Practical stability of approximating discrete-time filters with respect to model mismatch

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Practical stability is established in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

An efficient online secondary path estimation for feedback active noise control systems

In practical cases for active noise control (ANC), the secondary path has usually a time varying behavior. For these cases, an online secondary path modeling method that uses a white noise as a training signal is required to ensure convergence of the system. The modeling accuracy and the convergence rate are increased when a white noise with a larger variance is used. However, the larger variance increases the residual noise, which decreases performance of the system and additionally causes instability problem to feedback structures. A sudden change in the secondary path leads to divergence of the online secondary path modeling filter. To overcome these problems, this paper proposes a new approach for online secondary path modeling in feedback ANC systems. The proposed algorithm uses the advantages of white noise with larger variance to model the secondary path, but the injection is stopped at the optimum point to increase performance of the algorithm and to prevent the instability effect of the white noise. In this approach, instead of continuous injection of the white noise, a sudden change in secondary path during the operation makes the algorithm to reactivate injection of the white noise to correct the secondary path estimation. In addition, the proposed method models the secondary path without the need of using off-line estimation of the secondary path. Considering the above features increases the convergence rate and modeling accuracy, which results in a high system performance. Computer simulation results shown in this paper indicate effectiveness of the proposed method.

Cross-layer design and optimization for wireless networked control systems

Wireless networked control systems (WNCSs) have been widely used in the areas of manufacturing and industrial processing over the last few years. They provide real-time control with a unique characteristic: periodic traffic. These systems have a time-critical requirement. Due to current wireless mechanisms, the WNCS performance suffers from long time-varying delays, packet dropout, and inefficient channel utilization. Current wirelessly networked applications like WNCSs are designed upon the layered architecture basis. The features of this layered architecture constrain the performance of these demanding applications. Numerous efforts have attempted to use cross-layer design (CLD) approaches to improve the performance of various networked applications. However, the existing research rarely considers large-scale networks and congestion network conditions in WNCSs. In addition, there is a lack of discussions on how to apply CLD approaches in WNCSs. This thesis proposes a cross-layer design methodology to address the issues of periodic traffic timeliness, as well as to promote the efficiency of channel utilization in WNCSs. The design of the proposed CLD is highlighted by the measurement of the underlying network condition, the classification of the network state, and the adjustment of sampling period between sensors and controllers. This period adjustment is able to maintain the minimally allowable sampling period, and also maximize the control performance. Extensive simulations are conducted using the network simulator NS-2 to evaluate the performance of the proposed CLD. The comparative studies involve two aspects of communications, with and without using the proposed CLD, respectively. The results show that the proposed CLD is capable of fulfilling the timeliness requirement under congested network conditions, and is also able to improve the channel utilization efficiency and the proportion of effective data in WNCSs.

Cross-layer design for traffic management in wireless networked control systems

Wireless networked control systems (WNCSs) have been increasingly deployed in industrial applications. As they require timely data packet transmissions, it is difficult to make efficient use of the limited channel resources, particularly in contention based wireless networks in the layered network architecture. Aiming to maintain the WNCSs under critical real-time traffic condition at which the WNCSs marginally meet the real-time requirements, a cross-layer design (CLD) approach is presented in this paper to adaptively adjust the control period to achieve improved channel utilization while still maintaining effective and timely packet transmissions. The effectiveness of the proposed approach is demonstrated through simulation studies.

A deadline-constrained 802.11 MAC Protocol with QoS differentiation for soft real-time control

As one of the most widely used wireless network technologies, IEEE 802.11 wireless local area networks (WLANs) have found a dramatically increasing number of applications in soft real-time networked control systems (NCSs). To fulfill the real-time requirements in such NCSs, most of the bandwidth of the wireless networks need to be allocated to high-priority data for periodic measurements and control with deadline requirements. However, existing QoS-enabled 802.11 medium access control (MAC) protocols do not consider the deadline requirements explicitly, leading to unpredictable deadline performance of NCS networks. Consequentially, the soft real-time requirements of the periodic traffic may not be satisfied, particularly under congested network conditions. This paper makes two main contributions to address this problem in wireless NCSs. Firstly, a deadline-constrained MAC protocol with QoS differentiation is presented for IEEE 802.11 soft real-time NCSs. It handles periodic traffic by developing two specific mechanisms: a contention-sensitive backoff mechanism, and an intra-traffic-class QoS differentiation mechanism. Secondly, a theoretical model is established to describe the deadline-constrained MAC protocol and evaluate its performance of throughput, delay and packet-loss ratio in wireless NCSs. Numerical studies are conducted to validate the accuracy of the theoretical model and to demonstrate the effectiveness of the new MAC protocol.

Rendering stiffer walls: a hybrid haptic system using continuous and discrete time feedback

Instability in conventional haptic rendering destroys the perception of rigid objects in virtual environments. Inherent limitations in the conventional haptic loop restrict the maximum stiffness that can be rendered. In this paper we present a method to render virtual walls that are much stiffer than those achieved by conventional techniques. By removing the conventional digital haptic loop and replacing it with a part-continuous and part-discrete time hybrid haptic loop, we were able to render stiffer walls. The control loop is implemented as a combinational logic circuit on an field-programmable gate array. We compared the performance of the conventional haptic loop and our hybrid haptic loop on the same haptic device, and present mathematical analysis to show the limit of stability of our device. Our hybrid method removes the computer-intensive haptic loop from the CPU-this can free a significant amount of resources that can be used for other purposes such as graphical rendering and physics modeling. It is our hope that, in the future, similar designs will lead to a haptics processing unit (HPU).

