Robust H Infinity Control and Robust State Learning for Dynamic Systems

Abstract

Robustness of a dynamic system usually means the capacity of resisting the effect of external disturbance and model uncertainty. Due to the complex environment and inaccurate system modeling, the unexpected external disturbance and model uncertainty are often unavoidable for many practical dynamic systems. Therefore, improving the robustness of a system is a key issue in the fields of control and filtering, and has attracted great attention in the last decades.

Plenty of robust controllers and robust filters have been successfully applied to real-world applications such as, path following of unmanned vehicles, autonomous navigation and Global Positioning System. However, there are some limitations in the existing results. 1. In some practical systems, there may exist more than one type of model uncertainty. Therefore, to improve robustness, it is necessary to design a controller to stabilize systems with multiple kinds of uncertainties, such as H_∞-norm bounded and strictly negative imaginary uncertainties. 2. Lots of the existing robust filters are derived under the assumption of having additive unimodal noise only. How to design robust filters in the presence of multimodal additive noise and multiplicative noise is worth studying. 3. In many distributed filtering methods, the transmission channel is assumed to have Gaussian noise, and the statistical information of channel noise, such as the mean and covariance, is assumed to be known as a priori. However, It is more practical to consider the distributed filtering over non-Gaussian transmission channels where the statistical information of channel noise is unknown.

Therefore, it is necessary to design robust controllers and filters to overcome the above limitations. The main results of this thesis are summarized as follows:

1. For a class of continuous time linear systems, a static output feedback controller is designed to stabilize systems consisting of either strictly negative imaginary or H_∞-norm bounded uncertainty. Sufficient conditions are derived based on negative imaginary lemma and bounded real lemma. An iterative linear matrix inequality based algorithm is proposed to compute the desired controller. Furthermore, an initialization process is given to find an initial point for the above iterative algorithm. Finally, two numerical examples are presented to illustrate the correctness and efficiency of the proposed method.

2. The problem of robust negative imaginary H_∞ controller designing for a class of continuous time linear systems with optimal H₂ performance is studied. A static output feedback controller is designed such that the closed-loop system can stabilize either strictly negative imaginary or H_∞-norm bounded uncertainty, meanwhile its H₂-norm is minimized. By using the positive semidefinite-convex-concave decomposition technique, the problem of designing output feedback controller is equivalently turned to designing an output injection feedback controller. A linearization based algorithm is proposed, and a numerical example is presented to verify the proposed method.

3. For a class of discrete time linear systems with multimodal heavy tailed noises, the problem of robust state filtering is investigated. In the considered problem, the probability density function of the measurement noise is assumed to be multimodal and have a heavy tailed feature. Inspired by the application of the maximum correntropy criterion to robust regression tasks, a multi-kernel correntropy based filter is derived. A fixed-point iteration algorithm is proposed to compute the optimal state estimate. A sufficient condition is derived to guarantee the convergence of the iteration algorithm. Finally, a benchmark example is demonstrated to show the effectiveness of the proposed filter.

4. For a class of discrete time nonlinear systems, a filtering algorithm is proposed for such systems in presence of multiplicative and additive noises. In order to improve robustness with respect to outliers , the filter is derived under the assumption of heavy tailed additive noise. The unscented transform technique is used to compute the prior estimate, and variational Bayesian approach is used to compute the posterior estimate. In the proposed filtering algorithm, the mean and variance of multiplicative noise does not need to be known as a priori. Finally, two benchmark examples are given to show the effectiveness and desirable performance of the proposed robust filter.

5. The problem of robust channel estimation for the distributed filtering framework is studied. To deal with the outliers, packet dropout and unknown channel statistical information of transmission channels in the distributed filtering framework, a two-phased robust channel estimation method is proposed. In phase 1, the EM algorithm is utilized to estimate transmission data and channel statistical information. In phase 2, to reduce computational loading, a maximum correntropy based estimator is proposed to achieve robust channel estimation. A sufficient condition is derived to guarantee the convergence of the proposed algorithm. Finally, two numerical examples are presented to show the correctness of the proposed estimation method.

Date of Award	31 May 2022
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Junlin Xiong (External Supervisor) & Wing Cheong Daniel HO (Supervisor)