Foundations -- Overview of Optimisation Theory -- Fixed Horizon Optimal Control with Constraints -- Receding Horizon Optimal Control with Constraints -- Constrained Linear Quadratic Optimal Control -- Global Characterisation of Constrained Linear Quadratic Optimal Control -- Regional Characterisation of Constrained Linear Quadratic Optimal Control -- Computational Issues in Constrained Optimal Control -- Constrained Estimation -- Duality Between Constrained Estimation and Control -- Further Developments -- The Hessian in the QP Problem: Singular Value Structure and Related Algorithms -- Output Feedback Optimal Control with Constraints -- Finite Alphabet Controllers and Estimators -- Case Studies -- Rudder Roll Stabilisation of Ships -- Cross-Directional Control -- Control over Communication Networks.This book provides a comprehensive treatment of the principles underlying optimal constrained control and estimation. The contents progress from optimisation theory, fixed horizon discrete optimal control, receding horizon implementations and stability conditions, explicit solutions and numerical algorithms, moving horizon estimation, and connections between constrained estimation and control. Several case studies and further developments illustrate and expand the core principles. Specific topics covered include: • An overview of optimisation theory. • Links to optimal control theory, including the discrete minimum principle. • Linear and nonlinear receding horizon constrained control including stability. • Constrained control solutions having a finite parameterisation for specific classes of problems. • Numerical procedures for solving constrained optimisation problems. • Output feedback optimal constrained control. • Constrained state estimation. • Duality between constrained estimation and control. • Applications to finite alphabet control and estimation problems, cross-directional control, rudder-roll stabilisation of ships, and control over communication networks. The book gives a self-contained treatment of the subject assuming that the reader has basic background in systems theory, including linear control, stability and state space methods. It is suitable for use in senior level courses and as material for reference and self-study. A companion website is continually updated by the authors.