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Convergence guarantees for adaptive model predictive control with kinky inference

Riccardo Zuliani, Raffaele Soloperto, John Lygeros

TL;DR

The paper addresses convergence guarantees for adaptive model predictive control applied to unknown nonlinear systems by learning a nominal model through kinky inference. It constructs data-driven uncertainty bounds and proves recursive feasibility and input-to-state stability, culminating in asymptotic convergence to the origin despite model uncertainty. A key contribution is showing convergence with only a tracking cost, avoiding the need for explicit excitation. The numerical example demonstrates that incorporating kinky inference enables effective regulation to the origin, highlighting practical impact for safe, data-driven control of nonlinear systems.

Abstract

We analyze the convergence properties of a robust adaptive model predictive control algorithm used to control an unknown nonlinear system. We show that by employing a standard quadratic stabilizing cost function, and by recursively updating the nominal model through kinky inference, the resulting controller ensures convergence of the true system to the origin, despite the presence of model uncertainty. We illustrate our theoretical findings through a numerical simulation.

Convergence guarantees for adaptive model predictive control with kinky inference

TL;DR

The paper addresses convergence guarantees for adaptive model predictive control applied to unknown nonlinear systems by learning a nominal model through kinky inference. It constructs data-driven uncertainty bounds and proves recursive feasibility and input-to-state stability, culminating in asymptotic convergence to the origin despite model uncertainty. A key contribution is showing convergence with only a tracking cost, avoiding the need for explicit excitation. The numerical example demonstrates that incorporating kinky inference enables effective regulation to the origin, highlighting practical impact for safe, data-driven control of nonlinear systems.

Abstract

We analyze the convergence properties of a robust adaptive model predictive control algorithm used to control an unknown nonlinear system. We show that by employing a standard quadratic stabilizing cost function, and by recursively updating the nominal model through kinky inference, the resulting controller ensures convergence of the true system to the origin, despite the presence of model uncertainty. We illustrate our theoretical findings through a numerical simulation.
Paper Structure (9 sections, 3 theorems, 38 equations, 2 figures)

This paper contains 9 sections, 3 theorems, 38 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Problem Setup
  3. System description:
  4. Kinky inference:
  5. Theoretical analysis
  6. a) Recursive feasibility:
  7. b) Input-to-state stability:
  8. Numerical example
  9. Conclusion

Key Result

lemma 1

Condition eq:TA_model_updates_bounded_1 can be equivalently re-stated as follows

Figures (2)

  • Figure 1: Kinky inference bounds for $\lambda=1$ (thin continuous lines) and mean function (dashed line, in red) compared against the true function (thick and continuous line, in blue) for a one-dimensional system.
  • Figure 2: State evolution.

Theorems & Definitions (6)

  • lemma 1
  • proof
  • lemma 2
  • proof
  • theorem 1
  • proof