Robust state estimation for uncertain discrete-time stochastic systems with missing measurements

In this paper, results of robust estimation of Zhou (2010a) are extended to state estimation with missing measurements. A new procedure is derived which inherits the main properties of that of Zhou (2010a). In this extension, a covariance matrix used in the recursions is replaced by its estimate which makes its asymptotic property investigation mathematically difficult. Though introducing a monotonic function and using the so-called squeeze rule, this new robust estimator is proved to converge to a stable system. Numerical simulation results indicate that the proposed estimator may have an estimation accuracy better than the estimator of Wang, Yang, Daniel, and Liu (2005).     

On a robust modification of Breslow's cumulated hazard estimator

The Fisher consistency and asymptotic properties of a robust modification of Breslow's estimator are discussed. Sensitivity of the Breslow estimator is described both from the analytical and empirical point of view. The estimator's typical behavior is shown for simulated data and described in a real data case.     

Delay-independent robust stability of uncertain linear systems

In this paper we present some new sufficient conditions for robust stability of linear systems with uncertain time delay as well as structured parameter uncertainty. The stability robustness bounds obtained from the new sufficient conditions are independent of the size of time delay. Some illustrative examples are given.     

Delay-dependent robust asymptotic state estimation of Takagi-Sugeno fuzzy Hopfield neural networks with mixed interval time-varying delays

This paper investigates delay-dependent robust asymptotic state estimation of fuzzy neural networks with mixed interval time-varying delay. In this paper, the Takagi-Sugeno (T-S) fuzzy model representation is extended to the robust state estimation of Hopfield neural networks with mixed interval time-varying delays. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time delays, the dynamics of the estimation error is globally asymptotically stable. Based on the Lyapunov-Krasovskii functional which contains a triple-integral term, delay-dependent robust state estimation for such T-S fuzzy Hopfield neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. The unknown gain matrix is determined by solving a delay-dependent LMI. Finally two numerical examples are provided to demonstrate the effectiveness of the proposed method.     

Performance index sensitivity of the constrained minimum variance input-output estimator

After some general considerations, the variations of the performance index under different error conditions are investigated. The specific effects discussed are the misestimation of the process parameters and that of the zero-shift noise covariance matrix and also the non-zero mean of the noise. The theoretical considerations are substantiated by simulation results.     

On a fast, robust estimator of the mode: Comparisons to other robust estimators with applications

Advances in computing power enable more widespread use of the mode, which is a natural measure of central tendency since it is not influenced by the tails in the distribution. The properties of the half-sample mode, which is a simple and fast estimator of the mode of a continuous distribution, are studied. The half-sample mode is less sensitive to outliers than most other estimators of location, including many other low-bias estimators of the mode. Its breakdown point is one half, equal to that of the median. However, because of its finite rejection point, the half-sample mode is much less sensitive to outliers that are all either greater or less than the other values of the sample. This is confirmed by applying the mode estimator and the median to samples drawn from normal, lognormal, and Pareto distributions contaminated by outliers. It is also shown that the half-sample mode, in combination with a robust scale estimator, is a highly robust starting point for iterative robust location estimators such as Huber's M-estimator. The half-sample mode can easily be generalized to modal intervals containing more or less than half of the sample. An application of such an estimator to the finding of collision points in high-energy proton–proton interactions is presented.     

A time domain approach to robust fault detection of linear time-varying systems

This paper gives the optimal solutions to several robust fault detection problems such as ?₋/?_∞, ?₂/?_∞ and ?_∞/?_∞ problems for linear time-varying systems in a time domain, which extends the previous results on linear time-invariant systems in a frequency domain. It is shown that all three problems have the same optimal detection filter and the filter is a simple observer obtained by solving a standard differential Riccati equation. Finally, an example is given to illustrate our results.     

Design of PID controllers satisfying gain margin and sensitivity constraints on a set of plants

This paper presents a method for the design of PID-type controllers, including those augmented by a filter on the D element, satisfying a required gain margin and an upper bound on the (complementary) sensitivity for a finite set of plants. Important properties of the method are: (i) it can be applied to plants of any order including non-minimum phase plants, plants with delay, plants characterized by quasi-polynomials, unstable plants and plants described by measured data, (ii) the sensors associated with the PI terms and the D term can be different (i.e., they can have different transfer function models), (iii) the algorithm relies on explicit equations that can be solved efficiently, (iv) the algorithm can be used in near real-time to determine a controller for on-line modification of a plant accounting for its uncertainty and closed-loop specifications, (v) a single plot can be generated that graphically highlights tradeoffs among the gain margin, (complementary) sensitivity bound, low-frequency sensitivity and high-frequency sensor noise amplification, and (vi) the optimal controller for a practical definition of optimality can readily be identified.     

