This paper is concerned with the problem of a Kalman filter design for uncertain discrete-time systems. The system under consideration is subjected to time-varying norm-bounded parameter uncertainty in both the state and output matrices. The problem addressed is the design of a linear filter such that the variance of the filtering error is guaranteed to be within a certain bound for all admissible uncertainties. Furthermore, the guaranteed cost can be optimized by appropriately searching a scaling design parameter.<>

Location-based services (LBS) have attracted a great deal of attention recently. Outdoor localization can be solved by the GPS technique, but how to accurately and efficiently localize pedestrians in indoor environments is still a challenging problem. Recent techniques based on WiFi or pedestrian dead reckoning (PDR) have several limiting problems, such as the variation of WiFi signals and the drift of PDR. An auxiliary tool for indoor localization is landmarks, which can be easily identified based on specific sensor patterns in the environment, and this will be exploited in our proposed approach. In this work, we propose a sensor fusion framework for combining WiFi, PDR and landmarks. Since the whole system is running on a smartphone, which is resource limited, we formulate the sensor fusion problem in a linear perspective, then a Kalman filter is applied instead of a particle filter, which is widely used in the literature. Furthermore, novel techniques to enhance the accuracy of individual approaches are adopted. In the experiments, an Android app is developed for real-time indoor localization and navigation. A comparison has been made between our proposed approach and individual approaches. The results show significant improvement using our proposed framework. Our proposed system can provide an average localization accuracy of 1 m.

We consider distributed optimization problems in which a number of agents are to seek the global optimum of a sum of cost functions through only local information sharing. In this paper, we are particularly interested in scenarios, where agents are operating asynchronously over stochastic networks subject to random failures. Most existing algorithms require coordinated and decaying stepsizes to ensure zero gap between the estimated value of each agent and the exact optimum, restricting it from asynchronous implementation and resulting in slower convergence results. To deal with this issue, we develop a new asynchronous distributed gradient method (AsynDGM) based on consensus theory. The proposed algorithm not only allows for asynchronous implementation in a completely distributed manner but also, most importantly, is able to seek the exact optimum even with constant stepsizes. We will show that the assumption of boundedness of gradients, which is widely used in the literature, can be dropped by instead imposing the standard Lipschitz continuity condition on gradients. Moreover, we derive an upper bound of stepsize within which the proposed AsynDGM can achieve a linear convergence rate for strongly convex functions with Lipschitz gradients. A canonical example of sensor fusion problems is provided to illustrate the effectiveness of the proposed algorithm.

Some sufficient conditions for asymptotic stability of impulsive control systems with impulses at fixed times have recently been presented. In this paper, we derive some less conservative conditions for asymptotic stability of such impulsive control systems and the results are used to design impulsive control for a class of nonlinear systems. The class of nonlinear systems considered is also extended.