Algebraic Riccati equation

An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time or discrete time.

An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time or discrete time.

Bang-bang control

In control theory, a bang–bang controller (on–off controller), also known as a hysteresis controller, is a feedback controller that switches abruptly between two states.

In control theory, a bang–bang controller (on–off controller), also known as a hysteresis controller, is a feedback controller that switches abruptly between two states.

Bang–bang control

In control theory, a bang–bang controller (on–off controller), also known as a hysteresis controller, is a feedback controller that switches abruptly between two states.

In control theory, a bang–bang controller (on–off controller), also known as a hysteresis controller, is a feedback controller that switches abruptly between two states.

Bellman pseudospectral method

The Bellman pseudospectral method is a pseudospectral method for optimal control based on Bellman's principle of optimality.

The Bellman pseudospectral method is a pseudospectral method for optimal control based on Bellman's principle of optimality.

Caratheodory-π solution

A Carathéodory- solution is a generalized solution to an ordinary differential equation.

A Carathéodory- solution is a generalized solution to an ordinary differential equation.

Chebyshev pseudospectral method

The Chebyshev pseudospectral method for optimal control problems is based on Chebyshev polynomials of the first kind.

The Chebyshev pseudospectral method for optimal control problems is based on Chebyshev polynomials of the first kind.

Costate equations

Costate equations are related to the state equations used in optimal control.

Costate equations are related to the state equations used in optimal control.

Covector mapping principle

The covector mapping principle is a fundamental result in computational optimal control.

The covector mapping principle is a fundamental result in computational optimal control.

DIDO (optimal control)

DIDO is a MATLAB program for solving hybrid optimal control problems.

DIDO is a MATLAB program for solving hybrid optimal control problems.

DIDO (software)

DIDO is a MATLAB optimal control tool for solving general-purpose hybrid optimal control problems.

DIDO is a MATLAB optimal control tool for solving general-purpose hybrid optimal control problems.

DNSS point

DNSS points arise in optimal control problems that exhibit multiple optimal solutions.

DNSS points arise in optimal control problems that exhibit multiple optimal solutions.

Dynamic programming

In mathematics, computer science, economics, and bioinformatics, dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems.

In mathematics, computer science, economics, and bioinformatics, dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems.

Flat pseudospectral method

The flat pseudospectral method is part of the family of the Ross–Fahroo pseudospectral methods introduced by Ross and Fahroo.

The flat pseudospectral method is part of the family of the Ross–Fahroo pseudospectral methods introduced by Ross and Fahroo.

Gauss pseudospectral method

The Gauss pseudospectral method (GPM), one of many topics named after Carl Friedrich Gauss, is a direct transcription method for discretizing a continuous optimal control problem into a nonlinea...

The Gauss pseudospectral method (GPM), one of many topics named after Carl Friedrich Gauss, is a direct transcription method for discretizing a continuous optimal control problem into a nonlinea...

Hamilton-Jacobi-Bellman equation

The Hamilton–Jacobi–Bellman (HJB) equation is a partial differential equation which is central to optimal control theory.

The Hamilton–Jacobi–Bellman (HJB) equation is a partial differential equation which is central to optimal control theory.

Hamilton-Jacobi–Bellman equation

The Hamilton–Jacobi–Bellman equation is a partial differential equation which is central to optimal control theory.

The Hamilton–Jacobi–Bellman equation is a partial differential equation which is central to optimal control theory.

Hamiltonian (control theory)

The Hamiltonian of optimal control theory was developed by L. S. Pontryagin as part of his minimum principle.

The Hamiltonian of optimal control theory was developed by L. S. Pontryagin as part of his minimum principle.

Hamilton–Jacobi–Bellman equation

The Hamilton–Jacobi–Bellman (HJB) equation is a partial differential equation which is central to optimal control theory.

The Hamilton–Jacobi–Bellman (HJB) equation is a partial differential equation which is central to optimal control theory.

Legendre pseudospectral method

The Legendre pseudospectral method for optimal control problems is based on Legendre polynomials.

