Constrained Control and Estimation

Cover -- Preface -- Acknowledgements -- Table of Contents -- Part I Foundations -- 1 Introduction -- 1.1 Overview -- 1.2 Introduction to Constrained Control -- 1.3 Introduction to Constrained Estimation -- 1.4 Connections Between Constrained Control and Estimation -- 1.5 The Remainder of the Book -- 1.6 Further Reading -- 2 Overview of Optimisation Theory -- 2.1 Overview -- 2.2 Preliminary Concepts -- 2.3 Convex Analysis -- 2.4 Unconstrained Optimisation -- 2.5 Constrained Optimisation -- 2.6 Lagrangian Duality -- 2.7 Multiconvex Problems -- 2.8 Further Reading -- 3 Fixed Horizon Optimal Control with Constraints -- 3.1 Overview -- 3.2 Optimal Control Problems -- 3.3 Necessary Conditions for Optimality -- 3.4 Sufficient Conditions for Optimality Using Dynamic Programming -- 3.5 An Interpretation of the Adjoint Variables -- 3.6 Further Reading -- 4 Receding Horizon Optimal Control with Constraints -- 4.1 Overview -- 4.2 The Receding Horizon Optimisation Principle -- 4.3 Background on Stability Theory -- 4.4 Stability of Receding Horizon Optimal Control -- 4.5 Terminal Conditions for Stability -- 4.6 Further Reading. -- 5 Constrained Linear Quadratic Optimal Control -- 5.1 Overview -- 5.2 Problem Formulation -- 5.3 Quadratic Programming -- 5.4 Embellishments -- 5.5 Observers and Integral Action -- 5.6 Stability -- 5.7 Stability with Observers -- 5.8 Further Reading -- 6 Global Characterisation of Constrained Linear Quadratic Optimal Control -- 6.1 Overview -- 6.2 Global Characterisation for Horizon 2 via Dynamic Programming -- 6.3 The Geometry of Quadratic Programming -- 6.4 Geometric Characterisation for Horizon 2 -- 6.5 Geometric Characterisation for Arbitrary Horizon -- 6.6 Characterisation Using the KKT Conditions -- 6.7 Further Reading. -- 7 Regional Characterisation of Constrained Linear Quadratic Optimal Control -- 7.1 Overview -- 7.2 Regional Characterisation for Horizon 2 -- 7.3 Regional Characterisation for Arbitrary Horizon -- 7.4 Further Reading -- 8 Computational Issues in Constrained Optimal Control -- 8.1 Overview -- 8.2 Implementation of the Piecewise Affine RHC Characterisation -- 8.3 Algorithms for Quadratic Programming -- 8.4 Suboptimal RHC Strategies -- 8.5 Further Reading -- 9 Constrained Estimation -- 9.1 Overview -- 9.2 Simple Linear Regression -- 9.3 Linear State Estimation with Constraints -- 9.4 Extensions to Other Constraints and Distributions -- 9.5 Dynamic Programming -- 9.6 Linear Gaussian Unconstrained Problems -- 9.7 Nonlinear Problems -- 9.8 Relationship to Chapman ... Kolmogorov Equation -- 9.9 Moving Horizon Estimation -- 9.10 Further Reading -- 10 Duality Between Constrained Estimation and Control -- 10.1 Overview -- 10.2 Lagrangian Duality of Constrained Estimation and Control -- 10.3 An Equivalent Formulation of the Primal Problem -- 10.4 Symmetry of Constrained Estimation and Control -- 10.5 Scalar Case -- 10.6 More General Constraints -- 10.7 Symmetry Revisited -- 10.8 Further Reading -- Part II Further Developments -- 11 The Hessian in the QP Problem: Singular Value Struct.