Exploiting Differential Flatness for Efficient Learning-based Model Predictive Control of Constrained Multi-Input Control Affine Systems

2026-04-27

AI Summary

This work addresses the computational inefficiency and real-time implementation challenges of learning-based controllers for uncertain nonlinear systems by proposing an efficient differential flatness–based learning model predictive control (MPC) framework. By leveraging system extension and a block-diagonal cost structure, the method is the first to accommodate general multi-input nonlinear control-affine systems subject to both input constraints and half-space constraints on flat outputs, overcoming limitations of existing approaches that are restricted to single-input systems, ignore constraints, or rely on specific platforms. The algorithm integrates sequential convex programming with Gaussian process modeling and ensures Lyapunov descent in a probabilistic sense through two convex optimization steps. Simulations demonstrate performance comparable to Gaussian process MPC with several-fold speedup in computation, while hardware experiments confirm excellent trajectory tracking capabilities.

Technology Category

• Search and Optimization: Learning to Search
• Multiagent Systems: Multiagent Learning
• Machine Learning: Learning with Manifolds

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

Learning-based control techniques use data from past trajectories to control systems with uncertain dynamics. However, learning-based controllers are often computationally inefficient, limiting their practicality. To address this limitation, we propose a learning-based controller that exploits differential flatness, a property of many robotic systems. Recent research on using flatness for learning-based control either is limited in that it (i) ignores input constraints, (ii) applies only to single-input systems, or (iii) is tailored to specific platforms. In contrast, our approach uses a system extension and block-diagonal cost formulation to control general multi-input, nonlinear, affine systems. Furthermore, it satisfies input and half-space flat state constraints and guarantees probabilistic Lyapunov decrease using only two sequential convex optimizations. We show that our approach performs similarly to, but is multiple times more efficient than, a Gaussian process model predictive controller in simulation, and achieves competitive tracking in real hardware experiments.

Problem

• differential flatness
• learning-based control
• model predictive control
• multi-input systems
• input constraints

Innovation

• differential flatness
• learning-based control
• model predictive control
• multi-input systems
• convex optimization