:: POLYTECHNIC UNIVERSITY :: Department of Electrical and Computer Engineering

RESEARCH PROJECTS

Fields and Waves

Signals, Control and Signal Processing

Telecommunications and Wireless

VLSI, Electronics and Power

· Analysis and Control of Communication Networks

· Stability of Nonlinear Dynamical Systems

· Applied Nonlinear Control

· Robust Adaptive Nonlinear Control System Designs

· Development of Hardware/Software Architecture for Autonomous Unmanned Vehicles

· Nonlinear Control for Electric Motors

· Development of an Ultra-Accurate High-Speed Six DOF Manipulator and Other Robotic Systems

· Decentralized Control of Nonlinear Large-Scale Interconnected Systems

· Joint Transmitter-Receiver Design for Interference and Noise Suppression

· Video Coding using a 3-D Motion-Selective Wavelet Transform

· The Design of Specialized Wavelet Transforms

· Non-Gaussian Probability Models for Wavelet-Based Denoising

· A Motion-Selective 3-D Wavelet Transform for Enhancement of Imagery in Video Data

· Wavelet Processing for Positron Emission Tomography

· On-Demand P2P Video Streaming System

· Video Transport over Wireless Ad Hoc Networks

Analysis and Control of Communication Networks

In the past decade, the analysis and control of communication networks attracts great research interests. As an example, optimization tools have been successfully applied to flow control problems in Internet. The design objective of optimization-based flow control is to maximize the overall network utility function, subject to the constraints of link capacities. In [5], we solve this problem using a modified Aitken Extrapolation algorithm. Furthermore, we perform convergence speed analysis for optimization-based flow control algorithms.

Except for the utility and cost optimization problem, recently, great attention is paid to Internet congestion control since congestion causes packet loss and results in network under-utilization (Figure 1). We notice that, compared with the large body of work on stability analysis for existing congestion control schemes, the synthesis of nonlinear controllers with improved performance has not received enough attention. We focus on designing new AQM schemes to stabilize the nonlinear network model, with particular interest in output feedback design, owing to the advantage of only measuring limited output information--buffer queue length. Previously, the output feedback design for AQM schemes is based on linearized model with known network parameters. With the help of Lyapunov design technique, adaptive feedback linearization and filtering techniques, we design a new, nonlinear controller to achieve both asymptotic stabilization and adaptation to unknown parameters [2]. The output feedback solution represents a nontrivial application of modern nonlinear control theory. We also believe that the design in [2] should provide benefits to future networking technical developments and serve as guidance for distributed protocol designs.

There have been continued interests in applying modern control theory to systematically address new challenges in large-scale networks. Currently, many existing work on controlling communication networks are based upon linear control techniques. Hard nonlinearities, such as saturation caused by capacity constraints, have not been thoroughly addressed, especially when designing control schemes for large-scale networks. In this project, we apply nonlinear control theory to cope with saturation constraints and nonlinear disturbances. In [1], [3] and [4], the constrained regulation of a class of network systems is studied. Explicit conditions are identified under which the problem of asymptotic regulation against unknown traffic interferences is solvable, with control and state saturations. We achieve either asymptotic or practical regulation for a single-node system in [1]. We also propose decentralized, discontinuous control laws to achieve asymptotic regulation of cascaded nodes and large-scale networks in [3], [4]. Our research demonstrates that tools from nonlinear system theory can play an important role in tackling “hard nonlinearities” and “unknown disturbances” for controlling communication networks. The control architecture for a single-node system is shown in Figure 2.

Another line of our research is the analysis and design of wireless ad hoc broadcasting protocols. Ad hoc network is composed of a set of self-organized users that agree to relay packets for each other. Different from conventional cellular wireless systems, ad hoc networks have no fixed infrastructure and central administration. Furthermore, each user can move randomly and the topology changes occur frequently. In such distributed and dynamic networks, broadcasting is widely used to distribute small control packets such as route request packets and warning packets. Numerous broadcasting protocols are proposed in literature to minimize overhead and maximize reception ratio. Different from conventional simulation based analysis methods, we theoretically analyze these protocols. Our results in [6], [7], [9] reveal the relation between broadcasting efficiency and network parameters. Furthermore, we have proposed a mobility sensitive mechanism to improve protocol performance in highly-mobile environment [8]. Broadcasting protocols based on the proposed mechanism are adaptive to nodal movement and hence reduce packet loss rate due to mobility.

