H ∞ Filtering for Networked Controlled Systems S. Ahmed Electrical Engineering Bahria University Islamabad Campus. Email: sahmed@bui.edu.pk M. Hasan Electrical Engineering Bahria University Islamabad Campus. Email: meraj.hasan@bui.edu.pk F. Subhan Faculty of Engg. and IT NUML, Islamabad Campus. Email: fsubhan@numl.edu.pk Abstract—Networked controlled systems comprise a team of dynamic systems which are linked together through a shared networked. From control systems perspective, the introduction of a shared networked brings its own challenges such as packet dropouts, time delays and clock synchronization. A popular application of networked controlled systems is to consider a team of collaborative mobile robots. Networked controlled robots involve a team of mobile robots working together with each other to accomplish a specific task. Each individual mobile robot has finite battery sources, which must be efficiently utilized. The efficient utilization of battery sources limits the communication capabilities of the robots. Furthermore, a shared network among the networked robots introduces time delays in the data received. This paper presents the design of an optimal H∞ filter to minimize the effects of time delays in the received data. A numerical example is presented to demonstrate the effectiveness of the proposed approach. I. I NTRODUCTION Networked controlled systems (NCSs) involve a group of dynamic systems. Each system shares information with another system using a shared networked. The introduction of a shared networked, for information exchange among systems, brings its own challenges such as packet dropouts (loss of received data), time delays in data received and lack of time synchronization among the networked systems. NCSs are widely used in chemical process plants, oil and gas industries and air traffic control systems. A popular application to study NCSs is to consider a team of networked controlled mobile robots. Networked controlled robots involve a team of robotic sys- tems working together to accomplish some task. The success of task completion depends on the capabilities of each individual robot, the team formation and the control strategies. There have been various approaches to maintain a team formation among the networked controlled robots. One of the popular team formation strategies is the leader-follower formation, which has got various applications in wheeled mobile robots, flying robots and aircrafts ([1], [2], [3]). The leader-follower formation consists of a leader and several follower robotic control systems. The goal of the leader robot is to track a reference trajectory while each follower robot needs to maintain a certain distance and angle relative to the leader robot as well as other follower robots. There have been various distributed control design tech- niques available in the literature to ensure the leader-follower formation among networked controlled robots (see e.g. [2], [3], [4], [5]). In this paper, it is assumed that the networked robots have only communication capabilities for exchanging informa- tion. If communication is the only information exchange chan- nel, then almost all of the available control design techniques require the desired reference trajectory and the actual position of the leader robot to be communicated to the follower robots. In actual implementation, each mobile robot has a finite source of battery and energy. Hence, the energy sources must be efficiently utilized. The efficient utilization of battery sources introduce constraints on the communication capabilities of the robots. Communication among robots consume about 80% of the battery sources. To conserve energy, the actual output of the leader robot is only communicated to the follower robots. The reference trajectory is only available to the leader robot and not to the follower robots. Hence, it is necessary for the follower robots to reconstruct the reference input/trajectory from the measurements received. The reconstruction of reference input from output signal can be treated as an observer design problem. However, the problem becomes complex when the system is hybrid where the reference input is in continuous- time and the measured output is in discrete-time. There exists no state-space or transfer matrix representation for a hybrid system. In this paper, a filter design technique for hybrid system is presented. The conservation of battery sources also restricts the syn- chronization capabilities of the robots. It is assumed that to efficiently utilize the battery sources, the synchronization among the robots takes places after a long time. Hence, the clocks of the networked controlled robots are not synchronized at regular intervals. The non-synchronization of clocks leads to sampling jitters which is the deviation of the clock to sample a signal. A signal which is sampled by a sampler having sampling jitters is equivalent to sampling a delayed or advanced version of the same signal by a sampler without sampling jitter. Moreover, the network medium between the networked controlled systems is shared which introduces some delays in the communication channels. Hence, sampling jitter and network delay for a specific channel can be added to obtain a lumped delay for that channel. There have been various approaches in the literature to design a stabilizing and optimum controller in the presence of delays. However, to the best knowledge of the authors, the optimum filter design problem to minimize the effects of delays has not been considered in networked control systems. The main contribution of this paper is to propose a design technique for optimal H ∞ filter, which minimizes the effects of delays and reconstruct the reference input. The remainder of this paper is organized as follows: Section 2 presents a method of discretization for hybrid systems. The problem formulation and the networked robot system model are discussed in section 3. The design procedure for obtaining an optimal filter is presented in section 4. Numerical examples to demonstrate the effectiveness of the proposed technique are 2014 IEEE 2014 International Conference on Computer, Communication, and Control Technology (I4CT 2014), September 2 - 4, 2014 - Langkawi, Kedah, Malaysia 978-1-4799-4555-9/14/$31.00 ©2014 IEEE 101