F-16 Pitch Control: Nominal MPC, Tube MPC, and UC-MPC (Uncertainty Compensation)

This repo contains MATLAB code for constrained control of an F-16 pitch attitude model under matched and unmatched uncertainties, including:

• Nominal MPC with constraint tightening (nominal plan)
• Vanilla MPC (baseline MPC without ancillary feedback / tightening)
• Tube MPC (nominal MPC on tightened sets + robust ancillary feedback)
• UC-MPC （nominal MPC + robust ancillary feedback + adaptive uncertainty compensation)

The model and example are based on the linearized F-16 pitch dynamics

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Repo structure

Core scripts

• nominal_MPC_unmatched.m
  Builds the nominal MPC problem with tightened constraints and simulates the nominal closed-loop system:

  • output: umpchist_nominal.mat (nominal MPC input trajectory)
  • output: xhist_nominal.mat (nominal MPC state trajectory)
  • output: utotalhist_nominal.mat (total input u + Kx x if used)

• vanilla_MPC_unmatched.m Runs baseline MPC (no ancillary feedback in dynamics) and simulates the uncertain system directly.

  • output: MPC_umpc.mat, MPC_x.mat, MPC_u.mat

• tube_MPC_unmatched.m (Tube MPC script)
  Constructs:

  • disturbance set W
  • disturbance invariant tube set Z (finite approximation)
  • tightened constraints X_bar = X ⊖ Z, U_bar = U ⊖ KZ
    Then runs nominal MPC on tightened sets and simulates the true system using: [ u = u_{\text{nom}} + K(x_{\text{real}} - x_{\text{nom}}) ]
  • output: TMPC_umpc.mat, TMPC_x.mat, TMPC_u.mat

• main_L1MPC_f16.m Runs L1 adaptive augmentation on top of a precomputed nominal MPC trajectory. Important: this script expects nominal system trajectory umpchist_nominal.mat and xhist_nominal.mat to exist.

  • output: L1MPC_f.mat, L1MPC_w.mat, L1MPC_sigma1.mat, L1MPC_u.mat, L1MPC_ul1.mat, L1MPC_x.mat, L1MPC_xnom.mat

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Dependency files / functions

These functions are called by the main scripts:

• sim_L1MPC.m
  Fast-time simulation that applies baseline + L1 adaptive control and constraint tightening logic.

• compute_L1_bounds.m
  Computes/updates the L1 performance bounds used for constraint tightening, including:

  • rho_til_x: bound on ||x - x_nom||
  • rho_u: bound on ||u_L1||
  • derived rho_til_u = |Kx| rho_til_x + rho_u

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Requirements

• MATLAB (tested with Control System Toolbox)
• YALMIP installed and on MATLAB path
• MOSEK installed (solver used by YALMIP)

In scripts, paths are currently added via:

addpath(genpath('.../YALMIP'))
addpath(genpath('.../Mosek/...'))