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1.
This paper presents the sliding mode mean-square and mean-module state filtering and parameter identification problems for linear stochastic systems with unknown parameters over linear observations, where unknown parameters are considered Wiener processes. The original problems are reduced to the sliding mode mean-square and mean-module filtering problems for an extended state vector that incorporates parameters as additional states. The obtained sliding mode filters for the extended state vector also serve as the optimal identifiers for the unknown parameters. Performance of the designed sliding mode mean-square and mean-module state filters and parameter identifiers are verified for both, stable and unstable, linear uncertain systems.  相似文献   

2.
This paper considers the identification problem of bilinear systems with measurement noise in the form of the moving average model. In particular, we present an interactive estimation algorithm for unmeasurable states and parameters based on the hierarchical identification principle. For unknown states, we formulate a novel bilinear state observer from input-output measurements using the Kalman filter. Then a bilinear state observer based multi-innovation extended stochastic gradient (BSO-MI-ESG) algorithm is proposed to estimate the unknown system parameters. A linear filter is utilized to improve the parameter estimation accuracy and a filtering based BSO-MI-ESG algorithm is presented using the data filtering technique. In the numerical example, we illustrate the effectiveness of the proposed identification methods.  相似文献   

3.
This paper presents solution of the optimal linear-quadratic controller problem for unobservable integral Volterra systems with continuous/discontinuous states under deterministic uncertainties, over continuous/discontinuous observations. Due to the separation principle for integral systems, the initial continuous problem is split into the optimal minmax filtering problem for integral Volterra systems with deterministic uncertainties over continuous/discontinuous observations and the optimal linear-quadratic control (regulator) problem for observable deterministic integral Volterra systems with continuous/discontinuous states. As a result, the system of the optimal controller equations are obtained, including the linear equation for the optimally controlled minmax estimate and two Riccati equations for its ellipsoid matrix (optimal gain matrix of the filter) and the optimal regulator gain matrix. Then, in the discontinuous problems, the equation for the optimal controller and the equations for the optimal filter and regulator gain matrices are obtained using the filtering procedure for deriving the filtering equations over discontinuous observations proceeding from the known filtering equations over continuous ones and the dual results in the optimal control problem for integral systems. The technical example illustrating application of the obtained results is finally given.  相似文献   

4.
This paper mainly focuses on the event-based state and fault estimation problem for a class of nonlinear systems with logarithmic quantization and missing measurements. The sensors are assumed to have different missing probabilities and a constant fault is considered here. Different from a constant threshold in existing event-triggered schemes, the threshold in this paper is varying in the state-independent condition. With resort to the state augmentation approach, a new state vector consisting of the original state vector and the fault is formed, thus the corresponding state and fault estimation problem is transmitted into the recursive filtering problem. By the stochastic analysis approach, an upper bound for the filtering error covariance is obtained, which is expressed by Riccati difference equations. Meanwhile, the filter gain matrix minimizing the trace of the filtering error covariance is also derived. The developed recursive algorithm in the current paper reflects the relationship among the upper bound of the filtering error covariance, the varying threshold, the linearization error, the probabilities of missing measurements and quantization parameters. Finally, two examples are utilized to verify the effectiveness of the proposed estimation algorithm.  相似文献   

5.
The optimal widely linear state estimation problem for quaternion systems with multiple sensors and mixed uncertainties in the observations is solved in a unified framework. For that, we devise a unified model to describe the mixed uncertainties of sensor delays, packet dropouts and uncertain observations by using three Bernoulli distributed quaternion random processes. The proposed model is valid for linear discrete-time quaternion stochastic systems measured by multiple sensors and it allows us to provide filtering, prediction and smoothing algorithms for estimating the quaternion state through a widely linear processing. Simulation results are employed to show the superior performance of such algorithms in comparison to standard widely linear methods when mixed uncertainties are present in the observations.  相似文献   

6.
This paper is devoted to the investigation of the delay-dependent H∞ filtering problem for a class of discrete-time singular Markov jump systems with Wiener process and partly unknown transition probabilities. The class of stochastic singular model under consideration is more general and covers the stochastic singular Markov jump time-varying delay systems with completely known and completely unknown transition probabilities as two special cases. Firstly, based on a stochastic Lyapunov–Krasovskii candidate function and an auxiliary vector function, by employing some appropriate free-weighting matrices, the discretized Jensen inequality and combining them with the structural characteristics of the filtering error system, a set of delay-dependent sufficient conditions are established, which ensure that the filtering error system is stochastically admissible. And then, a singular filter is designed such that the filtering error system is not only regular, causal and stochastically stable, but also satisfy a prescribed H∞ performance for all time-varying delays no larger than a given upper bound. Furthermore, the sufficient conditions for the solvability of the H∞ filtering problem are obtained in terms of a new type of Lyapunov–Krasovskii candidate function and a set of linear matrix inequalities. Finally, simulation examples are presented to illustrate the effectiveness of the proposed method in the paper.  相似文献   

