Lecture

Optimal Control: OCPs

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture covers Optimal Control Problems (OCPs) focusing on the Calculus of Variations, Geometric Optimality Conditions, and the Principle of Optimality. It delves into the necessary conditions of optimality, the existence of optimal controls, and the performance criteria in OCPs. The lecture also discusses the numerical solutions of OCPs, including the Hamilton-Jacobi-Bellman equation, the Pontryagin's Maximum Principle, and the shooting algorithms for solving OCPs.

Official source

Related concepts (32)

Optimal control

Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure.

Pontryagin's maximum principle

Pontryagin's maximum principle is used in optimal control theory to find the best possible control for taking a dynamical system from one state to another, especially in the presence of constraints for the state or input controls. It states that it is necessary for any optimal control along with the optimal state trajectory to solve the so-called Hamiltonian system, which is a two-point boundary value problem, plus a maximum condition of the control Hamiltonian.

Model predictive control

Model predictive control (MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the 1980s. In recent years it has also been used in power system balancing models and in power electronics. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification.

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

Bellman equation

A Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. It writes the "value" of a decision problem at a certain point in time in terms of the payoff from some initial choices and the "value" of the remaining decision problem that results from those initial choices. This breaks a dynamic optimization problem into a sequence of simpler subproblems, as Bellman's “principle of optimality" prescribes.

Related lectures (64)

Optimal Control Theory: Basics

Covers the fundamentals of optimal control theory, focusing on defining OCPs, existence of solutions, performance criteria, physical constraints, and the principle of optimality.

Nonlinear Programming: Part I

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

Optimal Control Theory: OCPs

Covers Optimal Control Theory, focusing on Optimal Control Problems (OCPs) and the calculus of variations.

Nonlinear Model Predictive Control: Stability and Design Steps

Explores Nonlinear Model Predictive Control principles, stability analysis, design steps, and practical considerations.

Nonlinear Model Predictive Control