The exhaustive list of topics in Optimal Control in which we provide Help with Homework Assignment and Help with Project is as follows:

• Effects of scaling or adding a constant to an objective function and understanding of constrained and unconstrained optimization problems.
• Concept of Lagrange multipliers and its application to unconstrained optimization problem
• Steepest descent method.
• Newton's method.
• Davison-Fletcher-Powell method.
• Exterior point method.
• Numerical examples are considered to illustrate the algorithmic steps of the above methods.
• Solution of constrained minimization problems using Karush-Kuhn-Tucker (KKT) necessary and sufficient conditions.
• Numerical examples are considered to illustrate the technique.
• Understanding the following terms convex sets,
• Convex and concave functions
• Properties of convex function
• Definiteness of a matrix and test for concavity of function.
• Solution of quadratic programming problems using KKT necessary condition
• Basic concept of interior penalties and solution of convex optimization problem via interior point method.
• Numerical examples are considered to illustrate the techniques mentioned
• Linear programming: Simple method
• Matrix form of the simplex method.
• Two-phase simplex method
• Primal and dual problem: Determination of primal solution from its dual form solution and vice-versa
• Properties of dual problems and sensitivity analysis.
• Basic concept of multi-objective optimization problem and some definitions.
• Solution of multi-objective optimization problem and illustrate the methodoly with numerical examples.
• Concept of functional
• Variational problems and performance indices.
• Euler-Lagrange equation to find the extremal of a functional.
• Transversality condition
• Application of variation approach to control problems.
• Optimal solution of LQR problem
• Different techniques for solution of algebraic Riccati equation.
• Frequency domain interpretation of LQR problem.
• Stability and robustness properties of LQR design.
• Optimal control with constraints on input.
• Optimal saturating controllers.
• Dynamic programming principle of optimality.
• Concept of time optimal control problem and mathematical formulation of problem.
• Solution of time-optimal control problem and explained with a numerical example.
• Concept of system and signal norms.
• Small-gain theorem
• Physical interpretation of H8norm.
• Computation of H8 Norm, statement of H8 control problem.
• H8 control problem: Synthesis.