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
- Gradient descent method.
- 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.