Search

The robust Kalman filter design problem for two-dimensional uncertain linear discrete time-varying systems with stochastic noises is investigated in this study. First, we prove that the solution to a certain deterministic regularized least squares problem constrained by the nominal two-dimensional system model is equivalent to the generalized two-dimensional Kalman filter. Then, based on this relationship, the robust state estimation problem for two-dimensional uncertain systems with stochastic noises is interpreted as a deterministic robust regularized least squares problem subject to two-dimensional dynamic constraint. Finally, by solving the robust regularized least squares problem and using a simple approximation, a recursive robust two-dimensional Kalman filter is determined. A heat transfer process serves as an example to show the properties and efficacy of the proposed filter.

An approximate exponential quantum projection filtering scheme is developed for a class of open quantum systems described by Hudson- Parthasarathy quantum stochastic differential equations, aiming to reduce the computational burden associated with online calculation of the quantum filter. By using a differential geometric approach, the quantum trajectory is constrained in a finite-dimensional differentiable manifold consisting of an unnormalized exponential family of quantum density operators, and an exponential quantum projection filter is then formulated as a number of stochastic differential equations satisfied by the finite-dimensional coordinate system of this manifold. A convenient design of the differentiable manifold is also presented through reduction of the local approximation errors, which yields a simplification of the quantum projection filter equations. It is shown that the computational cost can be significantly reduced by using the quantum projection filter instead of the quantum filter. It is also shown that when the quantum projection filtering approach is applied to a class of open quantum systems that asymptotically converge to a pure state, the input-to-state stability of the corresponding exponential quantum projection filter can be established. Simulation results from an atomic ensemble system example are provided to illustrate the performance of the projection filtering scheme. It is expected that the proposed approach can be used in developing more efficient quantum control methods.

This paper investigates the problem of fault detection filter design for discrete-time polynomial fuzzy systems with faults and unknown disturbances. The frequency ranges of the faults and the disturbances are assumed to be known beforehand and to reside in low, middle or high frequency ranges. Thus, the proposed filter is designed in the finite frequency range to overcome the conservatism generated by those designed in the full frequency domain. Being of polynomial fuzzy structure, the proposed filter combines the H − / H ∞ performances in order to ensure the best robustness to the disturbance and the best sensitivity to the fault. Design conditions are derived in Sum Of Squares formulations that can be easily solved via available software tools. Two illustrative examples are introduced to demonstrate the effectiveness of the proposed method and a comparative study with LMI method is also provided.

We present a novel distributionally robust optimization approach for integrated design and assessment of fault detection system. Its salient feature is the guaranteed robustness against the inexactness of probability distribution of unknown disturbances. The integrated design problem is formulated as a distributionally robust chance constrained program (DRCCP). It maximizes fault detectability subject to the constraint on the worst-case false alarm rate among a continuum of probability distributions. The moment-based and Wasserstein ambiguity sets are used as two different ways of uncertainty description, which differ manifestly from generic settings where disturbances follow either Gaussian or norm-bounded assumptions. We show that the use of two different ambiguity sets in fault detection leads to specific statistical properties. To solve DRCCPs efficiently, we develop exact reformulations and tailored solution algorithms, and in some cases the optimal solution turns out to be classical fault detection design. In addition, a distributionally robust assessment strategy is developed, which evaluates the worst-case and best-case detectability under known faults by solving tractable convex programs. The efficacy of the proposed approach is illustrated on the fault detection of a laboratory three-tank system.

Driven by the increasing needs in the process industry for designing fault-tolerant control systems based on process data and maintaining its performance during online operation, data-driven realization and design of feed-forward fault-tolerant control systems with embedded residual generation are studied. To this end, a parameterized and data-driven realization form of stable image representation in a feedback control loop is derived first. On this basis, a feed-forward controller design scheme is proposed for fault-tolerant purpose. It is followed by a recursive approach for online tuning the feed-forward controller in case of malfunctions, which is triggered by a fault detection scheme based on the so-called stable kernel representation. The effectiveness of the proposed fault-tolerant method is demonstrated by a case study on the laboratory three-tank system.

