Gain Perturbations Research Articles

Robust and resilient state-dependent control of discrete-time nonlinear systems with general performance criteria

A novel state-dependent control approach for discrete-time nonlinear systems with general performance criteria is presented. This controller is robust for unstructured model uncertainties, resilient against bounded feedback control gain perturbations in achieving optimality for general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. For the system model, unstructured uncertainty description is assumed, which incorporates commonly used types of uncertainties, such as norm-bounded and positive real uncertainties as special cases. By solving a state-dependent linear matrix inequality (LMI) at each time step, sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this paper unify existing results on nonlinear quadratic regulator, H∞ and positive real control to provide a novel robust control design. The effectiveness of the proposed technique is demonstrated by simulation of the control of inverted pendulum.

Stochastically resilient extended Kalman filtering for discrete-time nonlinear systems with sensor failures

Missing sensor data is a common problem, which severely influences the overall performance of modern data-intensive control and computing applications. In order to address this important issue, a novel resilient extended Kalman filter is proposed for discrete-time nonlinear stochastic systems with sensor failures and random observer gain perturbations. The failure mechanisms of multiple sensors are assumed to be independent of each other with different failure rates. The locally unbiased robust minimum mean square filter is designed for state estimation under these conditions. The performance of the proposed estimation method is verified by means of numerical Monte Carlo simulation of two different nonlinear stochastic systems, involving a sinusoidal system and a Lorenz oscillator system.

Robust and resilient state-dependent control of continuous-time nonlinear systems with general performance criteria

A novel state-dependent control approach for continuous-time nonlinear systems with general performance criteria is presented in this paper. This controller is optimally robust for model uncertainties and resilient against control feedback gain perturbations in achieving general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. For the system model, unstructured uncertainty description is assumed, which incorporates commonly used types of uncertainties, such as norm-bounded and positive real uncertainties as special cases. By solving a state-dependent linear matrix inequality at each time, sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this paper unify existing results on nonlinear quadratic regulator, H∞ and positive real control. The efficacy of the proposed technique is demonstrated by numerical simulations of the nonlinear control of the inverted pendulum on a cart system.

Robust NonfragileH∞Filtering for Uncertain T-S Fuzzy Systems with Interval Delay: A New Delay Partitioning Approach

This paper investigates the problem of robust nonfragile fuzzyH∞filtering for uncertain Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays. Attention is focused on the design of a filter such that the filtering error system preserves a prescribedH∞performance, where the filter to be designed is assumed to have gain perturbations. By developing a delay decomposition approach, both lower and upper bound information of the delayed plant states can be taken into full consideration; the proposed delay-fractional-dependent stability condition for the filter error systems is obtained based on the direct Lyapunov method allied with an appropriate and variable Lyapunov-Krasovskii functional choice and with tighter upper bound of some integral terms in the derivation process. Then, a new robust nonfragile fuzzyH∞filter scheme is proposed, and a sufficient condition for the existence of such a filter is established in terms of linear matrix inequalities (LMIs). Finally, some numerical examples are utilized to demonstrate the effectiveness and reduced conservatism of the proposed approach.

Robust resilient controllers synthesis for uncertain fractional-order large-scale interconnected system

The problem of the decentralized stabilization for fractional order large-scale interconnected uncertain system with norm-bounded parametric uncertainties and controller gain perturbations is studied. It is solved under two circumstances: one is under the additive controller gain perturbations; the other is under the multiplicative ones. Sufficient conditions on the decentralized stabilization of fractional order large-scale interconnected system with a commensurate order 0<α<1 are established by applying a complex Lyapunov inequality method. The state feedback non-fragile controller designs for fractional order large-scale interconnected uncertain system under the two classes of gain perturbations are obtained in terms of solutions to LMIs. Numerical examples are used to illustrate the effectiveness of the proposed method.

Robust and resilient finite-time bounded control of discrete-time uncertain nonlinear systems

Finite-time state-feedback stabilization is addressed for a class of discrete-time nonlinear systems with conic-type nonlinearities, bounded feedback control gain perturbations, and additive disturbances. First, conditions for the existence of a robust and resilient linear state-feedback controller for this class of systems are derived. Then, using linear matrix inequality techniques, a solution for the controller gain and the maximum allowable bound on the gain perturbation is obtained. The developed controller is robust for all unknown nonlinearities lying in a known hypersphere with an uncertain center and all admissible disturbances. Moreover, it is resilient against any bounded perturbations that may alter the controller’s gain by at most a prescribed amount. The paper is concluded with a numerical example showcasing the applicability of the main result.