Key-words: Congestion control, TCP/IP, Broadcasting, Large-scale systems.

Participating Faculty: Z. P. Jiang (zjiang@control.poly.edu) and S. Panwar (panwar@catt.poly.edu)

Websites: http://ctrl.poly.edu/, http://catt.poly.edu/CATT/

Research supported in part by the CATT and NSF.

[1] Y. Fan, Z.P.Jiang and H. Zhang, Network flow control under capacity constraints: a case study, Systems & Control Letters, Vol. 55, No. 8, pp. 681-688, 2006.

[2] Y. Fan and Z. P. Jiang and S. Panwar, An adaptive control scheme for stabilizing TCP, Proc. 5th World Congress on Intelligent Control and Automation, Hangzhou, China, 2004.

[3] Y. Fan and Z.P.Jiang, A nonlinear flow control scheme under capacity constraints, Acta Automatica Sinica, vol. 31, no. 1, pp. 64-74, Jan. 2005.

[4] Y. Fan, Z.P. Jiang and X. Wu, A control-theoretic approach to stabilizing queues in large-scale networks, IEEE Communications Letters, Vol. 9, No. 10, pp. 951-953, 2005.

[5] H. Zhang, Z.P. Jiang, Y. Fan and S. Panwar, Optimization-based flow control with improved performance, Communications in Information and Systems, vol. 4, No. 3, pp. 235-252, 2004.

[6] H. Zhang and Z.P.Jiang, Analysis of two ad hoc broadcasting protocols, IEEE wireless Communications and Networking Conference (WCNC), Atlanta, GA, March, 2004.

[7] H. Zhang and Z.P. Jiang, Performance analysis of broadcasting schemes in mobile ad hoc networks, IEEE Communications Letters, vol. 8, no. 12, pp. 718-720, Dec. 2004.

[8] H. Zhang and Z.P.Jiang, Mobility sensitive broadcast algorithms in highly mobile ad hoc networks, to appear in Ad Hoc & Sensor Wireless Networks.

[9] H. Zhang and Z.P. Jiang, Modeling and performance analysis of ad hoc broadcasting schemes, Performance Evaluation, Vol. 63, pp. 1196—1215, 2006.

Stability of Nonlinear Dynamical Systems

Stability theory has played an important role in many scientific and engineering disciplines. In the domain of automatic control, advances in modern control system design are closely tied to Lyapunov theory. According to Lyapunov theory [1], the stability of a general dynamical system can be tested based upon existence of an appropriate function, widely known as Lyapunov function. Recently, Sontag has generalized Lyapunov theory to continuous-time dynamical systems with disturbance inputs, and coined this under the name of input-to-state stability (ISS) theory. Basically, ISS captures both internal (transient performance) and external (bounded-input bounded-state) stability properties. ISS theory has gained wide popularity and has been applied to numerous control issues of fundamental importance such as observer design, robust control, adaptive tracking, nonlinear feedback stabilization and decentralized nonlinear control. Because of the discrete nature of computer-aided control system design, we have extended ISS theory to discrete-time dynamical systems with disturbance inputs. A converse Lyapunov theorem for robust discrete-time stability and small-gain theorems for nonlinear and interconnected discrete-time systems have been proposed. Sufficient and necessary conditions for input-to-state stabilization of discrete-time control systems are obtained, along with several equivalent characterizations of discrete input-to-state stability. Some applications to nonlinear discrete control have also been discussed. Another line of our recent research on stability theory is the extension of the celebrated LaSalle’s Invariance Principle for complex dynamical systems; see [5] for such an extension to general nonlinear and time-varying systems. Further control applications of these novel stability criteria are ongoing research topics.

Key-words: nonlinear systems, input-to-state stability, discrete-time.

Participating Faculty: Z. P. Jiang (e-mail: zjiang@control.poly.edu, Web: http://ctrl.poly.edu)