New approaches to robust filtering design for uncertain dynamical systems with time delay

Abstract

State estimation of dynamical systems has long been an interesting problem in the control and signal processing fields. Among various filtering schemes, one landmark design approach is the celebrated Kalman filtering, which minimizes the variance of the estimation error under the assumptions that system dynamics under considera- tion is exactly known and the external disturbances are stationary Gaussian noises with known statistical properties. However, in many practical situations, a priori in- formation on external noises is not precisely known and/or an accurate system model is hard to obtain or the system may drift, all of which result in uncertainties. In such cases, various approaches have been developed to improve the robustness of the traditional Kalman filters and some alternatives, such as H1, generalized H2 and mixed H2=H1 filtering schemes were introduced and have received a lot of attention over the past few decades. On the other hand, in addition to system parametric uncertainties, it is well known that time-delays are frequently encountered in vari- ous practical control systems, such as manufacturing systems, power systems, and networked control systems. It has been well recognized that time-delay is an impor- tant source of instability and poor performance of a control system. Filtering design for dynamical systems with time-delays is a research subject of great practical and theoretical significance, which has received considerable attention in the past few years. In this thesis, some new approaches will be developed to solve the robust filtering design problems for several kinds of uncertain dynamical systems with time-delays, in- cluding the classical polytopic-type uncertain systems, nonlinear systems represented by T-S fuzzy models, and switched systems. The main attention will be focused on the case of time-varying delay with an interval-like type, which means that both the lower and upper bounds of the time-varying delay are available. It is noted that in modern engineering systems, the sensors, controllers, actuators and plants are usually connected via a common network medium which might include time-delays. It has also been pointed out that the systems over a network connection are essentially the systems with time-varying delays. The merit of the proposed approaches lies in their less design conservatism, which is realized by utilizing some more advanced techniques such as new delay-dependent criteria, more powerful relaxation techniques with dif- ferent filter structures and filtering schemes, and new matrix inequality linearization methods. Firstly, we revisit the problem of delay-dependent robust H1 filtering design for a class of polytopic-type uncertain linear systems with interval-like time-varying delay. Based on a new parameter-dependent Lyapunov-Krasovskii functional combined with Finsler's lemma and Projection lemma, some novel sufficient conditions for delay- dependent H1 performance analysis are derived. Moreover, under conditions whether the unknown parameters can be measured online or not, the parameter-dependent and parameter-independent filters are respectively developed which guarantee the asymptotic stability of the resulting filtering error systems with a prescribed robust H1 performance level. Secondly, attention goes to the filtering design for a class of nonlinear systems with time-varying state delay. Nonlinear filtering is of both theoretical and practical importance in signal processing community and has been receiving a lot of atten- tion. It is also noted that the well known Takagi-Sugeno (T-S) fuzzy model has been well recognized to be effective in approximating a complex nonlinear system. Con- sequently, it is of great significance to develop some new approaches for the filtering design of nonlinear systems with time-varying delay via a T-S fuzzy model approach. By using a novel fuzzy-basis-dependent Lyapunov-Krasovskii functional combined with Finsler's lemma, a new robust H1 performance analysis result is proposed and then the filter synthesis is developed by using a new and simple linearization tech- nique incorporating a bounding inequality. A unified framework is developed such that both the full-order and reduced-order filters can be obtained by solving a set of linear matrix inequalities. It is noted that under this new linearization technique, all the slack variables can be set to be fuzzy-basis-dependent and a non-PDC (parallel distributed compensation) type filter structure is utilized. This kind of filter struc- ture covers the traditional PDC type structure by choosing some slack variables to be common. Then, attention is focused on the filtering design for a class of switched systems, which are an important class of hybrid systems consisting of a family of subsys- tems and a rule orchestrating the switching among them. Specially, the mode and parameter-dependent robust mixed H2=H1 filtering design for a class of discrete-time switched polytopic linear systems is considered. The switching signal is assumed to be unknown a priori, but its instantaneous valuable is available in real-time imple- mentation. Based on a switched parameter-dependent Lyapunov function, some new conditions for robust H2 and H1 performance analysis are firstly proposed and in turn the filter synthesis is developed by using a new matrix inequality linearization approach and a bounding technique. Under this new linearization approach, no in- verses of the Lyapunov matrices are involved and all the slack variables are set to be switched. It is also noted that when applying the new linearization technique to the mixed H2=H1 filtering scheme, only the slack variable associated with the filter gain variables is set to be the same for two different performance channels. Finally, we extend the results given in the previous chapters to the switched poly- topic linear time-delay systems with average dwell-time switching scheme. The robust energy-to-peak filtering scheme is considered and an exponential stability condition is presented. It is shown that the filtering performance is dependent on the parameter ¹ for a given system decay rate. Specially, it is observed that the larger ¹ results in the better performance, which is at the expense of longer average dwell-time in the system.

Date of Award	15 Jul 2009
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Gang Gary FENG (Supervisor)