Ellipsoidal Calculus for Estimation and Control

I. Evolution and Control: The Exact Theory.- 1.1 The System.- 1.2 Attainability and the Solution Tubes.- 1.3 The Evolution Equation.- 1.4 The Problem of Control Synthesis: A Solution Through Set-Valued Techniques.- 1.5 Control Synthesis Through Dynamic Programming Techniques.- 1.6 Uncertain Systems: Attainability Under Uncertainty.- 1.7 Uncertain Systems: The Solvability Tubes.- 1.8 Control Synthesis Under Uncertainty.- 1.9 State Constraints and Viability.- 1.10 Control Synthesis Under State Constraints.- 1.11 State Constrained Uncertain Systems: Viability Under Counteraction.- 1.12 Guaranteed State Estimation: The Bounding Approach.- 1.13 Synopsis.- 1.14 Why Ellipsoids.- II. The Ellipsoidal Calculus.- 2.1 Basic Notions: The Ellipsoids.- 2.2 External Approximations: The Sums Internal Approximations: The Differences.- 2.3 Internal Approximations: The Sums External Approximations: The Differences.- 2.4 Sums and Differences: The Exact Representation.- 2.5 The Selection of Optimal Ellipsoids.- 2.6 Intersections of Ellipsoids.- 2.7 Finite Sums and Integrals: External Approximations.- 2.8 Finite Sums and Integrals: Internal Approximations.- III. Ellipsoidal Dynamics: Evolution and Control Synthesis.- 3.1 Ellipsoidal-Valued Constraints.- 3.2 Attainability Sets and Attainability Tubes: The External and Internal Approximations.- 3.3 Evolution Equations with Ellipsoidal-Valued Solutions.- 3.4 Solvability in Absence of Uncertainty.- 3.5 Solvability Under Uncertainty.- 3.6 Control Synthesis Through Ellipsoidal Techniques.- 3.7 Control Synthesis: Numerical Examples.- 3.8 Ellipsoidal Control Synthesis for Uncertain Systems.- 3.9 Control Synthesis for Uncertain Systems: Numerical Examples.- 3.10 Target Control Synthesis Within Free Time Interval.- IV. Ellipsoidal Dynamics: State Estimation and Viability Problems.- 4.1 Guaranteed State Estimation: A Dynamic Programming Perspective.- 4.2 From Dynamic Programming to Ellipsoidal State Estimates.- 4.3 The State Estimates, Error Bounds, and Error Sets.- 4.4 Attainability Revisited: Viability Through Ellipsoids.- 4.5 The Dynamics of Information Domains: State Estimation as a Tracking Problem.- 4.6 Discontinuous Measurements and the Singular Perturbation Technique.