Solve Riccati Differential Equation (solve_riccati_ode)

Version 3.1.0 (240 KB) by Tamas Kis
Solves the Riccati differential equation for the finite-horizon linear quadratic regulator.
198 Downloads
Updated Thu, 08 Dec 2022 15:02:31 +0000

solve_riccati_ode View Solve Riccati Differential Equation (solve_riccati_ode) on File Exchange

Solves the Riccati differential equation for the finite-horizon linear quadratic regulator.

NOTE: This function requires the IVP Solver Toolbox.

Syntax

[t,P] = solve_riccati_ode(A,B,Q,R,[],PT,tspan)
[t,P] = solve_riccati_ode(A,B,Q,R,S,PT,tspan)

Description

[t,P] = solve_riccati_ode(A,B,Q,R,[],PT,tspan) solves the Riccati differential equation for , given the state matrix , input matrix , state weighting matrix , input weighting matrix , terminal condition , and the time span tspan over which to solve. tspan can be specified either as the 1×2 double [t0,T] where is the initial time and is the final time, or as a 1×(N+1) vector of times [t0,t1,...,tNminus1,T] at which to return the solution for . It is assumed that the cross-coupling weighting matrix is .

[t,P] = solve_riccati_ode(A,B,Q,R,S,PT,tspan) does the same as the syntax above, but this time the cross-coupling weighting matrix is specified.

Time Vector and Solution Array

The time vector, , is defined as

The ith "layer" of P (i.e. P(:,:,i)) stores , where is the time stored in the ith element of the time vector, .

Examples and Additional Documentation

  • See "EXAMPLES.mlx" or the "Examples" tab on the File Exchange page for examples.
  • See Riccati_Differential_Equation.pdf (also included with download) for additional documentation.

Cite As

Tamas Kis (2024). Solve Riccati Differential Equation (solve_riccati_ode) (https://github.com/tamaskis/solve_riccati_ode-MATLAB/releases/tag/v3.1.0), GitHub. Retrieved .

MATLAB Release Compatibility
Created with R2021b
Compatible with any release
Platform Compatibility
Windows macOS Linux

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Version Published Release Notes
3.1.0

See release notes for this release on GitHub: https://github.com/tamaskis/solve_riccati_ode-MATLAB/releases/tag/v3.1.0

3.0.4

See release notes for this release on GitHub: https://github.com/tamaskis/solve_riccati_ode-MATLAB/releases/tag/v3.0.4

3.0.3

See release notes for this release on GitHub: https://github.com/tamaskis/solve_riccati_ode-MATLAB/releases/tag/v3.0.3

3.0.2

See release notes for this release on GitHub: https://github.com/tamaskis/solve_riccati_ode-MATLAB/releases/tag/v3.0.2

3.0.1.0

See release notes for this release on GitHub: https://github.com/tamaskis/solve_riccati_ode-MATLAB/releases/tag/v3.0.1

3.0.0.0

See release notes for this release on GitHub: https://github.com/tamaskis/solve_riccati_ode-MATLAB/releases/tag/v3.0.0

1.0.2

See release notes for this release on GitHub: https://github.com/tamaskis/odericcati-MATLAB/releases/tag/v1.0.2

1.0.1.0

See release notes for this release on GitHub: https://github.com/tamaskis/solve_riccati_ode-MATLAB/releases/tag/v1.0.1

1.0.0

To view or report issues in this GitHub add-on, visit the GitHub Repository.
To view or report issues in this GitHub add-on, visit the GitHub Repository.