nonlinear_dd_mpc_example_params.yaml

---
# Nonlinear Data-Driven MPC Parameters
# Based on the Nonlinear Data-Driven MPC implementation example for the
# control of a nonlinear continuous stirred tank reactor (CSTR) from Section V
# of the paper:
# [2] J. Berberich, J. Köhler, M. A. Müller and F. Allgöwer, "Linear Tracking
#     MPC for Nonlinear Systems—Part II: The Data-Driven Case," in IEEE
#     Transactions on Automatic Control, vol. 67, no. 9, pp. 4406-4421, Sept.
#     2022, doi: 10.1109/TAC.2022.3166851.

nonlinear_data_driven_mpc_params:
  n: 3  # Estimated system order

  N: 120  # Initial input-output trajectory length
  L: 40  # Prediction horizon

  # Weighting matrices
  # Each weighting parameter can be either a scalar or a list.
  #   - Scalar → Applies the same weight to all variables.
  #   - List → Assigns specific weights to each variable. Must have `n_vars`
  #            elements, where:
  #              - Q_weights → `n_vars = p` (number of outputs)
  #              - R_weights → `n_vars = m` (number of inputs)
  #              - S_weights → `n_vars = p` (number of outputs)
  #
  # Example (scalar):
  #   Q_weights: 0.1  # Same weight for all outputs
  #   Q_weights: [0.1, 2.5, 40]  # Different weights per output

  Q_weights: 1  # Output weighting matrix Q weights
  R_weights: 5.0e-2  # Input weighting matrix R weights
  S_weights: 10  # Output setpoint weighting matrix S weights

  lambda_alpha: 3.0e-6  # Regularization parameter for alpha
  lambda_sigma: 1.0e+7  # Regularization parameter for sigma

  # Parameters for input bounds and ranges
  # Note: Each input must have an associated vector of
  # bounds or ranges [min, max].

  # Bounds for the predicted input
  U:
    - [0.1, 2]

  # Bounds for the predicted input setpoint (must be a subset of U)
  Us:
    - [0.11, 1.99]

  # Range of the persistently exciting input u
  u_range:
    - [0.1, 1]

  # Alpha regularization type:
  # - 0 = Approximated → Regularized w.r.t. an approximation of
  #                      alpha_Lin^sr(D_t) (Remark 1 of [2]).
  # - 1 = Previous → Regularized w.r.t. a previous optimal alpha value to
  #                  encourage stationary behavior (Section V of [2]).
  # - 2 = Zero → Regularized w.r.t. zero.
  alpha_reg_type: 1

  # Nonlinear MPC parameters for alpha_reg_type = 0 (Approximated)
  lambda_alpha_s: null  #  Regularization parameter for alpha_s (optional)
  lambda_sigma_s: null  #  Regularization parameter for sigma_s (optional)

  y_r: [0.6519]  # System output setpoint

  # Control system structure (Extendended Output and Input Increments):
  # - true → Controller uses an extended output representation
  #          (y_ext[k] = [y[k], u[k]]) and input increments where the control
  #          input is updated incrementally as: u[k] = u[k-1] + du[k-1].
  # - false → Standard controller operation. Direct control input, without
  #           extensions.
  ext_out_incr_in: true

  # Tracking cost value threshold
  # Online input-output data updates are disabled when the tracking cost value
  # is less than this value. This ensures prediction data is persistently
  # exciting (Section V of [2]).
  #
  # If set to `null` or 0, input-output data is always updated online.
  update_cost_threshold: 1.0e-5

  # Enable n-Step Data-Driven MPC:
  # - true = n-Step Data-Driven MPC
  # - false = 1-Step Data-Driven MPC
  n_n_mpc_step: true