The Legendre pseudospectral method for optimal control problems is based on Legendre polynomials.

Legendre-Clebsch condition

In the calculus of variations the Legendre-Clebsch condition is a second-order condition which a solution of the Euler-Lagrange equation must satisfy in order to be a maximum (and not a minimum ...

In the calculus of variations the Legendre-Clebsch condition is a second-order condition which a solution of the Euler-Lagrange equation must satisfy in order to be a maximum (and not a minimum ...

Legendre–Clebsch condition

In the calculus of variations the Legendre-Clebsch condition is a second-order condition which a solution of the Euler-Lagrange equation must satisfy in order to be a maximum (and not a minimum ...

In the calculus of variations the Legendre-Clebsch condition is a second-order condition which a solution of the Euler-Lagrange equation must satisfy in order to be a maximum (and not a minimum ...

Linear-quadratic regulator

One of the main results in the theory is that the solution is provided by the linear-quadratic regulator (LQR), a feedback controller whose equations are given below.

One of the main results in the theory is that the solution is provided by the linear-quadratic regulator (LQR), a feedback controller whose equations are given below.

Linear-quadratic-Gaussian control

In control theory, the linear-quadratic-Gaussian (LQG) control problem is one of the most fundamental optimal control problems.

In control theory, the linear-quadratic-Gaussian (LQG) control problem is one of the most fundamental optimal control problems.

Optimal control

Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies.

Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies.

Optimal projection equations

The reduced-order LQG problem (fixed-order LQG problem) overcomes this by fixing a-priori the number of states of the LQG controller.

The reduced-order LQG problem (fixed-order LQG problem) overcomes this by fixing a-priori the number of states of the LQG controller.

Pontryagin's minimum principle

Pontryagin's maximum (or minimum) 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 presenc...

Pontryagin's maximum (or minimum) 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 presenc...

PROPT

The PROPT MATLAB Optimal Control Software is a new generation platform for solving applied optimal control (with ODE or DAE formulation) and parameters estimation problems.

The PROPT MATLAB Optimal Control Software is a new generation platform for solving applied optimal control (with ODE or DAE formulation) and parameters estimation problems.

Pseudospectral knotting method

In applied mathematics, the pseudospectral knotting method is a generalization and enhancement of a standard pseudospectral method for optimal control.

In applied mathematics, the pseudospectral knotting method is a generalization and enhancement of a standard pseudospectral method for optimal control.

Pseudospectral optimal control

According to Ross et al., pseudospectral optimal control is a joint theoretical-computational method for solving optimal control problems.

According to Ross et al., pseudospectral optimal control is a joint theoretical-computational method for solving optimal control problems.

Ross' π lemma

Ross' lemma, named after I. Michael Ross, is a result in computational optimal control.

Ross' lemma, named after I. Michael Ross, is a result in computational optimal control.

Ross-Fahroo lemma

Named after I. Michael Ross and F. Fahroo, the Ross–Fahroo lemma is a fundamental result in optimal control theory.

Named after I. Michael Ross and F. Fahroo, the Ross–Fahroo lemma is a fundamental result in optimal control theory.

Ross-Fahroo pseudospectral method

The Ross–Fahroo pseudospectral methods are a broad collection of pseudospectral methods for optimal control introduced by I. Michael Ross and F. Fahroo, at the turn of the millennium.

The Ross–Fahroo pseudospectral methods are a broad collection of pseudospectral methods for optimal control introduced by I. Michael Ross and F. Fahroo, at the turn of the millennium.

Ross-Fahroo Pseudospectral Methods

The Ross-Fahroo pseudospectral methods are a broad collection of pseudospectral methods for optimal control introduced by Ross and Fahroo, at the turn of the millennium.

The Ross-Fahroo pseudospectral methods are a broad collection of pseudospectral methods for optimal control introduced by Ross and Fahroo, at the turn of the millennium.

Sethi model

The Sethi model was developed by Suresh P. Sethi and describes the process of how sales evolve over time in response to advertising.

The Sethi model was developed by Suresh P. Sethi and describes the process of how sales evolve over time in response to advertising.