7.
In this paper, the mean-square and mean-module filtering problems for polynomial system states over polynomial observations are studied proceeding from the general expression for the stochastic Ito differentials of the estimate and the error variance. The paper deals with the general case of nonlinear polynomial states and observations. As a result, the Ito differentials for the estimates and error variances corresponding to the stated filtering problems are first derived. The procedure for obtaining an approximate closed-form finite-dimensional system of the sliding mode filtering equations for any polynomial state over observations with any polynomial drift is then established. In the examples, the obtained sliding mode filters are applied to solve the third-order sensor filtering problems for a quadratic state, assuming a conditionally Gaussian initial condition for the extended second-order state vector. The simulation results show that the designed sliding mode filters yield reliable and rapidly converging estimates.  相似文献   

8.
This paper addresses the optimal controller problem for a linear system over linear observations with respect to different Bolza–Meyer criteria, where (1) the integral control and state energy terms are quadratic and the non-integral term is of the first degree or (2) the control energy term is quadratic and the state energy terms are of the first degree. The optimal solutions are obtained as sliding mode controllers, each consisting of a sliding mode filter and a sliding mode regulator, whereas the conventional feedback LQG controller fails to provide a causal solution. Performance of the obtained optimal controllers is verified in the illustrative example against the conventional LQG controller that is optimal for the quadratic Bolza–Meyer criterion. The simulation results confirm an advantage in favor of the designed sliding mode controllers.  相似文献   

9.
This paper focuses on parameter estimation problems for non-uniformly sampled Hammerstein nonlinear systems. By combining the lifting technique and state space transformation, we derive a nonlinear regression identification model with different input and output updating rates. Furthermore, the unmeasurable state vector is estimated by Kalman filter, and by using the hierarchical identification principle, we develop a hierarchical recursive least squares algorithm for estimating the unknown parameters of the identification model. Finally, illustrative examples are given to indicate that the proposed algorithm is effective.  相似文献   

10.
In this paper, we develop two new model reference adaptive control (MRAC) schemes for a class of nonlinear dynamic systems that is robust with respect to an uncertain state (output) dependent nonlinear perturbations and/or external disturbances with unknown bounds. The design is based on a controller parametrization with an adaptive integral action. Two types of adaptive controllers are considered—the state feedback controller with a plant parameter identifier, and the output feedback controller with a linear observer.  相似文献   

11.
This paper investigates the problem of extended dissipative filtering for bidirectional associative memory inertial neural networks, where the Markov chain is introduced to describe the switching characteristic in the structure and parameters. Moreover, considering the limited network bandwidth, the weighted try-once-discard protocol, as a significant scheduling mechanism in determining which nodes can be accessed between the sensor nodes and the filter, is employed to avoid the data collisions under the constrained communication channel. The objective of the paper is to develop a filter that can ensure that the filtering error system is stochastically stable with extended dissipative performance. Based on the Lyapunov function and an improved decoupling approach, a set of sufficient conditions satisfying the above objective are derived, and the filter gains are obtained. Finally, an illustrative example is employed to verify the validity of the proposed method.  相似文献   

12.
This paper focuses on the extended dissipative filter design problem for a class of uncertain semi-Markov jump systems in the discrete-time context, where the parameter uncertainties are assumed to be occurred in a special probabilities way. The aim of this paper is to design a mode-dependent filter ensuring the stochastic stability of the resulting filtering error system. To reduce the burden of communication network, the event-triggered scheme and quantized measurement are employed. By constructing a new Lyapunov functional, the filter design methodology is put forward. Finally, two numerical examples are proposed to demonstrate the usefulness of the filter design methodology.  相似文献   

13.
Single beacon navigation methods with unknown effective sound velocity (ESV) have recently been proposed to solve the performance degeneration induced by ESV setting error. In these methods, a local linearization-based state estimator, which only exhibits local convergence, is adopted to estimate the navigation state. When the initial ESV setting error or vehicle initial position error is large, the local linearization-based state estimators have difficulty guaranteeing the filtering convergence. With this background, this paper proposes a linear time-varying single beacon navigation model with an unknown ESV that can realize global convergence under the condition of system observability. A Kalman filter is adopted to estimate the model state, and the corresponding stochastic model is inferred for the application of the Kalman filter. Numerical simulation confirms that the proposed linear time-varying single beacon navigation model can realize fast convergence in the case of a large initial error, and has superior steady-state performance compared with the existing methods.  相似文献   

14.
This paper investigates the problem of robust H∞ fixed-order filtering for a class of linear parameter-varying (LPV) switched delay systems under asynchronous switching that the system parameter matrices and the time delays are dependent on the real-time measured parameters. The so-called asynchronous switching means that there are time delays between the switching of filters and the switching of system modes. By constructing the parameter-dependent and mode-dependent Lyapunov-Krasovskii functional which is allowed to increase during the running time of active subsystem with the mismatched filter, and using the mode-dependent average dwell time (MDADT) switching method, the sufficient conditions for exponential stability and satisfying a novel weighted H∞ criterion are derived. As there exist couplings between Lyapunov-Krasovskii functional matrices and system parameter matrices, we utilize slack matrices to decouple them. Based on the above results, a suitable weighted H∞ fixed-order filter can be obtained in the form of the parameter linear matrix inequalities (PLMIs). By virtue of approximate basis function and gridding technique, the design of weighted H∞ fixed-order filter can be transformed into the solution of the finite dimensional LMIs. Finally, a numerical example is presented to verify both the effectiveness and the low conservatism of the parameter-dependent and mode-dependent fixed-order filtering method proposed in this paper.  相似文献   

