Optimal tracking performance of discrete-time systems with quantization

Abstract

This paper studies optimal tracking performance issues for linear time invariant system with two-channel constraints. The specific problem under consideration is quantization for up-link and down-link communication channel which satisfies some constraints. Logarithmic quantization law is employed in the quantizers. The tracking performance is defined in an square sense, and the reference signal under consideration in this paper is a step signal. The system's reference signal is considered as a step signal. The tracking performance is measured by the minimum mean square error between the reference input and the system's output. By using dynamic programming approach, discrete-time algebraic Riccati equation (ARE) is obtained. The optimal tracking performance is obtained by output feedback control, in terms of the space equation of the given system and the unique solution of the discrete-time algebraic Riccati equation. And, the impact of quantizer for optimal tracking performance is analyzed. Finally, simulation example is given to illustrate the theoretical results.

Tracking Performance Limitations of MIMO Networked Control Systems with Multiple Communication Constraints

“…They have been applied in many important areas, e.g., industry control applications, automobiles, factory automation, intelligent traffic, etc. Nowadays, the main issues addressed include modeling and stabilization analysis of NCSs with communication restrictions, including data-rate constraints [9], [10], bandwidth restrictions [11], [12], time-delays [13], [14], quantization [15], [16], packet losses [17], [18] as well as communication noises [19], [20]. Notwithstanding the spectacular achievements of these studies, even more thought-provoking cases of best accomplishable tracking capability in certain network condition still require to be further analyzed.…”

“…Qi et al [36] give a fundamental conditions of stabilizability. In recent years, we have also obtained some optimal performance results of NCSs, such as upstream and downstream channels with constraints [37], channel energy constaint [38], some novel trade-off factors and constraint channels [39], discrete-time(DT) systems with quantization [15], AWGN fading channels [40], SIMO systems with packetdropouts [41]. In spite of the significant progress on optimal performance studies, there are still many gaps in the optimal performance of NCSs.…”

“…about ten years in regard to finite-dimensional, LTI NCSs. Some existing literatures above tracking performance limitations of NCSs concentrate upon simulated path models emphasizing specific fields of the wholesome case, such as [11], [15], [30], [35], [41], [42] etc. However, multiple communication constraints are often encountered in general practice, and the performance limitations problem may become more complex and realistic.…”

“…Therefore, interference noises of the reference signal (or call reference noises) is considered as the input signal in our control system performance model. This is also widely used method when studying control system performance in recent years, such as [11], [15], [29], [35], [41]- [43] et al In addition, we adopt the 2DOF controller, which can be recognized as a controller structure that achieves better performance [23], [26], because this kind of controller structure has more design freedom.…”