Delay-dependent non-fragile robust dissipative filtering for uncertain nonlinear stochastic singular time-delay systems with Markovian jump parameters

The problem of delay-dependent non-fragile and robust dissipative filtering is investigated for a class of uncertain nonlinear stochastic singular time-delay Ito-type systems with Markovian jump parameters. With the system uncertainty and the filter gain perturbations, the closed-loop filtering error system is robust asymptotically stable and satisfies the dissipation performance. By constructing a Lyapunov-Krasovskii function and applying the Ito differential formula to compute the differential function along the system, a sufficient condition for the existence of a robust and non-fragile dissipative filter is derived in the form of linear matrix inequality (LMI). An illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach.

Robust resilient controllers synthesis for uncertain fractional order large-scale interconnected system in the case of 1

The paper solves the problem of stabilization of large-scale fractional order interconnected system with a commensurate order 1 <α < 2 under controller gain perturbations. On the basis of the stability criterion of fractional order system, sufficient conditions on the decentralized stabilization of fractional order large-scale interconnected system with norm-bounded uncertainties are presented by applying a complex Lyapunov inequality. Furthermore, decentralized stabilization resilient controllers are designed. Numerical examples are used to illustrate the effectiveness of the proposed method.

High Gain Observer for Drag Tracking in Mars Entry Longitudinal Guidance

An extended high gain state and perturbation observer combined with feedback linearization was applied in drag tracking for Mars entry longitudinal guidance. The observer estimates the drag, the drag rate and the perturbation due to model uncertainty and disturbance for drag tracking. Mars entry simulation was performed to assess the performance of the adaptive guidance law. The results demonstrate that the proposed guidance law is robust to model error, and can recover the ideal performance of the feedback linearization control.

Static Output Non-Fragile Control of Fuzzy Bilinear System

This paper focuses on the problem of non-fragile static output feedback control for discrete-time fuzzy bilinear systems. Based on the parallel distributed compensation approach, the sufficient conditions are derived in the presence of the additive controller gain perturbations. The stabilization conditions are further formulated into linear matrix inequalities (LMI) so that the desired controller can be easily obtained by using the LMI toolbox.

Robust DOA Estimation Using Independent Component Analysis

The paper deals with robust direction of arrival (DOA) estimation based on independent component analysis (ICA) in the presence of sensor gain perturbation and unknown noise fields. It has been shown that the noise subspace based estimator suffers from the drawback of being very sensitivity to orthogonality between the estimated noise subspace and true signal subspace. However, no single subspace feature extraction gives satisfactory results under different environments, but the proposed two-step subspace feature extraction method can efficiently cope with the limits. The noise-subspace demixing procedure of complex-valued FastICA is presented here, which is based on minor component analysis (MCA) for individual noise-eigenvector projection, and Newton’s iteration algorithm exploiting the minimization of the approximate negentropy of non-Gaussian signal for array signal processing. When a new noise subspace is attained, the proposed method can form the maximizing orthogonality especially for imperfect antenna array and make to facilitate the conventional noise-subspace based estimate method. Several computer simulation examples confirm the effectiveness of the proposed method and the performance improvement over the MUSIC estimator.

Improved resilient feedback stabilisation method for uncertain systems

The problem of resilient stabilisation for a class of continuous-time uncertain systems having norm-bounded parametric uncertainties is investigated. Both static and dynamic output-feedback resilient controller design is considered. The goal is to robustly quadratically stabilise the uncertain plant considering the controller gain perturbations. Sufficient conditions for the existence of static output feedback and dynamic output feedback resilient controllers are derived in terms of linear matrix inequalities. A numerical example for each type of controllers is illustrated to demonstrate their effectiveness.

Robust Adaptive Beamforming Based on Interference Covariance Matrix Reconstruction and Steering Vector Estimation

Adaptive beamformers are sensitive to model mismatch, especially when the desired signal is present in training snapshots or when the training is done using data samples. In contrast to previous works, this correspondence attempts to reconstruct the interference-plus-noise covariance matrix instead of searching for the optimal diagonal loading factor for the sample covariance matrix. The estimator is based on the Capon spectral estimator integrated over a region separated from the desired signal direction. This is shown to be more robust than using the sample covariance matrix. Subsequently, the mismatch in the steering vector of the desired signal is estimated by maximizing the beamformer output power under a constraint that prevents the corrected steering vector from getting close to the interference steering vectors. The proposed adaptive beamforming algorithm does not impose a norm constraint. Therefore, it can be used even in applications where gain perturbations affect the steering vector. Simulation results demonstrate that the performance of the proposed adaptive beamformer is almost always close to the optimal value across a wide range of signal to noise and signal to interference ratios.

