Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises

Copyright [2002] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, a robust finite-horizon Kalman filter is designed for discrete time-varying uncertain systems with both additive and multiplicative noises. The system under consideration is subject to both deterministic and stochastic uncertainties. Sufficient conditions for the filter to guarantee an optimized upper bound on the state estimation error variance for admissible uncertainties are established in terms of two discrete Riccati difference equations. A numerical example is given to show the applicability of the presented method

Stabilization of Linear Systems with Structured Perturbations

The problem of stabilization of linear systems with bounded structured uncertainties are considered in this paper. Two notions of stability, denoted quadratic stability (Q-stability) and μ-stability, are considered, and corresponding notions of stabilizability and detectability are defined. In both cases, the output feedback stabilization problem is reduced via a separation argument to two simpler problems: full information (FI) and full control (FC). The set of all stabilizing controllers can be parametrized as a linear fractional transformation (LFT) on a free stable parameter. For Q-stability, stabilizability and detectability can in turn be characterized by Linear Matrix Inequalities (LMIs), and the FI and FC Q-stabilization problems can be solved using the corresponding LMIs. In the standard one-dimensional case the results in this paper reduce to well-known results on controller parametrization using state-space methods, although the development here relies more heavily on elegant LFT machinery and avoids the need for coprime factorizations

Robust Multivariable controller Design with the simultaneous H2 /H∞/µ for Single Person Aircraft

In a physical system several targets are normally being considered in which each of nominal and robust performance has their own strengths and weaknesses. In nominal performance case, system operation without uncertainty has decisive effect on the operation of system, whereas in robust performance one, operation with uncertainty will be considered. The target of present paper is a balance between nominal and robust performance of state feedback A new approach of present paper is the combination of two controllers of μ and H2/H∞.  The controller for robust stability status, nominal performance, robust performance and noise rejection are designed simultaneous. Controller will be achieved from solving constraint optimization problem. Where a simultaneous H2 /H∞/µ robust multivariable controller has been designed over an X-29 Single Person.  This model has three inputs and three outputs, where the state space equations of the system response to an unstable one. Simulation results show the effectiveness and benefits of the method.DOI:http://dx.doi.org/10.11591/ijece.v3i2.235

Behavioral approach to robustness analysis

This paper introduces a general and powerful framework for modeling and analysis of uncertain systems. One immediate concrete result of this work is a practical method for computing robust performance in the presence of norm-bounded perturbations and both norm-bounded and white-noise disturbances

Combining Prior Knowledge and Data for Robust Controller Design

We present a framework for systematically combining data of an unknown linear time-invariant system with prior knowledge on the system matrices or on the uncertainty for robust controller design. Our approach leads to linear matrix inequality (LMI) based feasibility criteria which guarantee stability and performance robustly for all closed-loop systems consistent with the prior knowledge and the available data. The design procedures rely on a combination of multipliers inferred via prior knowledge and learnt from measured data, where for the latter a novel and unifying disturbance description is employed. While large parts of the paper focus on linear systems and input-state measurements, we also provide extensions to robust output-feedback design based on noisy input-output data and against nonlinear uncertainties. We illustrate through numerical examples that our approach provides a flexible framework for simultaneously leveraging prior knowledge and data, thereby reducing conservatism and improving performance significantly if compared to black-box approaches to data-driven control

Combined system identification and robust control of a gimbal platform

Gimbaled imaging systems require very high performance inertial stabilization loops to achieve clear image acquisition, precise pointing, and tracking performance. Therefore, higher bandwidths become essential to meet recent increased performance demands. However, such systems often posses flexible dynamics around target bandwidth and time delay of gyroscope sensors which put certain limit to achievable bandwidths. For inertial stabilization loops, widely used design techniques have difficulty in achieving large bandwidth and satisfying required robustness simultaneously. Clearly, high performance control design hinges on accurate control-relevant model set. For that reason, combined system identification and robust control method is preferred. In the system identification step, accurate nominal model is obtained, which is suitable for subsequent robust control synthesis. Model validation based uncertainty modeling procedure constructs the robust-control-relevant uncertain model set, which facilitates the high performance controller design. Later, with skewed-mu synthesis, controller is designed which satisfies large bandwidth and robustness requirements. Finally, the experimental results show that significant performance improvement is achieved compared to common manual loop shaping methods. In addition, increased performance demands for new imaging systems are fulfilled