Reduced_Bilevel_MPC

Overview

This repository provides MATLAB implementations of the reduced bilevel MPC proposed in our paper, along with several baseline methods for comparison:

• Hierarchical MPC (P0)
• Original bilevel MPC (P1)
• Reduced bilevel MPC (P2)
• Centralized MPC (P3)
• Move-blocking variants (P1(M), P2(M))

The code allows users to reproduce numerical results and compare control performance across these formulations.

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Background

This repository accompanies the following paper:

"Bilevel MPC for Linear Systems: A Tractable Reduction and Continuous Connection to Hierarchical MPC" Submitted to IEEE CDC

The main purpose of this code is to reproduce the results presented in the paper, including:

• Toy example
• Quadrotor example

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Features

• Solve and compare multiple MPC formulations (P0–P3, P1(M), P2(M))
• Plot state and input trajectories over the prediction horizon
• Evaluate the effect of move-blocking matrices on performance
• Compute and visualize upper bounds proposed in the paper
• Run closed-loop simulations for all methods
• Reproduce both toy and quadrotor experiments via configurable settings

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Repository Structure

.
├── figs/                    # Saved figures
├── bilvlMPC.m               # Main script (OCP comparison & closed-loop simulation)
├── MB_bounding.m            # Script for move-blocking performance bounds
├── ToySetting.m             # Toy example configuration
├── Quadrotor_setting.m      # Quadrotor configuration
└── (other auxiliary files)

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Requirements

• MATLAB R2024b
• Optimization Toolbox
• Control System Toolbox

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Usage

Step 1: Select problem setting

In bilvlMPC.m, specify the problem:

prob = ToySetting;            % or Quadrotor_setting

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Step 2: Select execution mode

In bilvlMPC.m, set:

mode = *;  % choose from below

Available modes:

-1 : Single OCP comparison at x = x0
 0 : P0 (hierarchical MPC) closed-loop simulation
 1 : P1 (bilevel MPC) closed-loop simulation
 2 : P2 (reduced bilevel MPC) closed-loop simulation
 3 : P3 (centralized MPC) closed-loop simulation
10 : P1(M) (move-blocking bilevel MPC)
20 : P2(M) (move-blocking reduced bilevel MPC)

Or, you can specify the execution mode by giving it as an argument, e.g.:

bilvlMPC(1);

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Step 3-A: Single OCP comparison

Set mode = -1; in bilvlMPC.m and run

run('bilvlMPC.m')

Or, just

bilvlMPC(-1);

This compares P0–P3, P1(M), and P2(M) for a fixed initial state.

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Step 3-B: Move-blocking performance analysis

In MB_bounding.m, select toy or quadrotor setting inside the script, and run

run('MB_bounding.m')

This generates:

• Optimal values of P1(M), P2(M), and P0
• Upper bounds proposed in the paper

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Step 3-C: Closed-loop simulation

Set mode = 0,1,2,3,10,20; in bilvlMPC.m and run

run('bilvlMPC.m')

Or, just specify it in the argument, e.g.:

bilvlMPC(0);

This executes closed-loop simulations for the selected method and plots the results.

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Notes

• Results may slightly vary depending on solver tolerances.
• Figures are saved in the figs/ directory.
• The configuration files (ToySetting.m, Quadrotor_setting.m) define system dynamics, cost, and constraints.

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License

MIT License

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Author

• Ryuta Moriyasu, Stanford University / Toyota Motor North America, moriyasu@stanford.edu
• Carmen Amo Alonso, Stanford University, camoalon@stanford.edu
• Marco Pavone, Stanford University / NVIDIA Research, pavone@stanford.edu