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Robust Output-Feedback MPC for Nonlinear Systems with Applications to Robotic Exploration

Scott Brown, Mohammad Khajenejad, Aamodh Suresh, Sonia Martinez

TL;DR

This work addresses robust output-feedback MPC for nonlinear discrete-time systems where direct state measurements may be unavailable. It develops an interval observer and a forward interval predictor augmented by a stabilizing feedback term to guarantee containment of the true state and future trajectories, while keeping computation tractable. Under mild observability and stabilizability assumptions, the framework achieves recursive feasibility and, with an appropriate terminal condition, asymptotic stability within the feasible region. The method is validated on a linear CSTR and a nonlinear robotic-exploration scenario, showing improved robustness to noise and practical applicability to autonomous exploration tasks that use an entropy-based exploration objective.

Abstract

This paper introduces a novel method for robust output-feedback model predictive control (MPC) for a class of nonlinear discrete-time systems. We propose a novel interval-valued predictor which, given an initial estimate of the state, produces intervals which are guaranteed to contain the future trajectory of the system. By parameterizing the control input with an initial stabilizing feedback term, we are able to reduce the width of the predicted state intervals compared to existing methods. We demonstrate this through a numerical comparison where we show that our controller performs better in the presence of large amounts of noise. Finally, we present a simulation study of a robot navigation scenario, where we incorporate a time-varying entropy term into the cost function in order to autonomously explore an uncertain area.

Robust Output-Feedback MPC for Nonlinear Systems with Applications to Robotic Exploration

TL;DR

This work addresses robust output-feedback MPC for nonlinear discrete-time systems where direct state measurements may be unavailable. It develops an interval observer and a forward interval predictor augmented by a stabilizing feedback term to guarantee containment of the true state and future trajectories, while keeping computation tractable. Under mild observability and stabilizability assumptions, the framework achieves recursive feasibility and, with an appropriate terminal condition, asymptotic stability within the feasible region. The method is validated on a linear CSTR and a nonlinear robotic-exploration scenario, showing improved robustness to noise and practical applicability to autonomous exploration tasks that use an entropy-based exploration objective.

Abstract

This paper introduces a novel method for robust output-feedback model predictive control (MPC) for a class of nonlinear discrete-time systems. We propose a novel interval-valued predictor which, given an initial estimate of the state, produces intervals which are guaranteed to contain the future trajectory of the system. By parameterizing the control input with an initial stabilizing feedback term, we are able to reduce the width of the predicted state intervals compared to existing methods. We demonstrate this through a numerical comparison where we show that our controller performs better in the presence of large amounts of noise. Finally, we present a simulation study of a robot navigation scenario, where we incorporate a time-varying entropy term into the cost function in order to autonomously explore an uncertain area.

Paper Structure

This paper contains 20 sections, 7 theorems, 21 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Formulation
  4. System Dynamics
  5. Control Objective
  6. System Assumptions
  7. Interval Observer and Predictor Design
  8. Interval Observer
  9. Interval Predictor
  10. Feedback Parameterization
  11. Predictor Design
  12. Output-feedback MPC
  13. Cost function
  14. Terminal region and controller
  15. Optimization problem
  16. ...and 5 more sections

Key Result

Proposition 1

MK-FS-SZY:22a If the Jacobian of $f$ is bounded, i.e., it satisfies $\ul{J}_f \le J_f(x) \le \overline{J}_f$ for all $x \in \mathcal{X}$, then $f$ can be written in additive-remainder form, where the $(i,j)^{th}$ element of $A \in \mathbb{R}^{n \times n}$ satisfies and the function $\mu$ is JSS. $\bullet$

Figures (3)

  • Figure 1: Trajectories of $x^2_k$ (the second state component) for one trial of the experiment in Section \ref{['sec:comp']}, using the approach from ADRDS-DE-TR-XP:22 (DERP) and IROF-MPC. The objective is to operate as close to the constraint as possible.
  • Figure 2: Mean square error of several experiments varying the magnitude of state and process noise, using the method from ADRDS-DE-TR-XP:22 (DERP) and our IROF-MPC.
  • Figure 3: Comparison of nominal output-feedback MPC versus IROF-MPC over $100$ time steps in the robot exploration scenario.

Theorems & Definitions (15)

  • Definition 1
  • Proposition 1
  • Definition 2
  • Proposition 2
  • Proposition 3
  • Remark 1
  • Proposition 4
  • proof
  • Remark 2
  • Proposition 5
  • ...and 5 more