Proportional-Integral Observer Design for Multirate-Networked Systems Under Constrained Bit Rate: An Encoding–Decoding Mechanism

In this article, the proportional-integral observer design problem is studied for a class of multirate networked systems subject to constrained bit rate. The sensor sampling period is allowed to be different from the system updating period and, to facilitate the observer design, the underlying multirate system is cast into a general single-rate one by resorting to the lifting technique. In order to curb the communication burden and promote the data security, the encoding–decoding procedure is implemented on the sensor-to-observer channel to convert the measurement signals into binary codewords. A sufficient condition is first proposed to reveal the fundamental relationship between the bit-rate constraints and the decoding accuracy, and then the exponentially ultimate boundedness of the error dynamics is assessed with the aid of the Lyapunov method. Subsequently, the desired observer gains are determined by solving two optimization problems with the aim to achieve two distinct performance indices, namely, the smallest ultimate bound and the fastest decay rate. Finally, the validity of the developed observer design approach is thoroughly demonstrated via the simulation examples.

I. Introduction

Due to its extraordinary performance in suppressing steady-state error and enhancing robustness, the integral action has been introduced into the Luenberger observer in [38], and this gives birth to the so-called proportional-integral observer (PIO). In contrast to the traditional Luenberger observer, the PIO is capable of supplying better estimation performance due to the simultaneous reflection of current and historical information in its structure. Accordingly, the PIO has captured a great deal of research attention with successful applications in a variety of practical scenarios, such as manufacturing industry, electricity circuit systems, network communication systems, and aerospace systems [2], [4], [6], [45]. To date, a rich body of work has been devoted to the PIO design problem with a series of results available in [16], [17], [30], [32], and [33].