Tidied up the MATLAB code. Updated the MATLAB plots. Updated the docu…

…mentation.

Julia/README.md

@@ -1,5 +1,5 @@
 # Julia
-[![Dev](https://img.shields.io/badge/docs-latest-blue.svg)](https://TUM-ITR.github.io/PGopt)
+[![Dev](https://img.shields.io/badge/docs-stable-blue?logo=Julia&logoColor=white)](https://TUM-ITR.github.io/PGopt)
 
 This folder contains the Julia implementation of `PGopt`, which does not require proprietary software. The open-source solver [Altro](https://github.com/RoboticExplorationLab/Altro.jl) is used for the optimization. The results presented in the paper were generated with this version, and the software reproduces these results exactly.
 

Julia/docs/src/index.md

@@ -12,9 +12,9 @@ This document describes the Julia implementation of `PGopt`, which does not requ
 Besides the Julia implementation, there is also a MATLAB implementation, which is more general and allows arbitrary cost functions $J_H(u_{1:H},x_{1:H},y_{1:H})$, measurement functions $y=g(x,u)$, and constraints $h(u_{1:H},x_{1:H},y_{1:H})$. Further information can be found [here](https://github.com/TUM-ITR/PGopt/tree/main/MATLAB).
 
 ## Installation
-PGopt can be installed using the Julia package manager. Start a Pkg REPL (press `]` in a Julia REPL), and install PGopt via
+`PGopt` can be installed using the Julia package manager. Start a Pkg REPL (press `]` in a Julia REPL), and install `PGopt` via
 ```
-pkg> add https://github.com/TUM-ITR/PGopt:Julia
+pkg>add https://github.com/TUM-ITR/PGopt:Julia
 ```
 
 Alternatively, to inspect the source code more easily, download the source code from [GitHub](https://github.com/TUM-ITR/PGopt). Navigate to the folder `PGopt/Julia`, start a Pkg REPL (press `]` in a Julia REPL), and install the dependencies via

MATLAB/examples/PG_OCP_generic_basis_functions.m

@@ -1,6 +1,6 @@
 % This code produces results for the optimal control approach with generic basis functions similar to the ones given in Section V-B (Fig. 3) of the paper
 % "Learning-Based Optimal Control with Performance Guarantees for Unknown Systems with Latent States", available as pre-print on arXiv: https://arxiv.org/abs/2303.17963.
-% Since the Julia implementation was used for the results in the paper, the results are not exactly reproduced due to different random numbers.
+% Since the Julia implementation was used for the results in the paper, the results are not exactly reproduced.
 
 % Clear
 clear;
@@ -170,7 +170,7 @@
 
 %% Test the learned models.
 % Test the models with the test data by simulating it forward in time.
-test_prediction(PG_samples, phi_sampling, g, R, 10, u_test, y_test);
+% test_prediction(PG_samples, phi_sampling, g, R, 10, u_test, y_test);
 
 %% Plot autocorrelation.
 % plot_autocorrelation(PG_samples, 'max_lag', 100)
@@ -198,8 +198,11 @@
 % This function is only used for the optimization as it is less efficient.
 phi = @(x, u) phi_opt(n_phi, n_z, L, j_vec, x, u);
 
+% Ipopt options
+Ipopt_options = struct('linear_solver', 'ma57', 'max_iter', 10000);
+
 % Solve the PG OCP.
-[u_opt, x_opt, y_opt, J_opt, solve_successful, ~, ~] = solve_PG_OCP(PG_samples, phi, g, R, H, cost_function, scenario_constraints, input_constraints, 'J_u', true, 'K_pre_solve', 10);
+[u_opt, x_opt, y_opt, J_opt, solve_successful, ~, ~] = solve_PG_OCP(PG_samples, phi, g, R, H, cost_function, scenario_constraints, input_constraints, 'J_u', true, 'K_pre_solve', 5, 'solver_opts', Ipopt_options);
 
 %% Test solution
 if solve_successful

MATLAB/examples/PG_OCP_known_basis_functions.m

@@ -140,11 +140,14 @@
 % Confidence parameter for the theoretical guarantees
 beta = 0.01;
 
+% Ipopt options
+Ipopt_options = struct('linear_solver', 'ma57', 'max_iter', 10000);
+
 % Solve the PG OCP.
-% [u_opt, x_opt, y_opt, J_opt, solve_successful, ~, ~] = solve_PG_OCP(PG_samples, phi, g, R, H, cost_function, scenario_constraints, input_constraints, 'J_u', true, 'K_pre_solve', 10);
+% [u_opt, x_opt, y_opt, J_opt, solve_successful, ~, ~] = solve_PG_OCP(PG_samples, phi, g, R, H, cost_function, scenario_constraints, input_constraints, 'J_u', true, 'K_pre_solve', 5);
 
 % Solve the PG OCP and determine complexity s and max constraint violation probability via greedy algorithm.
-[u_opt, x_opt, y_opt, J_opt, solve_successful, s, epsilon_prob, epsilon_perc, time_first_solve, time_guarantees, num_failed_optimizations] = solve_PG_OCP_greedy_guarantees(PG_samples, phi, g, R, H, cost_function, scenario_constraints, input_constraints, beta, 'J_u', true, 'K_pre_solve', 10);
+[u_opt, x_opt, y_opt, J_opt, solve_successful, s, epsilon_prob, epsilon_perc, time_first_solve, time_guarantees, num_failed_optimizations] = solve_PG_OCP_greedy_guarantees(PG_samples, phi, g, R, H, cost_function, scenario_constraints, input_constraints, beta, 'J_u', true, 'K_pre_solve', 5, 'solver_opts', Ipopt_options);
 
 %% Test solution
 if solve_successful