NON-FRAGILE GUARANTEED COST CONTROL OF T-S FUZZY TIME-VARYING DELAY SYSTEMS WITH LOCAL BILINEAR MODELS

This paper focuses on the non-fragile guaranteed cost control problem for a class of T-S fuzzy time-varying delay systems with local bi- linear models. The objective is to design a non-fragile guaranteed cost state feedback controller via the parallel distributed compensation (PDC) approach such that the closed-loop system is delay-dependent asymptotically stable and the closed-loop performance is no more than a certain upper bound in the presence of the additive controller gain perturbations. A sufficient condition for the existence of such non-fragile guaranteed cost controllers is derived via the linear matrix inequality (LMI) approach and the design problem of the fuzzy controller is formulated in term of LMIs. The simulation examples show that the proposed approach is effective.

Robust and Resilient Finite-Time Control of a Class of Continuous-Time Nonlinear Systems

Finite-time state-feedback stabilization of a class of continuous-time nonlinear systems with conic type nonlinearities, bounded feedback control gain perturbations, and additive disturbances is presented. Sufficient conditions for the existence of a robust and resilient linear finite-time state-feedback controller for this class of systems are derived. Then, using linear matrix inequality techniques, solutions for the controller gain and the upper bound on the gain perturbations are obtained. The developed controller is robust for all unknown nonlinearities lying in a hyper-sphere and all admissible disturbances. Furthermore, it is resilient against any bounded perturbations that may modify the controller's gain by at most a prescribed amount. We conclude the paper with a numerical example illustrating the applicability of the main result.

Stabilization for Uncertain Multi-channel Markov Jump Stochastic Systems with Additive Gain Perturbations

In this paper, stabilization problem for a class of multi-channel Markov jump stochastic systems with additive gain perturbations is addressed. In order to design the state feedback stabilization controller, a novel control strategy that guarantees the adequate cost bound is established. A sufficient condition for the existence of the controller is derived in term of matrix inequality. In the sequel, for practical plants since it is not always easy to access the transition modes, the mode-independent strategy set is considered. As a result, it is shown that such strategy set can be obtained by solving the linear matrix inequality (LMI). Furthermore, in order to reduce the cost performance, fuzzy control for each input is combined with the static gain as additive gain perturbations. As a result, even if dramatic random parameter changes occur in the system, it is shown that the robust stability and the reduction of the cost can be attained. Finally, a simple numerical example is given to demonstrate the availability of the proposed method.

A novel robust proportional-integral (PI) adaptive observer design for chaos synchronization

In this paper, chaos synchronization in the presence of parameter uncertainty, observer gain perturbation and exogenous input disturbance is considered. A nonlinear non-fragile proportional-integral (PI) adaptive observer is designed for the synchronization of chaotic systems; its stability conditions based on the Lyapunov technique are derived. The observer proportional and integral gains, by converting the conditions into linear matrix inequality (LMI), are optimally selected from solutions that satisfy the observer stability conditions such that the effect of disturbance on the synchronization error becomes minimized. To show the effectiveness of the proposed method, simulation results for the synchronization of a Lorenz chaotic system with unknown parameters in the presence of an exogenous input disturbance and abrupt gain perturbation are reported.

Decentralized State-Estimation of Interconnected Systems with Unknown Nonlinearities

An efficient state-estimation scheme is developed within the LMI framework for robust decentralized state estimation of systems composed of linear dynamic subsystems coupled by static nonlinear interconnections satisfying quadratic constraints. The procedure utilizes a general linear estimator structure, and consists of two steps, the first giving a block-diagonal Lyapunov matrix together with the robustness degree, and the second determining the filter parameters. Extension to the case of additive filter gain perturbations is established and numerical examples are provided to illustrate the applicability of the method.

Non-Fragile Decentralized Control for the Uncertain Singular Large-Scale Systems with Time-Delay

This paper is concerned with the non-fragile decentralized controller design problem for uncertain singular large-scale system with time-delay. Sufficient condition for the controller is expressed in terms of linear matrix inequalities(LMIs). When this condition is feasible, the desired controller can be obtained with additive gain perturbations and multiplicative gain perturbations. Finally, a numerical example is also given to illustrate the effectiveness.

A Nonlinear Adaptive Resilient Observer Design for a Class of Lipschitz Systems Using LMI

This paper addresses the parameter and state estimation problem in the presence of the observer gain perturbations for Lipschitz systems that are linear in the unknown parameters and nonlinear in the states. A nonlinear adaptive resilient observer is designed, and its stability conditions based on the Lyapunov technique are derived. The gain for this observer is derived systematically using the linear matrix inequality approach. A numerical example and a physical setup are provided to show the effectiveness of the proposed method.