Computationally Tractable Robust Nonlinear Model Predictive Control using DC Programming

TL;DR

A robust tube MPC scheme is developed that convexifies the online optimization by linearizing the concave components of the model, and guarantees of recursive feasibility and robust stability are provided.

Abstract

We propose a computationally tractable, tube-based robust nonlinear model predictive control (MPC) framework using difference-of-convex (DC) functions and sequential convex programming. For systems with differentiable discrete time dynamics, we show how to construct systematic, data-driven DC model representations using polynomials and machine learning techniques. We develop a robust tube MPC scheme that convexifies the online optimization by linearizing the concave components of the model, and we provide guarantees of recursive feasibility and robust stability. We present three data-driven procedures for computing DC models and compare performance using a planar vertical take-off and landing (PVTOL) aircraft case study.

Figures (16)

• Figure 1: ICNN architecture $z_L = f(x; \theta)$ where the kernel weights $\Theta_l$ are nonnegative $\forall l \geq 1$ and activation functions are convex non-decreasing.
• Figure 1: $J_{\mathcal{X},\mathcal{U}}^0$ and $J_{\mathcal{X},\mathcal{U}}^\mathcal{B}$ for all infeasibility detections.
• Figure 2: Polytopic tube cross section.
• Figure 3: Properties of a convex function
• Figure 4: Approximation of the PVTOL horizontal dynamics as a difference of SOS-convex polynomials.

Theorems & Definitions (22)

• Remark 1
• Theorem 1: Convex RBF
• proof
• Example 1
• Remark 2
• Remark 3
• Remark 4
• Proposition 2: Feasibility
• proof
• Lemma 3