Improved Dwell-times for Switched Nonlinear Systems using Memory Regression Extension

TL;DR

This work tackles the challenge of autonomous navigation in GPS-denied environments by embedding memory regressor extension (MRE) within a Lyapunov-based switched-system framework. During GPS-available periods, the method refines unknown parameter estimates $\theta$ using filtered regressors and concurrent learning, then uses the improved model to sustain operation in GPS-denied intervals. The key contributions include a CL-based parameter update with filtered signals, a switching observer and controller that guarantee bounded tracking and state estimation errors, and explicit dwell-time conditions that quantify how learning enables longer GPS-free operation. Simulations on a nonlinear second-order system demonstrate parameter convergence, bounded errors, and increasing allowable GPS-denied dwell-times as estimation improves.

Abstract

This paper presents a switched systems approach for extending the dwell-time of an autonomous agent during GPS-denied operation by leveraging memory regressor extension (MRE) techniques. To maintain accurate trajectory tracking despite unknown dynamics and environmental disturbances, the agent periodically acquires access to GPS, allowing it to correct accumulated state estimation errors. The motivation for this work arises from the limitations of existing switched system approaches, where increasing estimation errors during GPS-denied intervals and overly conservative dwell-time conditions restrict the operational efficiency of the agent. By leveraging MRE techniques during GPS-available intervals, the developed method refines the estimates of unknown system parameters, thereby enabling longer and more reliable operation in GPS-denied environments. A Lyapunov-based switched-system stability analysis establishes that improved parameter estimates obtained through concurrent learning allow extended operation in GPS-denied intervals without compromising closed-loop system stability. Simulation results validate the theoretical findings, demonstrating dwell-time extensions and enhanced trajectory tracking performance.

Figures (6)

• Figure 1: Comparison of the actual state trajectory $x(t)$ with the desired trajectory $x_d(t)$. Time intervals with GPS availability are highlighted in green, while GPS-denied intervals are shown in red. The degraded performance of the tracking controller is due to poor estimates of $\hat{\theta}$, however after the CL update the tracking performance is improved in first denied interval.
• Figure 2: Comparison of the estimated state trajectory $\hat{x}(t)$ with the desired trajectory $x_d(t)$.
• Figure 3: Time evolution of the parameter estimation error $\tilde{\theta}(t)$. The error components $\tilde{\theta}_1$ and $\tilde{\theta}_2$ converge toward a neighborhood of the origin during GPS-available intervals and remain constant during GPS-denied intervals.
• Figure 4: The components of state estimation error, $(e_1)_1$ and $(e_1)_2$ are shown over time.
• Figure 5: The components of trajectory tracking error, $(e_2)_1$ and $(e_2)_2$ are shown over time.

Theorems & Definitions (4)

• Theorem 1
• proof
• Theorem 2
• proof