In this technical note, a recursive set-membership filtering algorithm for discrete-time nonlinear dynamical systems subject to unknown but bounded process and measurement noises is proposed. The nonlinear dynamics is represented in a pseudo-linear form using the state dependent coefficient (SDC) parameterization. Matrix Taylor expansions are utilized to expand the state dependent matrices about the state estimates. Upper bounds on the norms of remainders in the matrix Taylor expansions are calculated on-line using a non-adaptive random search algorithm at each time step. Utilizing these upper bounds and the ellipsoidal set description of the uncertainties, a two-step filter is derived that utilizes the `correction-prediction' structure of the standard Kalman Filter variants. At each time step, correction and prediction ellipsoids are constructed that contain the true state of the system by solving the corresponding semi-definite programs (SDPs). Finally, a simulation example is included to illustrate the effectiveness of the proposed approach.
Adaptive model predictive control (MPC) methods using set-membership identification to reduce parameter uncertainty are considered in this work. Strong duality is used to reformulate the set-membership equations exactly within the MPC optimization. A predicted worst-case cost is then used to enable performance-oriented exploration. The proposed approach guarantees robust constraint satisfaction and recursive feasibility. It is shown that method can be implemented using homothetic tube and flexible tube parameterizations of state tubes, and a simulation study demonstrates performance improvemen…
This paper is concerned with the fuzzy $H_{\infty}$ filter design issue for nonlinear systems with time-varying delay. To overcome the shortcomings of the conventional methods with matched preconditions, the fuzzy $H_{\infty}$ filter to be designed and the T-S fuzzy model are assumed to have different premise membership functions and number of rules, thus, greater design flexibility and robustness to uncertainty can be achieved. However, such design will also make the derived results conservative, to relax the result, a novel integral inequality which is tighter than the traditional inequaliti…
School of Electrical Engineering at Southwest Jiaotong University（西南交通大学电气工程学院）；School of Electronic and Information Engineering, Xi’an Jiaotong University（西安交通大学电子与信息工程学院）
In this paper, a set-membership filtering-based leader-follower synchronization protocol for discrete-time linear multi-agent systems is proposed wherein the aim is to make the agents synchronize with a leader. The agents, governed by identical high-order discrete-time linear dynamics, are subject to unknown-but-bounded input disturbances. In terms of its own state information, each agent only has access to measured outputs that are corrupted with unknown-but-bounded output disturbances. Also, the initial states of the agents are unknown. To deal with all these unknowns (or uncertainties), a s…
Set-Membership Filter (SMF) has been extensively studied for state estimation in the presence of bounded noises with unknown statistics. Since it was first introduced in the 1960s, the studies on SMF have used the set-based description as its mathematical framework. One important issue that has been overlooked is the optimality of SMF. In this work, we put forward a new mathematical framework for SMF using concepts of uncertain variables. We first establish two basic properties of uncertain variables, namely, the law of total range (a non-stochastic version of the law of total probability) and…
This paper is concerned with cyberattack detection in discrete-time, leader-following, nonlinear, multi-agent systems subject to unknown but bounded (UBB) system noises. The Takagi-Sugeno (T-S) fuzzy model is employed to approximate the nonlinear systems over the true value of the state. A distributed cyberattack detection method, based on a new fuzzy set-membership filtering method, which consists of two steps, namely a prediction step and a measurement update step, is developed for each agent to identify two types of cyberattacks at the time of their occurrence. The attacks are replay attack…
This paper studies the immersion and invariance (I&I) adaptive tracking problem for a class of nonlinear systems with nonlinear parameterization in the ISS framework. Under some mild assumptions, a novel I&I adaptive control algorithm is proposed,leading to an interconnection of an ISS estimation error subsystem and an ISS tracking error subsystem. Using an ISS small-gain condition, the desired uniform global asymptotic stability of the resulting interconnected "error" system can be achieved and a sum-type strict Lyapunov function can be explicitly constructed. Taking advantage of this ISS-bas…
This paper investigates the fuzzy $H_{\infty}$ filter design issue for nonlinear systems with time-varying delay. In order to obtain less conservative fuzzy $H_{\infty}$ filter design method, a novel integral inequality is employed to replace the conventional Lebniz-Newton formula to analyze the stability conditions of the filtering error system. Besides, the information of the membership functions is introduced in the criterion to further relax the derived results. The proposed delay dependent filter design method is presented as LMI-based conditions, and corresponding definite expressions of…
Nonlinear pose (\textit{i.e,} attitude and position) filters are characterized with simpler structure and better tracking performance in comparison with other methods of pose estimation. A critical factor when designing a nonlinear pose filter is the selection of the error function. Conventional design of nonlinear pose filter design trade-off between fast adaptation and robustness. This paper introduces a new practical approach based on fuzzy rules for on-line continuous tuning of the nonlinear pose filter. Each of input and output membership functions are optimally tuned using graphical sear…
Nonlinear attitude filters have been recognized to have simpler structure and better tracking performance when compared with Gaussian attitude filters and other methods of attitude determination. A key element of nonlinear attitude filter design is the selection of error criteria. The conventional design of nonlinear attitude filters has a trade-off between fast adaptation and robustness. In this work, a new functional approach based on fuzzy rules for on-line continuous tuning of the nonlinear attitude filter adaptation gain is proposed. The input and output membership functions are optimally…
This paper conveys attitude and rate estimation without rate sensors by performing a critical comparison, validated by extensive simulations. The two dominant approaches to facilitate attitude estimation are based on stochastic and set-membership reasoning. The first one mostly utilizes the commonly known Gaussian-approximate filters, namely the EKF and UKF. Although more conservative, the latter seems to be more promising as it considers the inherent geometric characteristics of the underline compact state space and accounts -- from first principles -- for large model errors. We address the s…
This paper focuses on discrete-time wireless sensor networks with privacy-preservation. In practical applications, information exchange between sensors is subject to attacks. For the information leakage caused by the attack during the information transmission process, privacy-preservation is introduced for system states. To make communication resources more effectively utilized, a dynamic event-triggered set-membership estimator is designed. Moreover, the privacy of the system is analyzed to ensure the security of the real data. As a result, the set-membership estimator with differential priva…
