State and unknown input disturbance estimation for positive linear systems

Input and state estimation for linear systems with a rank-deficient direct feedthrough matrix

For nonlinear discrete systems with dual unknown inputs, there are many limitations regarding previous nonlinear filters. This paper proposes two new, improved square-root cubature Kalman filtering (ISRCKF) algorithms to estimate system states and dual unknown inputs. Improved square-root cubature Kalman filtering 1 (ISRCKF1) introduces an innovation that first obtains the unknown input estimates from the measurement equation, then updates the innovation to derive the unknown input estimates from the state equation, then uses the already obtained estimates of the dual unknown inputs to correct the one-step estimate of the state, and finally the minimum variance unbiased estimate of the state is obtained. Improved square-root cubature Kalman filtering 2 (ISRCKF2) builds a unified innovation feedback model, then applies the minimum variance unbiased estimation (MVUE) criterion to obtain the estimates of system states and dual unknown inputs, refining a more concise recursive filter but requiring stronger assumptions. Finally, simulation results demonstrate that the above two algorithms can achieve the optimal estimates of system states and dual unknown inputs simultaneously, and ISRCKF2 further enhances the accuracy of both state and dual unknown inputs estimation, which verifies the validity of the proposed algorithms.

This article presents a new approach to estimation of unknown inputs and faults in a class of nonlinear systems. The approach is based on the design of a cascade connection of two sliding mode observers. The first is used for estimation of state and unknown inputs and the second is used for fault detection. An important feature of the proposed approach is that the state trajectories do not leave the sliding manifold even in presence of unknown disturbances and faults. This allows for faults and disturbances to be reconstructed based on information retrieved from the equivalent output injection signal. The proposed approach is used to reconstruct unknown disturbances and faults in nonlinear model of Vertical Take-Off and Landing (VTOL) aircraft system.

Bond-Graph-Based Multivariable non linear UlO-type estimation

The H∞ and sliding mode observers are important in integer-order dynamic systems. However, these observers are not well explored in the field of fractional-order dynamic systems. In this paper, the H∞ filter and the fractional-order sliding mode unknown input observer are developed to estimate state of the linear time-invariant fractional-order dynamic systems with consideration of proper initial memory effect. As the first result, the fractional-order H∞ filter is introduced, and it is shown that the gain from the noise to the estimation error is bounded in the sense of the H∞ norm. Based on the extended bounded real lemma, the H∞ filter design is formulated in a linear matrix inequality form, and it will be seen that numerical methods to solve convex optimization problems are feasible in fractional-order systems (FOSs). As the second result of this paper, not only state but also unknown input disturbance are estimated by fractional-order sliding-mode unknown input observer, simultaneously. In this paper, it is shown that the design and stability analysis of the two estimation techniques are not related with the initial history. Through two numerical examples, the performance of the fractional-order H∞ filter and the fractional-order sliding-mode observer is illustrated with consideration of the initialization functions.

This paper presents a system augmentation-based unbiased minimum-variance input and state estimation for systems with unknown inputs which can be reconstructed with a multi-step delay. An estimable input generating model (EIGM)-based system augmented approach is proposed to facilitate the filter design. It is shown that, via this new filtering approach the optimal unknown input and state estimation can be simultaneously achieved through the previously proposed robust two-stage Kalman filter (RTSKF). An illustrative example is given to show the effectiveness of the proposed results.

The Time-Varying First Order Plus Dead Time (TV-FOPDT) model is an extension of the conventional FOPDT by allowing the system parameters, which are primarily defined on the transfer function description, i.e., the DC-gain, time constant and time delay, to be time dependent. The TV-FOPDT identification problem turns to estimate these time-varying parameters based on measured control input and system output. This work considers a TV-FOPDT identification problem in the presence of an unknown disturbance input. By regarding the unknown input as one extra system parameter, the considered identification problem is formulated as a Stochastic Mixed Integral Programming (SMIP) problem after discretizing the original problem. The sliding window technique with forgetting factor is employed to cope with time resolution issue, and the Least Mean Square (LMS) method is used to obtain the optimal solution of each individual optimization problem based on different time delay assumptions. The proposed method is firstly tested through a number of numerical examples, and then it is applied to estimate a TV-FOPDT model of the superheat dynamic of a supermarket refrigeration system.

This paper addressed the problem of the simultaneous estimation of unknown inputs and states in a multi-agent system with time-invariant and time-varying topology. A group of distributed cooperative recursive filters, in the sense of minimum-variance unbiased, was developed, where the estimations of unknown input and state were combined. A necessary and sufficient existing condition is presented and proven for the proposed distributed cooperative filters. Theoretical and numerical analyses demonstrate that the existing condition of the proposed filters is significantly relaxed, in comparison to that of conventional decentralized filters.

