Adaptive Tracking Control for Non-Periodic Reference Signals with Quantized Observations

Core Concepts

The paper designs an adaptive tracking control scheme to achieve asymptotically optimal tracking for non-periodic reference signals in stochastic regression systems with multi-threshold quantized observations.

Abstract

The paper considers an adaptive tracking control problem for stochastic regression systems with multi-threshold quantized observations. Unlike previous studies that focused on periodic reference signals, this paper deals with non-periodic reference signals, which poses additional challenges in ensuring the designed controller satisfies the required conditions for convergence of the parameter estimation. The key contributions are: The paper designs two backward-shifted polynomials with time-varying parameters and a special projection structure to overcome the difficulties in ensuring the persistent excitation and uniformly bounded conditions for the non-periodic reference signals. The proposed adaptive tracking control scheme not only ensures the convergence of the parameter estimates to their true values, but also achieves asymptotically optimal tracking for the non-periodic reference signals. The mean square convergence speed of the parameter estimation can reach the optimal rate of O(1/k) under suitable conditions. The paper first introduces the stochastic regression system model with multi-threshold quantized observations and the non-periodic reference signal. It then presents the adaptive control algorithm, which consists of a weighted conversion of the quantized observations, an online recursive projection-based parameter estimation, and the design of the control input using the certainty equivalence principle. The main theoretical results establish the convergence and convergence rate of the parameter estimation, as well as the asymptotic optimality of the proposed adaptive tracking control scheme. Finally, a simulation is provided to verify the effectiveness of the proposed approach.

Stats

Sentence This paper considers an adaptive tracking control problem for stochastic regression systems with multi-threshold quantized observations. Different from the existing studies for periodic reference signals, the reference signal in this paper is non-periodic. The adaptive tracking control law can achieve asymptotically optimal tracking for the non-periodic reference signal. The proposed estimation algorithm is proved to converge to the true values in almost sure and mean square sense, and the convergence speed can reach O(1/k) under suitable conditions.

Quotes

Quote "The main difficulty is how to ensure that the designed controller satisfies the uniformly bounded and excitation conditions that guarantee the convergence of the estimation in the controller under non-periodic signal conditions." "This paper designs two backward-shifted polynomials with time-varying parameters and a special projection structure, which break through periodic limitations and establish the convergence and tracking properties."

Key Insights Distilled From

Adaptive tracking control for non-periodic reference signals under quantized observations

by Chuiliu Kong... at arxiv.org 04-26-2024

https://arxiv.org/pdf/2404.16282.pdf

Deeper Inquiries

How can the proposed adaptive tracking control scheme be extended to handle higher-order quantized systems

To extend the proposed adaptive tracking control scheme to handle higher-order quantized systems, we can modify the estimation algorithm and control design to accommodate the increased complexity. One approach could involve incorporating additional backward-shifted polynomials with time-varying parameters to capture the dynamics of higher-order systems. By adjusting the projection structure and updating the identification algorithm, we can ensure that the controller satisfies the necessary conditions for convergence and tracking performance in higher-order systems. Additionally, refining the persistent excitation and uniformly bounded conditions to account for the increased system order will be crucial in ensuring the effectiveness of the adaptive control scheme for higher-order quantized systems.

What are the potential applications of the developed techniques in real-world scenarios beyond the specific problem considered in the paper

The developed techniques in the paper have potential applications in various real-world scenarios beyond the specific problem considered. One application could be in autonomous vehicles, where adaptive tracking control is essential for navigating complex environments with uncertainties and limited sensor information. By implementing the proposed scheme, autonomous vehicles can improve their tracking performance and robustness in non-periodic reference signal scenarios. Another application could be in industrial automation, where adaptive control is used to optimize manufacturing processes and ensure precise control of robotic systems. The techniques developed in the paper can enhance the adaptability and accuracy of control systems in industrial settings, leading to improved efficiency and productivity.

How can the adaptive tracking control framework be further improved to handle more general types of reference signals or system uncertainties

To further improve the adaptive tracking control framework and handle more general types of reference signals or system uncertainties, several enhancements can be considered. One approach is to incorporate robust control techniques to enhance the system's resilience to disturbances and uncertainties. By integrating robust control strategies with adaptive tracking, the system can maintain stability and performance in the presence of varying operating conditions. Additionally, exploring advanced machine learning algorithms, such as reinforcement learning, can enable the system to adapt and learn from its environment, enhancing its tracking capabilities in dynamic and uncertain scenarios. Furthermore, integrating predictive control methods can improve the system's ability to anticipate future reference signal variations and proactively adjust the control inputs for optimal tracking performance. These enhancements can broaden the applicability and effectiveness of the adaptive tracking control framework in handling diverse real-world challenges.