Bounded error moving horizon state estimator for non-linear continuous-time systems: application to a bioprocess system

This paper investigates moving horizon state estimation (MHSE) within a bounded-error context for continuous-time systems. Verified integration of the non-linear ordinary differential equations used as system equation is achieved with interval Taylor expansions. In addition, interval constraint propagation techniques are used in order to reduce the pessimism due to interval arithmetic. The new MHSE method is illustrated with a bio-process system, for several lengths of the time horizon.     

Robust fault detection of non-linear systems using set-membership state estimation based on constraint satisfaction

In this paper, the robust fault detection problem for non-linear systems considering both bounded parametric modelling errors and measurement noises is addressed. The non-linear system is monitored by using a state estimator with bounded modelling uncertainty and bounded process and measurement noises. Additionally, time-variant and time-invariant system models are taken into account. Fault detection is formulated as a set-membership state estimation problem, which is implemented by means of constraint satisfaction techniques. Two solutions are presented: the first one solves the general case while the second solves the time-variant case, being this latter a relaxed solution of the first one. The performance of the time-variant approach is tested in two applications: the well-known quadruple-tank benchmark and the dynamic model of a representative portion of the Barcelona's sewer network. In both applications, different scenarios are presented: a faultless situation and some faulty situations. All considered scenarios are intended to show the effectiveness of the presented approach.     

On-line state and parameter estimation of EPDM polymerization reactors using a hierarchical extended Kalman filter

A hierarchical extended Kalman filter (EKF) design is proposed to estimate unmeasured state variables and key kinetic parameters in a first principles model of a continuous ethylene–propylene–diene polymer (EPDM) reactor. The estimator design is based on decomposing the dynamic model into two subsystems by exploiting the triangular model structure and the different sampling frequencies of on-line and laboratory measurements directly related to the state variables of each subsystem. The state variables of the first subsystem are reactant concentrations and zeroth-order moments of the molecular weight distribution (MWD). Unmeasured state variables and four kinetic parameters systematically chosen to reduce bias are estimated from frequent and undelayed on-line measurements of the ethylene, propylene, diene and total polymer concentrations. The state variables of the second subsystem are first-order moments of the MWD. Given state and parameters estimates from the first subsystem EKF, the first-order moments and three non-stationary parameters added to the model for bias reduction are estimated from infrequent and delayed laboratory measurements of the ethylene and diene contents and number average molecular weight of the polymer. Simulation tests show that the hierarchical EKF generates satisfactory estimates even in the presence of measurement noise and plant/model mismatch.     

State estimation for nonlinear systems under model uncertainties: a class of sliding-mode observers

This paper deals with the classical problem of state estimation, considering partially unknown, nonlinear systems with noise measurements. Estimation of both, state variables and unstructured uncertain term, are performed simultaneously. In order to transform the measured disturbance into system disturbance, an alternative system representation is proposed, which lead a more advantageous observer structure. The observer proposed contains a proportional-type contribution and a sliding term for the measurement of error, which provides robustness against noisy measurements and model uncertainties. Convergence analysis of the estimation methodology proposed is performed, analysing the equation of the dynamics of the estimation error; it is shown that the observer exhibits asymptotic convergence. Estimation of monomer concentration, average molecular weight, polydispersity and filtering of temperature in a batch stirred polymerization reactor illustrates the good performance of the observer proposed.     

Least squares based iterative identification for a class of multirate systems

This paper studies modeling and identification problems for multi-input multirate systems with colored noises. The state-space models are derived for the systems with different input updating periods and furthermore the corresponding transfer functions are obtained. To solve the difficulty of identification models with unmeasurable noises terms, the least squares based iterative algorithm is presented by replacing the unmeasurable variables with their iterative estimates. Finally, the simulation results indicate that the proposed iterative algorithm has advantages over the recursive algorithms.     

Uniformization based sensitivity estimation for a class of discrete-event systems

Infinitestimal Perturbation Analysis (IPA) estimators are based on particular couplings of parameteric families of discrete event systems where small changes in the parameter value, typically, cause small changes in the timing of events and, for finite horizons, the sequence of states visisted remains the same. We consider another coupling approach based on the uniformization procedure and a simple generalization of it. In our case any small change in the parameter value causes a change in the state of the system; our parameterization of trajectories keeps them highly synchronized, hence the effect of such changes can be estimated, sometimes efficiently. In this framework, we define three tupes of performance sensitivity estimators for a broad class of performance measures and with respect to a range of parameter values. Performance measures on finite deterministic horizons are considered and it is shown that they are unbiased under mild conditions. We show that for some systems the derivative estimators can be calculated from a nominal sample path of the system.     