15.
This paper studies the distributed Kalman consensus filtering problem based on the event-triggered (ET) protocol for linear discrete time-varying systems with multiple sensors. The ET strategy of the send-on-delta rule is employed to adjust the communication rate during data transmission. Two series of Bernoulli random variables are introduced to represent the ET schedules between a sensor and an estimator, and between an estimator and its neighbor estimators. An optimal distributed filter with a given recursive structure in the linear unbiased minimum variance criterion is derived, where solution of cross-covariance matrix (CCM) between any two estimators increases the complexity of the algorithm. In order to avert CCM, a suboptimal ET Kalman consensus filter is also presented, where the filter gain and the consensus gain are solved by minimizing an upper bound of filtering error covariance. Boundedness of the proposed suboptimal filter is analyzed based on a Lyapunov function. A numerical simulation verifies the effectiveness of the proposed algorithms.  相似文献   

16.
A novel H∞ filter design methodology has been presented for a general class of nonlinear systems. Different from existing nonlinear filtering design, the nonlinearities are approximated using neural networks, and then are modeled based on linear difference inclusions, which makes the structure of the desired filter simpler and parameter turning easier and has the advantages of guaranteed stability, numeral robustness, bounded estimation accuracy. A unified framework is established to solve the addressed H∞ filtering problem by exploiting linear matrix inequality (LMI) approach. A numerical example shows that the filtering error systems will work well against bounded error between a nonlinear dynamical system and a multilayer neural network.  相似文献   

17.
In this paper, a dynamically event-triggered filtering problem is investigated for a class of discrete time-varying systems with censored measurements and parameter uncertainties. The censored measurements under consideration are described by the Tobit measurement model. In order to save the communication energy, a dynamically event-triggered mechanism is utilized to decide whether the measurements should be transmitted to the filter or not. The aim of this paper is to design a robust recursive filter such that the filtering error covariance is minimized in certain sense for all the possible censored measurements, parameter uncertainties as well as the effect induced by the dynamically event-triggered mechanism. By means of the mathematical induction, an upper bound is firstly derived for the filtering error covariance in terms of recursive matrix equations. Then, such an upper bound is minimized by designing the filter gain properly. Furthermore, the boundedness is analyzed for the minimized upper bound of the filtering error covariance. Finally, two numerical simulations are exploited to demonstrate the effectiveness of the proposed filtering algorithm.  相似文献   

18.
The conventional modal control theory is concerned with the problem of determining a state feedback matrix-valued gain which drives the system eigenvalues to prescribed positions. When the parameters of the open-loop system involve certain variations, the closed-loop eigenvalues, obtained by using a feedback gain determined as above, also contain variations. In the present paper the problem of choosing an additional state feedback gain such as to reduce the closed-loop eigenvalue variations as much as desired is solved. Specifically, upon the assumption that a nominal set of parameter values is given, and that a feedback modal control law which drives the eigenvalues of the nominal closed-loop system to the desired positions is known, two alternative expressions for the required additional reduced eigenvalue sensitivity feedback controller are derived. Both cases of known and unknown system state vector are considered. The theory is illustrated by several examples.  相似文献   

19.
This paper focuses on the joint parameter and state estimation issue for observer canonical state-space systems with white noises in state equations and moving average noises in output equations. By means of the Kalman filtering and the gradient search, we derive a Kalman filtering based extended stochastic gradient algorithm. For purpose of achieving the higher parameter estimation accuracy, a Kalman filtering based multi-innovation extended stochastic gradient algorithm is proposed on the basis of the multi-innovation identification theory. Finally, the effectiveness of the proposed algorithms is validated through a numerical example.  相似文献   

20.
This paper considers the filtering problem for a class of linear cyber-physical systems (CPSs) subject to the Round-Robin protocol (RRP) scheduling, where the RRP is adopted to efficiently avoid data collisions in multi-sensor application scenarios. Unlike most of the existing results concerning the scheduling effects of the RRP under reliable communication channels, the filtering problem over packet-dropping networks is investigated. In such a framework, an optimal Kalman-type recursive filter is derived in the minimum mean square error (MMSE) sense, which is different from the suboptimal filters with bounded error covariances proposed in the previous results. Due to the protocol-induced behaviors and the unreliability of the channels, the estimator may be unstable. Thus, the stability problem of the filter is mainly discussed. It can be proved that the filter is stable when the arrival rate of the measurements exceeds a certain threshold, where the threshold can be obtained by solving a quasi-convex optimization problem. Furthermore, a sufficient condition for the existence of the steady-state error covariance is presented and can be transferred into the feasibility of a certain linear matrix inequality (LMI). Finally, a simulation example is provided to demonstrate the developed results.  相似文献   

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