces....Pages 39-49Schur-forms, Hessenberg-forms and triangular decompositions....Pages 50-54Perturbation analysis....Pages 55-65Numerical preprocessing....Pages 66-69Defect correction....Pages 70-81Newton's method....Pages 82-89The sign function method....Pages 90-97Elementary transformation matrices....Pages 98-100Schur methods....Pages 101-104Unitary symplectic algorithms for special Hamiltonian or symplectic eigenvalue problems....Pages 105-112Nonunitary algorithms for real Hamiltonian or real symplectic eigenvalue problems....Pages 113-130Closed loop algorithms....Pages 131-139A combination algorithm for real Hamiltonian and symplectic eigenvalue problems....Pages 140-142Numerical algorithms for Riccati differential or difference equations....Pages 143-147A general algorithm....Pages 148-151Conclusion....Pages 152-155Statement....Pages 156-156

2025-10-16