+1 678 648 4277 
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.