毕业设计&课设-用于分析非线性系统可控性和可达性的MATLAB工具箱。.zip

# NLcontrollability MATLAB toolbox for analysing controllability and accessibility of nonlinear systems. # To use NLcontrollability you need to: 1. Download the code. 2. Open a MATLAB session. 3. Edit the `run.m` file and run it. You can find an example in the `run.m` file and more in `ctrl_reach_unit_test_script.m` # Options - **opts.LC** --> 1 if you want to check the Linearization Condition, 0 if not - **opts.ARC** --> 1 if you want to check the Accessibility Rank Condition, 0 if not - **opts.LARC** --> 1 if you want to check the Lie Algebraic Rank Condition, 0 if not - **opts.LARC** --> 1 if you want to check the Lie Algebraic Rank Condition, 0 if not - **opts.GSC** --> 1 if you want to check Sussmann's General Sufficient Condition, 0 if not - **'model_name'** --> Name of a .mat file placed in the 'models' folder - **opts.numericLC** --> 0 if you want to check the Linearization Condition symbolically, 1 for numeric computation - **opts.maxtime** --> max time for each test in seconds - **x0** --> Specific initial point. If no point is given it would try to compute equilibrium points. # Entering the model NLcontrollability reads models stored as MATLAB MAT-files (.mat). Models are defined as follows: First, all parameters, states, and any other entities (such as inputs or known constants) appearing in the model must be defined as symbolic variables. Example: syms x1 x2 x3 x4 lambda u1 Then we define the state variables, by creating a column vector named x. Example: x = [x1; x2; x3; x4]; Similarly, we define the known input vector, u. If there are no inputs, enter a blank vector. Example: u = u1; % Or, for more than one input --> u = [u1; u2]; The model ODEs (dx/dt=...) must also be entered as a column vector, called f, which must have the same length as the state vector x. Example: f = [u1; x1; x1^3; x3^2-lambda*x2^2*x1^4]; Finally, save all the variables in a MAT-file. Example: save(‘MAPK’,‘x’,‘u’,‘f’); This model description format is the same used by the [STRIKE-GOLDD](https://github.com/afvillaverde/strike-goldd) toolbox. Further details can be found in its [documentation](https://github.com/afvillaverde/strike-goldd/blob/master/STRIKE-GOLDD/doc/STRIKE-GOLDD_manual.pdf). # Software contents - **`run.m`**: file where the user enters the model and options. Running it executes the code. - **`ctrl_analysis_MAIN.m`:** main file; it calls the scripts with the accessibility and controllability tests. - **`ctrl_LC.m`**: implementation of the Linearization Condition. - **`ctrl_ARC.m`**: implementation of the Accessibility Rank Condition. - **`ctrl_LARC_GSC.m`**: implementation of the Lie Algebraic Rank Condition and Sussmann's General Sufficient Condition. - **`ctrl_reach_unit_tests_script.m`**: file with some examples ready to run. - **`Lie_bracket.m`**: auxiliary function that computes the Lie bracket of two vectors w.r.t. a variable. - **`frac_elem_sym.m`**: auxiliary function that changes a rational equation into its numerator and denominator. - **`make_affine_known_u.m`**: function that converts a model into affine in inputs form # Publications Publication of the methodology (pending)