Stabilization of Linear Systems with Input Delay and State/Input Quantization via Switched Predictor Feedback

Core Concepts

A switched predictor-feedback control design achieves global asymptotic stabilization of linear systems with input delay and quantized plant/actuator state measurements or quantized control input.

Abstract

The paper develops a switched predictor-feedback control law that can simultaneously compensate for input delay and state/input quantization in linear systems. The key elements are: A quantized version of the nominal predictor-feedback law, where the predictor state formula uses quantized measurements of the plant and actuator states. A switching strategy that dynamically adjusts the tunable parameter of the quantizer. Initially, the range of the quantizer is increased, and then the quantization error is decreased. The proof of global asymptotic stability in the supremum norm of the actuator state combines a backstepping transformation with small-gain and input-to-state stability arguments to address the error due to quantization. The result is extended to the case of input quantization, where the control input is quantized but the plant/actuator states are available. The control design and analysis approach systematically addresses the challenges arising from the digital implementation of predictor-feedback laws, preserving the stability guarantees of the original continuous-time designs.

Stats

|X(t)| + ∥u(t)∥∞ ≤ γ (|X0| + ∥u0∥∞) (2-ln Ω/T 1/|A|) e(ln Ω/T)t |X(t)| + ∥u(t)∥∞ ≤ γ̄ (|X0| + ∥u0∥∞) (2-ln Ω/T 1/|A|) e(ln Ω/T)t

Quotes

"A switched predictor-feedback control design achieves global asymptotic stabilization of linear systems with input delay and quantized plant/actuator state measurements or quantized control input." "The proof of global asymptotic stability in the supremum norm of the actuator state combines a backstepping transformation with small-gain and input-to-state stability arguments to address the error due to quantization."

Key Insights Distilled From

Simultaneous compensation of input delay and state/input quantization for linear systems via switched predictor feedback

by Florent Koud... at arxiv.org 04-18-2024

https://arxiv.org/pdf/2404.11194.pdf

Deeper Inquiries

How can the proposed control design be extended to handle more general nonlinear systems with input delay and quantization effects

To extend the proposed control design to handle more general nonlinear systems with input delay and quantization effects, one can consider incorporating techniques from nonlinear control theory. Nonlinear systems can exhibit complex behaviors that linear systems do not capture, such as limit cycles, bifurcations, and chaos. One approach could be to utilize nonlinear predictor-feedback control laws that account for the nonlinear dynamics of the system. This may involve using techniques like feedback linearization, sliding mode control, or adaptive control to handle the nonlinearities effectively. Additionally, the quantization effects can be addressed by designing quantization-aware controllers that take into account the non-idealities introduced by the quantization process. By combining these approaches, it is possible to develop a control design that can stabilize and control a broader class of nonlinear systems with input delay and quantization effects.

What are the potential applications of the developed techniques in areas such as robotics, autonomous vehicles, or industrial control systems

The developed techniques have significant potential applications in various fields, including robotics, autonomous vehicles, and industrial control systems. In robotics, the ability to stabilize linear systems with input delay and quantization can improve the performance and reliability of robotic manipulators, leading to more precise and efficient operations. For autonomous vehicles, the control design can enhance the stability and robustness of control systems, ensuring safe and reliable navigation in complex environments. In industrial control systems, the techniques can be applied to processes with input delays and quantization, such as chemical reactors or manufacturing systems, to optimize performance and increase productivity. Overall, the developed techniques have the potential to advance control systems in a wide range of applications, improving efficiency, safety, and performance.

Can the dynamic adjustment of the quantizer's parameters be further optimized to improve the convergence rate or reduce the conservatism of the stability conditions

The dynamic adjustment of the quantizer's parameters can be further optimized to improve the convergence rate and reduce the conservatism of the stability conditions. One way to achieve this is by incorporating adaptive quantization schemes that adjust the quantizer parameters based on the system's dynamics and performance requirements. By using adaptive algorithms, the quantizer can dynamically adapt to changing conditions, leading to improved control performance and faster convergence rates. Additionally, optimization techniques such as model predictive control (MPC) or reinforcement learning can be employed to optimize the quantizer parameters in real-time, taking into account system uncertainties and disturbances. By optimizing the quantizer's parameters dynamically, the control system can achieve better performance, reduced conservatism, and enhanced stability in the presence of input delay and quantization effects.