Lecture

Optimal Control: Convergence and Conditions

Related lectures (31)

Introduces constraints, Lagrange multipliers, and generalized coordinates in physics.

Covers constraints, Lagrange equations, generalized coordinates, cyclic coordinates, conservation laws, and Hamilton formalism.

Stationary Points and Lagrange Multiplier Theorem

Explores stationary points and the Lagrange multiplier theorem for function optimization.

Explicit RK Methods

Explains explicit Runge-Kutta methods up to order 4 and conditions for method's order.

Lagrange Multipliers Theorem

Explores the Lagrange Multipliers Theorem, covering extrema conditions and geometric interpretations.

Optimization: Lagrange Multipliers

Covers the method of Lagrange multipliers to find extrema subject to constraints.

Optimization: Constrained Volume Problems

Explores constrained volume problems using Lagrange multipliers to find extrema under constraints in various examples.

Molecular dynamics under constraints

Explores molecular dynamics simulations under holonomic constraints, focusing on numerical integration and algorithm formulation.

Principle of Least Action

Covers the principle of least action, Euler-Lagrange equations, Lagrange multipliers, and variational calculus.

Molecular Dynamics Simulations: Energy Conservation

Explores energy conservation in Hamiltonian systems, numerical integration, time step choices, and constraint algorithms in molecular dynamics simulations.

Nonlinear Programming: Part I

Covers the fundamentals of Nonlinear Programming and its applications in Optimal Control, exploring techniques, examples, optimality definitions, and necessary conditions.

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Stationary Points Analysis

Covers the analysis of stationary points in functions, focusing on optimization methods.

High Order Methods: Space Discretisation

Covers high order methods for space discretisation in linear differential systems.

Calculus of Variations and Euler's Elastica

Covers variational methods, equilibrium shapes, Euler's Elastica, and numerical and analytical methods for solving Euler's Elastica.

Optimal Control: OCPs

Covers Optimal Control Problems focusing on necessary conditions, existence of optimal controls, and numerical solutions.

Optimization with Constraints: KKT Conditions

Covers the KKT conditions for optimization with constraints, essential for solving constrained optimization problems efficiently.

Optimization with Lagrange Multipliers

Covers advanced optimization techniques using Lagrange multipliers to find extrema of functions subject to constraints.

Controllability and Reachability

Explores reachability and controllability in multivariable control systems, discussing tests, proofs, and their implications.

Extremum of a Function: Constraints

Explores extremum of a function under constraints and finding candidate points in practice.