Robust Control Lyapunov-Value Functions for Nonlinear Disturbed Systems Analysis

Core Concepts

The authors introduce Robust CLVFs for nonlinear systems with disturbances, inheriting properties from CLVFs and providing efficient computation techniques.

Abstract

The paper introduces Robust Control Lyapunov-Value Functions (R-CLVF) for systems with bounded disturbances, inheriting properties from CLVFs. It extends the theory to include robust exponential stabilizability and provides numerical examples validating the theory. Control Lyapunov Functions (CLFs) are widely used in control systems but lack systematic construction methods for general nonlinear systems. The R-CLVF addresses this limitation by defining a method to find a non-smooth CLF for systems with bounded disturbances. The R-CLVF inherits properties from the CLVF, identifying the smallest robust control invariant set (SRCIS) and stabilizing the system with a user-specified exponential rate. Techniques like warmstart and system decomposition are introduced to address computational challenges. Numerical examples illustrate the trade-off between decay rate and region of exponential stabilizability, showcasing efficiency using warmstart and decomposition techniques.

Stats

The R-CLVF is Lipschitz continuous, satisfies dynamic programming principle, and is unique viscosity solution to corresponding VI. The SRCIS is defined as zero-level set of computed R-CLVF. Different choices of loss function norm result in different SRCIS, ROES, trajectories.

Quotes

Key Insights Distilled From

Robust Control Lyapunov-Value Functions for Nonlinear Disturbed Systems

by Zheng Gong,S... at arxiv.org 03-07-2024

https://arxiv.org/pdf/2403.03455.pdf

Deeper Inquiries

How can the concept of Robust CLVFs be applied in real-world autonomous systems

The concept of Robust Control Lyapunov-Value Functions (R-CLVFs) can be applied in real-world autonomous systems to ensure stability and safety. By using R-CLVFs, controllers can be designed to stabilize the system to a specific set with a user-specified exponential rate, even in the presence of disturbances and uncertainties. This is crucial for autonomous systems operating in dynamic environments where disturbances are common. R-CLVFs provide a systematic way to handle nonlinear systems with input or state constraints, ensuring that the system remains stable and safe during operation.

What potential limitations or criticisms could arise regarding the implementation of R-CLVFs in practical applications

One potential limitation of implementing R-CLVFs in practical applications is the computational complexity involved in solving the associated optimization problems. The curse of dimensionality often hinders efficient computation, especially for high-dimensional systems. Additionally, there may be challenges in accurately modeling all sources of uncertainty and disturbances present in real-world scenarios, which could affect the robustness of the control design based on R-CLVFs. Furthermore, tuning parameters such as the exponential rate γ requires careful consideration to balance stability and performance trade-offs effectively.

How might advancements in computational efficiency impact future developments in control theory

Advancements in computational efficiency have the potential to significantly impact future developments in control theory, particularly regarding complex systems like those found in autonomous vehicles or robotics. Improved computational techniques can enable faster and more accurate solutions for optimizing control strategies based on R-CLVFs. This could lead to enhanced real-time decision-making capabilities for autonomous systems by reducing latency and improving overall system performance. Additionally, increased computational efficiency opens up possibilities for applying advanced control algorithms that were previously computationally prohibitive, paving the way for more sophisticated control designs with better robustness properties.