Lei Guo

Fault detection and diagnosis for general stochastic systems using B-spline expansions and nonlinear filters

This paper presents a new fault detection and diagnosis (FDD) algorithm for general stochastic systems. Different from the classical FDD design, the distribution of system output is supposed to be measured rather than the output signal itself. The task of such an FDD algorithm design is to use the measured output probability density functions (PDFs) and the input of the system to construct a stable filter-based residual generator such that the fault can be detected and diagnosed. For this purpose, square root B-spline expansions are applied to model the output PDFs and the concerned problem is transformed into a nonlinear FDD algorithm design subjected to a nonlinear weight dynamical system. A linear matrix inequality based solution is presented such that the estimation error system is stable and the fault can be detected through a threshold. Moreover, an adaptive fault diagnosis method is also provided to estimate the size of the fault. Simulations are provided to show the efficiency of the proposed approach.

PID controller design for output PDFs of stochastic systems using linear matrix inequalities

This paper presents a pseudo proportional-integral-derivative (PID) tracking control strategy for general non-Gaussian stochastic systems based on a linear B-spline model for the output probability density functions (PDFs). The objective is to control the conditional PDFs of the system output to follow a given target function. Different from existing methods, the control structure (i.e., the PID) is imposed before the output PDF controller design. Following the linear B-spline approximation on the measured output PDFs, the concerned problem is transferred into the tracking of given weights which correspond to the desired PDF. For systems with or without model uncertainties, it is shown that the solvability can be casted into a group of matrix inequalities. Furthermore, an improved controller design procedure based on the convex optimization is proposed which can guarantee the required tracking convergence with an enhanced robustness. Simulations are given to demonstrate the efficiency of the proposed approach and encouraging results have been obtained.

Observer-Based Optimal Fault Detection and Diagnosis Using Conditional Probability Distributions

A new optimal fault detection and diagnosis (FDD) scheme is studied in this paper for the continuous-time stochastic dynamic systems with time delays, where the available information for the FDD is the input and the measured output probability density functions (pdfs) of the system. The square-root B-spline functional approximation technique is used to formulate the output pdfs with the dynamic weightings. As a result, the concerned FDD problem can be transformed into a robust FDD problem subjected to a continuous time uncertain nonlinear system with time delays. Feasible criteria to detect and diagnose the system fault are provided by using linear matrix inequality (LMI) techniques. In order to improve FDD performances, two optimization measures, namely guaranteed cost performance and Hinfin performance, are applied to optimize the observer design. Simulations are given to demonstrate the efficiency of the proposed approach

Applying constrained nonlinear generalized PI strategy to PDF tracking control through square root B-spline models

For stochastic systems with non-Gaussian variables, the classical control approaches where only expectation and variance are concerned cannot cover the control requirement of the closed loop in some practical processes. In this paper, the tracking control problem for output probability density functions (PDFs) is studied using square root B-spline expansions and non-linear weight dynamical models. After the measurable output PDFs are approximated by the B-spline expansions, a non-linear dynamical model can be established between the control input and the weights related to the PDFs. The tracking control problem for the output PDFs can be reduced to a constrained tracking problem for the non-linear weight dynamics. For this non-linear weight model, a generalized proportional-integral (PI) control strategy is proposed in discrete time context. The objective of the control is to make sure that the output PDFs of the system can follow a given target function, and the closed-loop system is exponentially stable and satisfies the constraint imposed on the state vector. The LMI-based convex optimization approach is adopted to design the parameters of the proposed PI controllers. This result also generalizes some previous works for classical constrained PI tracking control of non-linear discrete-time systems. Simulations are given to demonstrate the efficiency of the proposed approach.

Fault detection and diagnosis for general stochastic systems using B-spline expansions and nonlinear observers

This paper considers a new type of fault detection and diagnosis (FDD) problem for general stochastic systems. Different from the classical FDD problems, the measured information is the probability distribution of system output rather than the value of output. The objective is to find an observer-based residual by using the output distributions such that the fault can be detected and diagnosed. Square root B-spline expansions are applied to model the output probability density functions (PDFs) so that the concerned problem is transformed into a nonlinear FDD problem subject to the weight dynamical systems. An LMI-based solution is presented such that the estimation error system is stable and the fault can be detected through a threshold. Moreover, an adaptive fault diagnosis method is also provided to estimate the size of the fault.

Pseudo-PID tracking control for a class of output PDFs of general non-Gaussian stochastic systems

In this paper a pseudo-PID control strategy is presented for a class of non-Gaussian stochastic systems. To control the output probability density functions (PDFs) to track a given target function, the PID-type control structure is imposed a priori. Following the B-spline approximation on the measured output PDFs, the control objective is transferred into the tracking of given weights which correspond to the desired PDF. For systems with or without model uncertainties, it is shown that the solvability can be cast into a group of matrix inequalities. This leads to a feasible controller design procedure that can guarantee the required tracking convergence with enhanced robustness.

Guaranteed cost control of uncertain discrete-time delay systems using dynamic output feedback:

Guaranteed cost control problems for discrete-time systems with uncertainties and time delays are addressed in this paper. The delays may simultaneously appear not only in the state, but in control input and measurement output. Also, parametric uncertainties may exist in all system matrices of the systems considered in this paper. First, a new linear matrix inequality (LMI)-based approach is developed to construct dynamic guaranteed cost controllers for delay systems without uncertainties. Then this result is extended to discrete-time delay systems with uncertainties in linear fractional form in all system matrices. The solvability of these robust control problems for uncertain delay systems can be reduced to that for certain auxiliary systems without uncertainty. Numerical examples are provided to show the effectiveness of our approach.

Optimal output probability density function control for nonlinear ARMAX stochastic systems

In this paper a general optimal control problem is studied for the shape control of the conditional probability density functions (PDFs) of nonlinear stochastic systems. The controlled systems are described by general nonlinear ARMAX models with time-delays and with non-Gaussian inputs. A j-step ahead predictive cumulative cost function related to the time delay model is concerned as the control objective rather than an instantaneous performance index. A new relationship between the PDFs of the input and output is established after constructing a special joint conditional PDF between the auxiliary multiple inputs and outputs. Based on this relationship, explicit formulations to the construction of optimal controllers are obtained through the dynamic programming approach. Using the proposed predictive controllers, the conditional output PDFs can be made to follow the target one. Moreover, an approach is further developed to design a local stabilization suboptimal control strategy. It has been shown that these control algorithms can also be applied to the minimum entropy control for non-linear stochastic systems under a unified framework.

Minimum entropy filtering for multivariate stochastic systems with non-Gaussian noises

In this paper, a minimum entropy filtering algorithm is presented for a class of multivariate dynamic stochastic systems. The concerned systems are represented by a set of time-varying difference equations with multiple non-Gaussian stochastic inputs, and with nonlinearity in the measurement output. Several new concepts including hybrid random vectors, hybrid probability and hybrid entropy are introduced to describe the probabilistic property and randomness of the stochastic estimation errors. New relationships are established between the probability density functions (PDFs) of the multivariate stochastic input and output for different mapping cases. Recursive algorithms are then proposed to design the real-time optimal filters such that hybrid entropy of the estimation error is minimized.