Part I: Optimization Techniques
• Introduction
• Mathematical framework
• Unimodality and convexity
• Optimization problems
• Optimality conditions
• Convergence and stopping criteria
• Linear Programming
• The linear programming problem
• The simplex method
• System identification example
• Nonlinear Optimization without Constraints
• Newton and quasi-Newton methods
• Methods with direction determination and line search
• Constraints in Nonlinear Optimization
• Equality constraints
• Inequality constraints
• Convex Optimization
• Convex functions
• Convex problems: Norm evaluation of affine functions
• Convex problems: Linear matrix inequalities
• Convex optimization techniques
• Controller design example
• Global Optimization
• Local and global minima
• Random search
• Multi-start local optimization
• Simulated annealing
• Genetic algorithms
• Optimization Methods: Summary
• Simplification of the objective function and/or the constraints
• Determination of the most efficient available algorithm
• Determination of the stopping criterion
• The MATLAB Optimization Toolbox
• Linear programming
• Unconstrained nonlinear optimization
• Constrained nonlinear optimization
• Multi-Objective Optimization
• Problem statement
• Pareto optimality
• Solution methods for multi-objective optimization problems
• Integer Optimization
• Complexity
• Search
• Overview of integer optimization methods

Part II: Formulating the Controller Design Problem as an Optimization Problem
• Multi-Criteria Controller Design: The LTI SISO Case
• Introduction
• The basic feedback loop
• General formulation of the basic feedback loop
• Internally stabilizing controllers
• Convex Controller Design Specifications
• Definition of affine and convex transfer function sets
• Engineering specification with respect to overshoot
• Engineering specification with respect to tracking a reference signal
• Engineering specifications in terms of norms of transfer functions
• Robust stability and plant uncertainty
• An Example of Multi-Criteria Controller Design
• The plant
• Engineering specifications
• General formulation of the basic feedback loop
• Example formulation of a robust controller design problem
• Computing the noise sensitivity and its gradient
• Computing the robustness constraint and its subgradient
• MATLAB implementation
• Discussion of the results

Appendices
• Basic State Space Operations
• Cascade connection or series connection
• Parallel connection
• Change of variables
• State feedback
• Output injection
• Transpose
• Left (right) inversion
• Jury's Stability Criterion
• Singular Value Decomposition
• Least Squares Problems
• Ordinary least squares
• Total least squares
• Robust least squares