The provided content outlines the structure of a book titled "Predictive Control for Linear and Hybrid Systems" by Francesco Borrelli, Alberto Bemporad, and Manfred Morari. The book is divided into several sections, each focusing on different aspects of optimization and control theory. Key topics include: 1. **Optimization Basics**: Introduces fundamental concepts such as optimization problems, convexity, optimality conditions, Lagrange duality, and Karush-Kuhn-Tucker conditions. 2. **Linear and Quadratic Optimization**: Covers polyhedra, polytopes, linear programming, quadratic programming, and mixed-integer optimization. 3. **Numerical Methods for Optimization**: Discusses convergence, unconstrained optimization, and constrained optimization techniques. 4. **Polyhedra and P-Collections**: Explores general set definitions, operations, and representations of polyhedra. 5. **Multiparametric Programming**: Focuses on multiparametric nonlinear programming and geometric approaches to solving such problems. 6. **Optimal Control**: Provides an introduction to optimal control, including general formulations, batch and recursive approaches, and infinite horizon problems. 7. **Linear Quadratic Optimal Control**: Details the formulation, solutions, and comparisons of linear quadratic optimal control problems. 8. **Linear 1/∞ Norm Optimal Control**: Similar to the previous section, but specifically addressing linear 1/∞ norm optimal control. 9. **Constrained Optimal Control of Linear Systems**: Discusses controllability, reachability, invariance, and constrained optimal control solutions. 10. **Receding Horizon Control**: Introduces the RHC concept, implementation, main issues, and practical applications. 11. **Approximate Receding Horizon Control**: Explores stability, interpolation methods, and practical tuning. 12. **On-Line Control Computation**: Covers storage, evaluation, and computational methods for MPC. 13. **Constrained Robust Optimal Control**: Discusses problem formulation, feasible solutions, and state feedback solutions. 14. **Constrained Optimal Control of Hybrid Systems**: Focuses on hybrid system models, optimal control, and state feedback solutions. 15. **References and Index**: Provides a comprehensive list of references and an index for easy reference. The book aims to provide a comprehensive guide to predictive control for both linear and hybrid systems, covering both theoretical foundations and practical applications.The provided content outlines the structure of a book titled "Predictive Control for Linear and Hybrid Systems" by Francesco Borrelli, Alberto Bemporad, and Manfred Morari. The book is divided into several sections, each focusing on different aspects of optimization and control theory. Key topics include: 1. **Optimization Basics**: Introduces fundamental concepts such as optimization problems, convexity, optimality conditions, Lagrange duality, and Karush-Kuhn-Tucker conditions. 2. **Linear and Quadratic Optimization**: Covers polyhedra, polytopes, linear programming, quadratic programming, and mixed-integer optimization. 3. **Numerical Methods for Optimization**: Discusses convergence, unconstrained optimization, and constrained optimization techniques. 4. **Polyhedra and P-Collections**: Explores general set definitions, operations, and representations of polyhedra. 5. **Multiparametric Programming**: Focuses on multiparametric nonlinear programming and geometric approaches to solving such problems. 6. **Optimal Control**: Provides an introduction to optimal control, including general formulations, batch and recursive approaches, and infinite horizon problems. 7. **Linear Quadratic Optimal Control**: Details the formulation, solutions, and comparisons of linear quadratic optimal control problems. 8. **Linear 1/∞ Norm Optimal Control**: Similar to the previous section, but specifically addressing linear 1/∞ norm optimal control. 9. **Constrained Optimal Control of Linear Systems**: Discusses controllability, reachability, invariance, and constrained optimal control solutions. 10. **Receding Horizon Control**: Introduces the RHC concept, implementation, main issues, and practical applications. 11. **Approximate Receding Horizon Control**: Explores stability, interpolation methods, and practical tuning. 12. **On-Line Control Computation**: Covers storage, evaluation, and computational methods for MPC. 13. **Constrained Robust Optimal Control**: Discusses problem formulation, feasible solutions, and state feedback solutions. 14. **Constrained Optimal Control of Hybrid Systems**: Focuses on hybrid system models, optimal control, and state feedback solutions. 15. **References and Index**: Provides a comprehensive list of references and an index for easy reference. The book aims to provide a comprehensive guide to predictive control for both linear and hybrid systems, covering both theoretical foundations and practical applications.