renamed function and updated to be compatible with newer version of IVP Solver Toolbox

Author: tamaskis

EXAMPLES.mlx

@@ -1,4 +1,4 @@
-# `odericcati` [![View Solution of the Riccati Differential Equation (odericcati) on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://www.mathworks.com/matlabcentral/fileexchange/104030-solution-of-the-riccati-differential-equation-odericcati)
+# `solve_riccati_ode` [![View Solution of the Riccati Differential Equation (odericcati) on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://www.mathworks.com/matlabcentral/fileexchange/104030-solution-of-the-riccati-differential-equation-odericcati)
 
 Solves the Riccati differential equation for the finite-horizon linear quadratic regulator.
 
@@ -7,15 +7,15 @@ Solves the Riccati differential equation for the finite-horizon linear quadratic
 
 ## Syntax
 
-`[t,P] = odericcati(A,B,Q,R,[],PT,tspan)`\
-`[t,P] = odericcati(A,B,Q,R,S,PT,tspan)`
+`[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] = odericcati(A,B,Q,R,[],PT,tspan)` solves the Riccati differential equation <img src="https://latex.codecogs.com/svg.latex?\inline&space;\dot{\mathbf{P}}=-\left[\mathbf{A}^{T}\mathbf{P}+\mathbf{P}\mathbf{A}-(\mathbf{P}\mathbf{B}+\mathbf{S})\mathbf{R}^{-1}(\mathbf{B}^{T}\mathbf{P}+\mathbf{S}^{T})+\mathbf{Q}\right]" title="" /> for <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{P}(t)\in\mathbb{R}^{{n}\times{n}}" title="" />, given the state matrix <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{A}\in\mathbb{R}^{{n}\times{n}}" title="" />, input matrix <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{B}\in\mathbb{R}^{{n}\times{m}}" title="" />, state weighting matrix <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{Q}\in\mathbb{R}^{{n}\times{n}}" title="" />, input weighting matrix <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{R}\in\mathbb{R}^{{m}\times{m}}" title="" />, terminal condition <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{P}_{T}\in\mathbb{R}^{{n}\times{n}}" title="" />, and the time span `tspan` over which to solve. `tspan` can be specified either as the 1×2 double `[t0,T]` where <img src="https://latex.codecogs.com/svg.latex?\inline&space;t=t_{0}" title="" /> is the initial time and <img src="https://latex.codecogs.com/svg.latex?\inline&space;t=T" title="" /> is the final time, or as a 1×(N+1) vector of times `[t0,t1,...,tNminus1,T]` at which to return the solution for <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{P}(t)" title="" />. It is assumed that the cross-coupling weighting matrix is <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{S}=\mathbf{0}_{{n}\times{m}}" title="" />.
+`[t,P] = solve_riccati_ode(A,B,Q,R,[],PT,tspan)` solves the Riccati differential equation <img src="https://latex.codecogs.com/svg.latex?\inline&space;\dot{\mathbf{P}}=-\left[\mathbf{A}^{T}\mathbf{P}+\mathbf{P}\mathbf{A}-(\mathbf{P}\mathbf{B}+\mathbf{S})\mathbf{R}^{-1}(\mathbf{B}^{T}\mathbf{P}+\mathbf{S}^{T})+\mathbf{Q}\right]" title="" /> for <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{P}(t)\in\mathbb{R}^{{n}\times{n}}" title="" />, given the state matrix <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{A}\in\mathbb{R}^{{n}\times{n}}" title="" />, input matrix <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{B}\in\mathbb{R}^{{n}\times{m}}" title="" />, state weighting matrix <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{Q}\in\mathbb{R}^{{n}\times{n}}" title="" />, input weighting matrix <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{R}\in\mathbb{R}^{{m}\times{m}}" title="" />, terminal condition <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{P}_{T}\in\mathbb{R}^{{n}\times{n}}" title="" />, and the time span `tspan` over which to solve. `tspan` can be specified either as the 1×2 double `[t0,T]` where <img src="https://latex.codecogs.com/svg.latex?\inline&space;t=t_{0}" title="" /> is the initial time and <img src="https://latex.codecogs.com/svg.latex?\inline&space;t=T" title="" /> is the final time, or as a 1×(N+1) vector of times `[t0,t1,...,tNminus1,T]` at which to return the solution for <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{P}(t)" title="" />. It is assumed that the cross-coupling weighting matrix is <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{S}=\mathbf{0}_{{n}\times{m}}" title="" />.
 
-`[t,P] = odericcati(A,B,Q,R,S,PT,tspan)` does the same as the syntax above, but this time the cross-coupling weighting matrix <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{S}\in\mathbb{R}^{{n}\times{m}}" title="" /> *is* specified.
+`[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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{S}\in\mathbb{R}^{{n}\times{m}}" title="" /> *is* specified.
 
 
 ## Time Vector and Solution Array

README.md

@@ -1,21 +1,21 @@
 %==========================================================================
 %
-% odericcati  Solves the Riccati differential equation for the 
+% solve_riccati_ode  Solves the Riccati differential equation for the 
 % finite-horizon linear quadratic regulator.
 %
-%   [t,P] = odericcati(A,B,Q,R,[],PT,tspan)
-%   [t,P] = odericcati(A,B,Q,R,S,PT,tspan)
+%   [t,P] = solve_riccati_ode(A,B,Q,R,[],PT,tspan)
+%   [t,P] = solve_riccati_ode(A,B,Q,R,S,PT,tspan)
 %
 % Copyright © 2021 Tamas Kis
-% Last Update: 2022-06-07
+% Last Update: 2022-08-28
 % Website: https://tamaskis.github.io
 % Contact: [email protected]
 %
 % TECHNICAL DOCUMENTATION:
 % https://tamaskis.github.io/documentation/Riccati_Differential_Equation.pdf
 %
 % DEPENDENCIES:
-%   --> IVP Solver Toolbox (https://www.mathworks.com/matlabcentral/fileexchange/103975-ivp-solver-toolbox)
+%   • IVP Solver Toolbox (https://www.mathworks.com/matlabcentral/fileexchange/103975-ivp-solver-toolbox)
 %
 %--------------------------------------------------------------------------
 %
@@ -53,13 +53,8 @@
 %   4. (A-BR^(-1)S^T,Q-SR^(-1)S^T) detectable
 %       • if S = 0, this condition reduces to (A,Q^(1/2)) detectable
 %
-% -----
-% NOTE:
-% -----
-%   --> N+1 = length of time vector
-%
 %==========================================================================
-function [t,P] = odericcati(A,B,Q,R,S,PT,tspan)
+function [t,P] = solve_riccati_ode(A,B,Q,R,S,PT,tspan)
 
     % ----------------------
     % Determines dimensions.
@@ -91,17 +86,17 @@
     dPdt = @(t,P) -(A.'*P+P*A-(P*B+S)/R*(B.'*P+S.')+Q);
 
     % converts matrix-valued ODE to vector-valued ODE
-    dydt = odefun_mat2vec(dPdt);
+    dydt = mat2vec_ode(dPdt);
 
     % converts matrix initial condition to vector initial condition
-    yT = ivpIC_mat2vec(PT);
+    yT = mat2vec_IC(PT);
 
     % solves Riccati ODE
     [t,y] = ode45(dydt,tspan,yT);
 
     % transforms solution matrix for vector-valued ODE into solution array
     % for matrix-valued ODE
-    P = ivpsol_vec2mat(y);
+    P = vec2mat_sol(y);
 
     % reorders t so that time is increasing
     t = flipud(t);