BP-MPC: Optimizing Model Predictive Control with Backpropagation

Core Concepts

Backpropagation optimizes MPC performance by solving a policy optimization problem with nonlinear dynamics.

Abstract

The content discusses optimizing Model Predictive Control (MPC) using backpropagation. It introduces a backpropagation scheme to solve policy optimization problems with nonlinear system dynamics in MPC. The article covers the challenges of designing MPC controllers, the use of differentiable optimization, and the application of conservative Jacobians for convergence guarantees. It also explores extensions like successive linearization, state-dependent cost and constraints, handling infeasibility, and non-convex costs. Algorithms for backpropagation and closed-loop optimization are provided.

Stats

Problem (27) has the same solution as (7) if feasible and c2 > ∥λ∥∞.
Average computation times for BP-MPC iterations are 41.147 ms and 201.90 ms.

Quotes

Key Insights Distilled From

BP-MPC

by Riccardo Zul... at arxiv.org 03-18-2024

https://arxiv.org/pdf/2312.15521.pdf

Deeper Inquiries

How does the introduction of state-dependent elements impact MPC performance

State-dependent elements in MPC can have a significant impact on performance by allowing the controller to adapt dynamically based on the current state of the system. By incorporating state-dependent cost functions and constraints, the MPC controller can tailor its behavior to better suit the specific conditions at each time step. This flexibility enables the controller to respond more effectively to changes in the system dynamics, leading to improved closed-loop performance. State-dependent elements provide a way for the MPC controller to optimize its actions based on real-time information, resulting in enhanced control over complex systems.

What are the implications of calmness in ensuring convergence to local minima

Calmness plays a crucial role in ensuring convergence to local minima during optimization processes like MPC. When dealing with calm minimizers, it indicates that small perturbations around a solution do not significantly affect its optimality properties. In practical terms, calmness ensures stability and robustness of optimization algorithms by guaranteeing that small variations or disturbances will not lead to drastic changes in solutions obtained through optimization. By satisfying calmness conditions, we can ensure that our optimization process converges reliably towards optimal solutions even when faced with uncertainties or noise in the system.

How can the framework be extended to handle more complex cost functions in MPC optimization

To handle more complex cost functions in MPC optimization within this framework, one approach is to introduce additional terms into the objective function that depend on various variables such as states, inputs, or parameters. These additional terms could represent penalties for constraint violations, regularization terms for smoother control actions, or incentives for achieving certain objectives during closed-loop operation.
By extending the cost function appropriately and ensuring path-differentiability of these new components along with existing ones (such as quadratic costs), we can incorporate them into our backpropagation scheme seamlessly.
Furthermore, by adjusting penalty parameters and introducing suitable regularization techniques within our algorithmic procedures (such as Algorithm 4), we can efficiently optimize more intricate cost functions while maintaining convergence guarantees towards desired local minima.