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Automated Nonlinear Dynamic System Modeling. PhD dissertation project.
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Automated Nonlinear Dynamical Systems Modeling

ANDSM automatically generates nonlinear dynamical models from input-state-output training data into a state-space format


The generated models are guaranteed passive and optionally incrementally stable. The passivity property ensures that the models do not generate numerical energy, hence, suited for modeling nonlinear circuit networks (including active and passive), arterial (cardiovascular) networks, and potentially all systems that can be represented as circuits or bond graphs.


The underlying algorithm is a convex optimization program constrained by specially forged sum-of-squares (of-polynomials) constraints. These constraints theoretically guarantee that all feasible solutions within the set preserve desired system properties, such as passivity and incremental stability. Solving such an optimization problem essentially looks for a model whose parameters minimize against the training data, while at the same time every candidate models along the search path possess the system properties of interest.

Details and theories can be referred to here.

Installation and Dependencies

ANDSM utilizes YALMIP to transform SOS optimization problems into semidefinite progromming (SDP) problems. The resulting SDP problems are then resolved by MOSEK. The instructions of installing YALMIP, MOSEK, and ANDSM are described here.


The basic logic of using ANDSM is

  1. Prepare the training and the validation data sets

  2. Create a ANDSM object with the training and the validation sets

andsm = Andsm(training_data, validation_data);
  1. Train a set of models using different parameters
deg_e = 1;
deg_f = 1;
deg_h = 1;
deg_v = 2;

kappa = [1e-4, 1e-3, 1e-2, 1e-1, 1e0, 1e1, 1e2];
lambda = [1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1];

andsm.train([deg_e, deg_f, deg_h, deg_v], kappa, lambda);
  1. Take the best model with the lowest errors
[model, err, ind] = andsm.get_best_model
  1. Visulize the model performance by simulating it
t = validation_data.t{1};
u = validation_data.u{1};
y = validation_data.y{1};
x0 = [0;0;0];
tol = 'regular';

[tt, uu, xx, yy] = Andsm.sim(model, t, u, x0, tol);
  1. When satisfied with the accuracy, export the model in SimScape (Simulink) or Verilog-A formats
andsm.export('+drc2/drc2_model', 'simscape', 'i', option);
andsm.export('va/drc2_model_v', 'veriloga', 'v', option);
  1. Now, the generated model is ready for system-level integrations by interconnecting with other models.

For runnable demos, please refer the file for more detailed examples.

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