Finite-horizon reliable control with randomly occurring uncertainties and nonlinearities subject to output quantization

Abstract

This paper deals with the finite-horizon reliable H∞ output feedback control problem for a class of discrete time-varying systems with randomly occurring uncertainties (ROUs), randomly occurring nonlinearities (RONs) as well as measurement quantizations. Both the deterministic actuator failures and probabilistic sensor failures are considered in order to reflect the reality. The actuator failure is quantified by a deterministic variable varying in a given interval and the sensor failure is governed by an individual random variable taking value on 0, 1 . Both the nonlinearities and the uncertainties enter into the system in random ways according to Bernoulli distributed white sequences with known conditional probabilities. The main purpose of the problem addressed is to design a time-varying output feedback controller over a given finite horizon such that, in the simultaneous presence of ROUs, RONs, actuator and sensor failures as well as measurement quantizations, the closedloop system achieves a prescribed performance level in terms of the H∞-norm. Sufficient conditions are first established for the robust H∞ performance through intensive stochastic analysis, and then a recursive linear matrix inequality approach is employed to design the desired output feedback controller achieving the prescribed H∞ disturbance rejection level. A numerical example is given to demonstrate the effectiveness of the proposed design scheme.

Variance-constrainedH∞control for a class of nonlinear stochastic discrete time-varying systems: The event-triggered design

“…A large body of literature has been devoted to the stochastic control or filtering problem for different systems such as polynomial stochastic systems [1,2,4], Markovian jumping systems [20], switched stochastic systems [13], discrete-time stochastic systems with state-dependent noises [17], nonlinear stochastic systems [8,19] and stochastic sampled-data control system [21]. Among various stochastic control schemes, the covariance control (CC) theory has gained particular research attention due primarily to the fact that the performance requirements of many engineering control systems are naturally expressed as the upper bounds on the steady-state variances [11].…”

Estimation, filtering and fusion for networked systems with network-induced phenomena: New progress and prospects

“…The randomly occurring incomplete information may occur intermittently in a probabilistic way with certain types and intensity. For example, in a networked system such as the internet-based three-tank system for leakage fault diagnosis, the nonlinearities may occur in a probabilistic way due to random abrupt variations and the occurrence probability can be estimated via the statistical tests [94]. It is well recognized that the existence of the randomly occurring incomplete information would highly degrade the system performance if not handled properly.…”

“…It is well recognized that the existence of the randomly occurring incomplete information would highly degrade the system performance if not handled properly. So far, a series of estimation and filtering schemes has been developed for networked systems with randomly occurring incomplete information in the literature, and great efforts have been made to deal with the randomly occurring nonlinearities in [49], [95]- [99], the randomly occurring uncertainties in [94], [97], the randomly occurring sensor saturations in [40], [72], the randomly occurring sensor delays in [31], [32], [38], [100], [101], the randomly occurring signal quantization in [41], [102], and the randomly occurring faults in [103]. Accordingly, several techniques for analysis and synthesis of the networked systems have been given, including innovation analysis approach [31], [32], linear matrix inequality approach [97], Hamilton-Jacobi-Isaacs inequality method [100], difference linear matrix inequality method [41], Riccati difference equation approach [101], [102], and game theory method [54].…”

Variance-constrained state estimation for networked multi-rate systems with measurement quantization and probabilistic sensor failures

“…In computer-based control systems, the interface between the plant and the estimator is often connected via analog-to-digital (A/D) and digital-to-analog (D/A) devices, which normally leads to the quantization process [16]. Actually, quantization error never vanishes when the signals are processed by uniform quantizer [19], [21] or nonuniform quantizer [5], [12], [25], [28], [31]. Accordingly, signal quantization is considered as another source that has significant impact on the achievable performance of the NCSs.…”