In this paper, two controllers with a compound disturbance observer are proposed for a two-wheeled inverted robot (TWIR) with model uncertainty and unknown input disturbance. First, an equivalent linear model of the TWIR with uncertainty and input disturbance is proposed using the Taylor series expansion for the nonlinear model of the TWIR at an equilibrium point, in which the nonlinear part of the Taylor series and the model uncertainty are combined with unknown input disturbance as compound input disturbance. Then, the compound input disturbance is estimated by using the Newton method and reference model. As the estimated compound disturbance is used to compensate for the compound disturbance, the equivalent linear system becomes closely definite without compound input disturbance. Finally, two controllers are proposed using the equivalent linear system. Stability analysis of the proposed control methods is also given. To illustrate the proposed methods, some simulations for the TWIR are performed and compared with the existing methods. The main contribution of this work includes the following: (i) simple controllers based on compound input disturbance observer for trajectory tracking and balancing of TWIRs with unknown input disturbance and model uncertainty are proposed; (ii) the stability of proposed closed-loop control systems is proved; (iii) our proposed methods are simulated and compared with the existing methods.

This paper addresses the problem of the joint estimation of system state and generalized sensor bias (GSB) under a common unknown input (UI) in the case of bias evolution in a heterogeneous sensor network. First, the equivalent UI-free GSB dynamic model is derived and the local optimal estimates of system state and sensor bias are obtained in each sensor node; Second, based on the state and bias estimates obtained by each node from its neighbors, the UI is estimated via the least-squares method, and then the state estimates are fused via consensus processing; Finally, the multi-sensor bias estimates are further refined based on the consensus estimate of the UI. A numerical example of distributed multi-sensor target tracking is presented to illustrate the proposed filter.

In this paper, the problem of attack detection and defense for linear time-invariant systems with disturbances is studied. Unlike existing attack detection mechanisms, a new attack detection mechanism under disturbances is designed by output errors, whose trigger can be determined as attacks rather than disturbances. To solve the unobservable problem of the system under attacks, an augmented system and its auxiliary outputs are constructed until the observer matching condition is satisfied. Using estimates of augmented system states and unknown inputs, a state feedback controller is designed to defend against network attacks and ensure system stability. Theoretical analysis and simulation results verify the feasibility of the scheme.

This paper presents the design of a functional observer for delayed linear systems with an unknown input in the frequency domain. The unknown input is considered in the dynamic and output equations. The delay is present in the state and input vectors. The main interest is that the proposed observer estimates a functional state and an unknown input vector. The design of the frequency domain procedure is based on a polynomial approach using Matrix Fraction Descriptions (MFDs). A numerical example is given to show the efficiency of the proposed approach.

In this paper, the event-based state and unknown input estimation (SUIE) problem is investigated for a class of stochastic systems subject to parameter uncertainties and stochastic nonlinearities. For the purpose of reducing the energy consumption in data transmission, an event-triggering protocol is employed to regulate whether the current measurement is transmitted by the sensor. Utilising the event-triggered measurement, a recursive estimator is constructed to concurrently estimate the state and the unknown input. The upper bounds of estimation error covariances are given explicitly for both the state and the unknown input estimates. By means of the completing-the-square technique and Lagrange multiplier method, the estimator gain matrices are designed which minimise the obtained upper bounds. Finally, a numerical example is given to show the effectiveness of the proposed SUIE method.

This brief investigates the issue of state estimation and unbounded unknown input reconstruction for a class of one-sided Lipschitz nonlinear interconnected systems with uncertain output and mismatched unknown input distribution matrix. Based on descriptor augmentation strategy and coordinate transformation, the effect of measurement noise and matched unknown input parts are firstly decoupled. Then, a novel multi-intermediate estimator-assisted unknown input observer is constructed to estimate state and mismatched unknown input. In addition, sufficient conditions in linear matrix inequality (LMI) form is derived to guarantee the stability of the observer and to facilitate observer parameter tuning. Finally, a simulation example is provided to illustrate the effectiveness and merits of the proposed methods.

This paper focuses on the joint input and state estimation for linear stochastic discrete-time systems. To obtain unique estimators that are optimal in the sense of being both least-squares and minimum-variance unbiased (MVU) and their recursive solution, an objective function of the sum of squared errors of outputs is first minimized with respect to an extended state vector including states and unknown inputs. A recursive solution of the extended state vector is then derived with the aid of matrix manipulations. Finally, appropriate matrix decomposition and transformation are used to extract the recursive solutions only involving the current states and unknown inputs from the recursive solution obtained in the previous step. This approach avoids excessive computation due to the dimensions of the matrices that increase with time. As a result, the resulting recursive solution is referred to as a general Kalman filter with unknown inputs (GKF-UI), which covers the most general case of unknown inputs so far in the literature without resorting to transforming the outputs and/or unknown inputs. The unknown inputs to be estimated by the proposed GKF-UI could be arbitrary signals without any prior information and the properties of the proposed GKF-UI are also examined. A numerical example with partial feedthrough from three unknown inputs is used to demonstrate the effectiveness and accuracy of the proposed algorithm.