Bounded-input/bounded-output stability of linear multidimensional time- varying systems

The present study of the stability of systems governed by a linear multidimensional time-varying equation, which are encountered in spacecraft dynamics, economics, demographics, and biological systems, gives attention the lemma dealing with L(inf) stability of an integral equation that results from the differential equation of the system under consideration. Using the proof of this lemma, the main result on L(inf) stability is derived according; a corollary of the theorem deals with constant coefficient systems perturbed by small periodic terms. (O.C.)

Sequential design of decentralized control systems

Our main result is a new sequential method for the design of decentralized control systems. Controller synthesis is conducted on a loop-by-loop basis, and at each step the designer obtains an explicit characterization of the class C of all compensators for the loop being closed that results in closed-loop system poles being in a specified closed region D of the s-plane, instead of merely stabilizing the closed-loop system. Since one of the primary goals of control system design is to satisfy basic performance requirements that are often directly related to closed-loop pole location (bandwidth, percentage overshoot, rise time, settling time), this approach immediately allows the designer to focus on other concerns such as robustness and sensitivity. By considering only compensators from class C and seeking the optimum member of that set with respect to sensitivity or robustness, the designer has a clearly-defined limited optimization problem to solve without concern for loss of performance. A solution to the decentralized tracking problem is also provided. This design approach has the attractive features of expandability, the use of only 'local models' for controller synthesis, and fault tolerance with respect to certain types of failure.

Compensator for constant relative stability in process control systems

Process control systems are designed for a closed-loop peak magnitude of 2dB, which corresponds to a damping coefficient () of 0.5 approximately. With this specified constraint, the designer should choose and/or design the loop components to maintain a constant relative stability. However, the manipulative variable in almost all chemical processes will be the flow rate of a process stream. Since the gains and the time constants of the process will be functions of the manipulative variable, a constant relative stability cannot be maintained. Up to now, this problem has been overcome either by selecting proper control valve flow characteristics or by gain scheduling of controller parameters. Nevertheless, if a wrong control valve selection is made then one has to account for huge loss in controllability or eventually it may lead to an unstable control system. To overcome these problems, a compensator device that can bring back the relative stability of the control system was proposed. This compensator is similar to a dynamic nonlinear controller that has both online and offline information on several factors related to the control system. The design and analysis of the proposed compensator is discussed in this article. Finally, the performance of the compensator is validated by applying it to a two-tank blending process. It has been observed that by using a compensator in the process control system, the relative stability could be brought back to a great extent despite the effects of changes in manipulative flow rate.

Discrete-Time Controlled Markov Processes with Average Cost Criterion: A Survey

This work is a survey of the average cost control problem for discrete-time Markov processes. The authors have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades. The exposition ranges from finite to Borel state and action spaces and includes a variety of methodologies to find and characterize optimal policies. The authors have included a brief historical perspective of the research efforts in this area and have compiled a substantial yet not exhaustive bibliography. The authors have also identified several important questions that are still open to investigation.

Some algorithms for discrete time queues with finite capacity

We consider a discrete time queue with finite capacity and i.i.d. and Markov modulated arrivals, Efficient algorithms are developed to calculate the moments and the distributions of the first time to overflow and the regeneration length, Results are extended to the multiserver queue. Some illustrative numerical examples are provided.

Nonlinear oscillations in discrete and continuous systems

The first thesis topic is a perturbation method for resonantly coupled nonlinear oscillators. By successive near-identity transformations of the original equations, one obtains new equations with simple structure that describe the long time evolution of the motion. This technique is related to two-timing in that secular terms are suppressed in the transformation equations. The method has some important advantages. Appropriate time scalings are generated naturally by the method, and don't need to be guessed as in two-timing. Furthermore, by continuing the procedure to higher order, one extends (formally) the time scale of valid approximation. Examples illustrate these claims. Using this method, we investigate resonance in conservative, non-conservative and time dependent problems. Each example is chosen to highlight a certain aspect of the method.

The second thesis topic concerns the coupling of nonlinear chemical oscillators. The first problem is the propagation of chemical waves of an oscillating reaction in a diffusive medium. Using two-timing, we derive a nonlinear equation that determines how spatial variations in the phase of the oscillations evolves in time. This result is the key to understanding the propagation of chemical waves. In particular, we use it to account for certain experimental observations on the Belusov-Zhabotinskii reaction.

Next, we analyse the interaction between a pair of coupled chemical oscillators. This time, we derive an equation for the phase shift, which measures how much the oscillators are out of phase. This result is the key to understanding M. Marek's and I. Stuchl's results on coupled reactor systems. In particular, our model accounts for synchronization and its bifurcation into rhythm splitting.

Finally, we analyse large systems of coupled chemical oscillators. Using a continuum approximation, we demonstrate mechanisms that cause auto-synchronization in such systems.