Using the fuzzy-ellipsoid method for robust estimation of the state of a grid system node

Constructing a workload model for a node of a Grid system is considered in terms of control theory. A node is represented as a linear dynamic object acted upon by perturbations with unknown statistical properties. Fuzzy set estimates are used to evaluate the state of the object. They ensure the robustness of the algorithm proposed and its usability under the lack of a priori information on the unknown vector and the inaccuracy of current measurements. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 67–74, November–December 2008.     

On the robust control of stable minimum phase plants with large uncertainty in a time constant. A fractional-order control approach

This paper addresses the problem of designing controllers that are robust to a great uncertainty in a time constant of the plant. Plants must be represented by minimum phase rational transfer functions of an arbitrary order. The design specifications are: (1) a phase margin for the nominal plant, (2) a gain crossover frequency for the nominal plant, (3) zero steady state error to step commands, and (4) a constant phase margin for all the possible values of the time constant (T$T$): 0<T<∞$0<T<\infty$. We propose a theorem that defines the structure of the set of controllers that fulfil these specifications and show that it is necessary for these robust controllers to include a fractional-order PI$PI$ term. Examples are developed for both stable and unstable plants, and the results are compared with a standard PI$PI$ controller and a robust controller designed using the QFT$QFT$ methodology.     

Online constrained optimization based adaptive robust control of a class of MIMO nonlinear systems with matched uncertainties and input/state constraints

A performance oriented two-loop control approach is proposed for a class of multiple-input–multiple-output (MIMO) systems with input saturation, state constraints, matched parametric uncertainties and input disturbances. In the inner loop, a constrained adaptive robust control (ARC) law is synthesized to achieve the required robust tracking performances with respect to on-line replanned trajectory in the presence of input saturation and various types of matched uncertainties. In the outer loop, a replanned trajectory is generated by solving a constrained optimization algorithm online to minimize the converging time of the overall system response to the desired trajectory while not violating various constraints. Interaction of the two loops is explicitly characterized by a set of inequalities that the design variables of each loop have to satisfy. It is theoretically shown that the resulting closed-loop system can track feasible desired trajectories with a guaranteed converging time and steady-state tracking accuracy without violating the state constraints. Since the system in study is most appropriate to describe the dynamics of the robotic systems, the control of a two-axis planar robotic manipulator is used as an application example. Comparative simulation results demonstrate the advantage of the proposed approach over the traditional approaches in practical applications.     

Assessing the effect of hydrocarbon oil type and thickness on a remote sensing signal: A sensitivity study based on the optical properties of two different oil types and the HYMAP and Quickbird sensors

We measured the light absorption properties of two naturally occurring Australian hydrocarbon oils, a Gippsland light crude oil and a North West Shelf light condensate. Using the results from these measurements in conjunction with estimated sensor environmental noise thresholds, the theoretical minimum limit of detectability of each oil type (as a function of oil thickness) was calculated for both the hyperspectral HYMAP and multispectral Quickbird sensors. The Gippsland crude oil is discernable at layer thickness of 20 µm or more in the Quickbird green channel. The HYMAP sensor was found to be theoretically capable of detecting a layer of Gippsland crude oil with a thickness of 10 µm in approximately six sensor channels. By contrast, the North West Shelf light condensate was not able to be detected by either sensor for any thickness up to 200 µm. Optical remote sensing is therefore not applicable for detecting diagnostic absorption features associated with this light condensate oil type, which is typical of the chemistry of many hydrocarbon oils found in the Australian Northwest Shelf area and condensates world wide. We conclude that oil type is critical to the applicability of optical remote sensing for natural oil slick detection and identification. We recommend that a sensor- and oil-specific sensitivity study should be conducted prior to applying optical remote sensors for oil exploration.The oil optical properties were obtained using two different laboratory methods, a reflectance-based approach and transmittance-based approach. The reflectance-based approach was relatively complex to implement, but was chosen in order to replicate as closely as possible real world remote sensing measurement conditions of an oil film on water. The transmittance-based approach, based upon standard laboratory spectrophotometric measurements was found to generate results in good agreement with the reflectance-based approach. Therefore, for future oil- and sensor-specific sensitivity studies, we recommend the relatively accessible transmittance-based approach, which is detailed in this paper.