The main objective of this paper is to initiate a systematic application of gap metric techniques to the performance analysis and design issues of detecting and isolating multiplicative faults in uncertain systems. To be specific, in the first part of this paper, the K -gap and L 2 -gap metrics are introduced, which measure the distance between two kernel subspaces and serve as an efficient tool to deal with fault detection and isolation issues. Based on it, the K -gap and L 2 -gap aided analysis of residual dynamics with respect to model uncertainties is presented for the open-loop and feedback control systems, respectively. Furthermore, they are applied to deal with the performance analysis of fault detection systems. For this purpose, the concepts of fault detectability indicators and fault-to-uncertainty ratio are introduced. The second part of this paper is dedicated to the isolation of multiplicative faults. To this end, the definition for fault isolability is studied first with the aid of K -gap metric. The further efforts are devoted to the application of K -gap metric to two online fault isolation algorithms. The first one is an observer-based scheme, which adopts a bank of residual generators and an observer-based decision unit. The second scheme is based on the data-driven identification of the kernel representation of the faulty plant and the data-driven computation of the K -gap metric. Case and example studies are finally given to illustrate the proposed approaches.

This paper focuses on stabilization of second-order oscillatory systems using both feedback control and intentionally introduced time delay. The argument principle is employed as a key technique to divide the parameter space of time delay and controller gain into several regions. Every admissible value in these regions moves the poles of the closed-loop system towards the left of the complex plane such that stability improvement is achieved. The concept of potent asymptotic stability is first introduced, referring to the property that all the poles of the closed-loop system are stable and lie on the left of open-loop system poles in the complex plane. Analytical characterizations on parameter pairs of time delay and controller gain that result in potent asymptotic stability are established. All the poles and corresponding root locus with respect to gain are examined. Numerical examples and simulations are given to illustrate the usefulness and merits of the theoretical results.

An optimal state and fault estimation scheme is proposed for two-dimensional discrete systems subject to either deterministic disturbances or stochastic disturbances (noises). A direct solution to the deterministic estimation problem is obtained first, based on a well-designed regularized least squares problem with a dynamic constraint of a two-dimensional singular system, augmented from the original system state and unknown disturbance. After proving the solution equivalence between the deterministic scenario and the stochastic one in the sense of optimal state and fault estimation, a unified solution, based on a Riccati-like equation recursion, can be established by weighting parameterization for two-dimensional systems in deterministic and stochastic cases. The unified solution also works as the optimal state observer and generalized Kalman filter for two-dimensional singular systems. Generalization discussions concerning different system descriptions with respect to fault as well as the implementations of the proposed estimator are also presented. Simulation illustrates the effectiveness of the proposed method.

This work extends the previous quantum projection filtering scheme in [Gao Q., Zhang G., & Petersen I. R. (2019). An exponential quantum projection filter for open quantum systems. \emph{Automatica}, 99, 59-68.], by adding an optimality analysis result. A reformulation of the quantum projection filter is derived by minimizing the truncated Stratonovich stochastic Taylor expansion of the difference between the true quantum trajectory and its approximation on a lower-dimensional submanifold through quantum information geometric techniques. Simulation results for a qubit example demonstrate better approximation performance for the new quantum projection filter., 11 pages, 1 figure, submitted for publication. Comments are welcome

In this paper, a new approach to parity space-based fault detection (FD) is put forward for linear discrete time-varying (LDTV) systems. The focus of our study is on solving the problem with heavy online computational burden. The main contributions are two folds. Firstly, the problem of parity space-based FD is formulated as finding a minimum of quadratic form of unknown input. Secondly, by applying projection in Krein space, a solution of optimal parity space-based FD is obtained via recursively computing innovations. It is shown that the reduction of computation cost is achievable, especially with the increase of parity space order. Finally, a numerical example is given to demonstrate the application of the proposed method.

This paper deals with the data-driven design of observer-based fault detection and control systems. We first introduce the definitions of the data-driven forms of kernel and image representations. It is followed by the study of their identification. In the context of a fault-tolerant architecture, the design of observer-based fault detection, feed-forward and feedback control systems are addressed based on the data-driven realization of the kernel and image representations. Finally, the main results are demonstrated on the laboratory continuous stirred tank heater (CSTH) system.

The problem of adaptive robust control for uncertain linear systems with multiple delays occurring in the state variables is studied in this paper. The essential requirement for the uncertainties is that they satisfy matching conditions and are norm-bounded, but the bounds of the uncertainties are not necessarily known. An adaptive controller is developed based on linear matrix inequality technique and it is shown that the controller can guarantee the state variables of the closed loop system to converge, globally, uniformly and exponentially, to a ball in the state space with any pre-specified convergence rate. The effectiveness of our approach has been verified by its application in the control of river pollution process for the purpose of preserving standards of water constituents in streams.