Soft-Bound Interval Control System and Its Robust Fault-Tolerant Controller Design

Abstract

In this work, a soft-bound interval control problem 1 is proposed for general non-Gaussian systems with the aim 2 to control the output variable within a bounded region at a 3 specified probability level. To find a feasible solution to this 4 challenging task, the initial soft-bound interval control problem 5 has been transformed into an output probability density func-6 tion (PDF) tracking control problem with constrained tracking 7 errors, thereby the controller design can be handled under the 8 established framework of stochastic distribution control (SDC). 9 Fault tolerant control has been developed for soft-bound interval 10 control systems in presence of faults. Three fault detection 11 methods have been proposed based on criteria extracted from the 12 initial soft-bound control problem and the recast PDF tracking 13 problem. An integrated design for fault estimation and fault tol-14 erant control (FTC) is proposed based on a double proportional 15 integral (PI) structure. This integrated FTC is developed through 16 linear matrix inequality (LMI). Extensive simulation studies have 17 been conducted to examine key design factors, implementation 18 issues and effectiveness of the proposed approach. 19 Index Terms-Non-Gaussian systems, soft-bound control, 20 stochastic distribution control (SDC), probability density function 21 (PDF), fault detection, fault tolerant control (FTC). 22 I. INTRODUCTION 23 Stochastic control has been an active area in control engi-24 neering and applications since 1970's as most practical sys-25 tems have stochastic characteristics. Continuous efforts have 26 been made in development of minimum variance control [1]-27 [3], linear quadratic Gaussian (LQG) control [4], Markovian 28 stochastic control [5], stochastic adaptive control, stochastic 29 optimization and forecasting, sliding mode control [6]-[8], to 30 name a few. Most of these methods are focused on stochastic 31 features of system variables, mean and variance for exam-32 ple, under the assumption of Gaussian distribution. In real 33 applications, however, a large number of stochastic processes 34 are non-Gaussian, examples include molecular weight distri-35 bution control in polymerization [9], [10], pulp fiber length 36 distribution control in paper industries [11], particulate process 37 control in powder industries [12], crystal size distribution 38 control in crystallization [13], soil particle distribution control 39 [14], flame temperature distribution control in furnace systems 40 [15], [16] and power probability density function control in

Rational entropy‐based fuzzy fault tolerant control for descriptor stochastic distribution networked control systems with packet dropout

“…In order to guarantee the safe operation of SDC systems, it is necessary to consider the design of control algorithms, which can eliminate or offset the effect of fault even if the fault occurs, so that the system can maintain good performance and still achieve the desired control objective. Therefore, the research on fault tolerant control (FTC) for the SDC system [9][10][11][12][13][14] has attracted more and more attentions. An optimal FTC algorithm based on LMI [9] is proposed for the SDC system with disturbances and uncertainties.…”