Robust model predictive control for multirate systems with model uncertainties and circular scheduling

Abstract

In this article, the robust model predictive control (RMPC) problem on the basis of output feedback (OF) is dealt with for a class of multirate time-varying systems with polyhedral uncertainties and limited-bandwidth channels. For alleviating the communication burden caused by the limited transmission capacity, the Round-Robin (RR) protocol is exploited to allocate transmission permissions in a pre-scheduled order. Meanwhile, in order to reduce the communication cost while ensuring the system performance, the multirate mechanism is presented to govern the update rate of the plant and the sampling rate of the sensors. By means of the lifting technique, given a uniform sampling rate, a comprehensive augmentation system is established on the fixed moving horizon. The objective of the addressed RMPC problem is to design a set of OF-based RMPC controllers such that, in the presence of the multirate scheme and the RR transmission protocol, the desirable performance is guaranteed. Then, the desired RMPC gains are directly obtained, with the help of inequality analysis technique and RR-dependent Lyapunov-like approach, to ensure the asymptotic convergence of system states. Two illustrative examples are given, which include a DC motor system and a numerical simulation example, to demonstrate the effectiveness of the proposed protocol-based RMPC controller design strategy.

Robust predictive control with data-based multi-step prediction models

“…The bound (7) is global, since it holds for any regressor value inside Φ (p) and for any model compatible with the data, i.e. contained in the set Θ (p) .…”

“…To deal with the particular structure of the multi-step predictors, which prevents the use of a standard robust MPC approach, we adopt a novel multi-rate receding horizon strategy, for which we prove guaranteed constraint satisfaction and convergence properties. Many multirate schemes have been proposed in the literature for predictive control design, see for example [5], [8], [7] and the references therein, usually to cope with different sampling rates in outputs sampling, state update, and control implementation. On the contrary, here the multirate implementation stems from the particular form of the predictors.…”

An event‐triggered method to distributed filtering for nonlinear multi‐rate systems with random transmission delays

“…As such, the studies on SNs with multi-rate sampling schemes have stirred rapidly increasing research interests. [23][24][25] The earliest research on MRSs is attributed to the work of Kranc, 26 where the Z-transform method that solves the simultaneous algebraic equations to transform the data sampling system into a same-rate sampling system has been proposed, and the stability and performance analysis theory of single-rate systems has been utilized. In most recent studies, three classical methods are often adopted to transform MRSs into single-rate systems.…”

“…The multi‐rate systems (MRSs) are often encountered in civilian, military and industrial areas because different electronic components have different physical properties, and that is particularly suitable for SNs which consist of a large number of sensor nodes. As such, the studies on SNs with multi‐rate sampling schemes have stirred rapidly increasing research interests 23–25 . The earliest research on MRSs is attributed to the work of Kranc, 26 where the $$$ Z $$$‐transform method that solves the simultaneous algebraic equations to transform the data sampling system into a same‐rate sampling system has been proposed, and the stability and performance analysis theory of single‐rate systems has been utilized.…”

Identification of dual‐rate sampled nonlinear systems based on the cycle reservoir with regular jumps network

“…Due to different sensor sampling frequencies, hardware equipment and economic constraints, multirate sampled systems which have different sampling rates for inputs and outputs widely exist in industrial processes. [1][2][3][4] For example, in the thermal power generation control system, the oxygen content and carbon monoxide content cannot be measured as fast as other process variables due to laboratory analysis and detection. When there are only two sampling frequencies in the system, a dual-rate sampled system is obtained, which is a special case of multirate sampled systems.…”