I am working with Prof Demosthenis Teneketzis on sequential decentralized optimization problems that arise different application domains and analyze them using a common conceptual framework. This framework can be generalized to arbitrary sequential decentralized systems. I have worked on the following problems.

Real-Time Communication

In modern decentralized systems the design of a communication scheme is not a stand alone problem but an integrated component of a larger system; the objective is no longer just to communicate information but also to characterize how the flow of information affects the overall system performance. In such systems communication is delay sensitive, since the data is temporal in nature and loses its significance if not communicated and decoded in time. This motivates the need to study communication systems with a hard constraint on communication delay. Such communication systems are called real-time communication systems.

Real-time communication problems are drastically different from classical information theoretic formulations which does not model communication delay. The fundamental concepts of information theory such as source entropy, rate distortion, and channel capacity are asymptotic concepts and do not provide much insight for the real-time communication problem. So, we need a new mathematical formulation to analyze real-time communication. In my research, I formulate the real-time communication problem as a sequential decentralized optimization problem and develop a solution methodology to determine optimal communication schemes. I have considered two variations of the real-time communication for point-to-point communication system: (i) real-time communication with no feedback in [J3], [C2], and [C1], and (ii) real-time communication with noisy feedback in [J5] and [C4].

Control over limited noisy communication

In the classical formulation of the control system, it is assumed that the sensors and the controllers are co-located with the plant. Recently, there has been a lot of interest in network controlled systems (NCS) where the plant, sensor, and controller are spatially distributed and their operation is coordinated via a communication network. NCS are a good model for many distributed control applications such as sensor networks, micro-electromechanical systems, cellular telephony, and industrial control networks, where the communication channel between the components does not have a large bandwidth which makes it imperative to consider an integrated approach for the design of both control and communication components.

NCS bring out the fundamental conflicts between the design philosophies of control and communication theories. Communication theory is concerned with the reliable communication of information from one point to another, and does not care about the meaning or usefulness of the communicated information at the receiving node; control theory, on the other hand, is concerned with using the information at the controller to achieve some performance objective. Communication theory does not model the delay incurred during transmission of information while timeliness of information is of paramount importance in control theory. These conflicts pose fundamental questions for both fields which makes an integrated control and communication design a challenging problem. In my thesis, I provide partial answers to these questions. I have considered the problem of optimal design of communication and control strategies for a NCS with a noisy communication link between the sensor and the controller in [J2] and [C3].

Decentralized diagnosis with communication between diagnosers

Fault detection is an important task in the automated control of large scale systems. Large-scale systems have local diagnosers at various nodes of the system each having partial local information. It is usually technologically demanding and economically expensive to collect all this decentralized information at one single node. Yet it is often possible for the nodes to communicate limited information to one another. This has motivated the study of how to communicate information efficiently amongst nodes to ensure that faults are diagnosed, in particular how to minimize communication needed to detect faults. Such decentralized fault diagnosis problems arise in various application areas including document processing systems, heating, ventilation, and air-conditioning systems, intelligent transportation systems, chemical process control, and telecommunication networks. The design of such communication policies is intricate due to the complex interdependence between the communication and diagnosing policies of the diagnosers. In my thesis I have considered this problem using the discrete event system (DES) modelling formalism with the assumption of synchronous diagnosers. A paper documenting this work is currently in preparation.

Book Chapters

  1. Aditya Mahajan and Demosthenis Teneketzis Multi-Armed Bandits in Foundations and Applications of Sensor Management Springer-Verlag, 2007, pp. 121–151. (pdf)

Journal Publications

  1. Aditya Mahajan and Demosthenis Teneketzis On the Design of Globally Optimal communication strategies for Real-Time Noisy Communication with Noisy Feedback IEEE Journal on Selected Areas in Communication vol. 26, no. 4, pp. 580–595, May 2008. (abstract) (paper)
    A real-time communication system with noisy feedback is considered. The system consists of a Markov source, forward and backward discrete memoryless channels, and a receiver with limited memory. The receiver can send messages to the encoder over the backward noisy channel. The encoding at the encoder and the decoding, the feedback, and the memory update at the receiver must be done in real-time. A distortion metric that does not tolerate delays is given. The objective is to design an optimal real-time communication strategy, i.e., design optimal real-time encoding, decoding, feedback, and memory update strategies to minimize the total expected distortion over a finite horizon. This problem is formulated as a decentralized stochastic optimization problem and a methodology for its sequential decomposition is presented. This results in a set of nested optimality equations that can be used to sequentially determine optimal communication strategies. The methodology simplifies the search for determining an optimal real-time communication strategy.
  2. Aditya Mahajan and Demosthenis Teneketzis Globally Optimal Performance of Feedback Control Systems with Limited Communication over Noisy Channels SIAM Journal of Control and Optimization submitted for publication. (abstract) (paper)
    A discrete time stochastic feedback control system with a noisy communication channel between the sensor and the controller is considered. The sensor has limited memory and at each time, it transmits an encoded symbol over the channel and updates its memory. The controller receives a noise-corrupted copy of the transmitted symbol. It generates a control action based on all its past observations and all its past actions. This control action action is fed back into the system. At each time instant t, an instantaneous cost, which is a function of the state of the system at t and the control action at t, is incurred. The objective is to choose encoding, memory update and control strategies to minimize: an expected total cost over a finite horizon, or an expected discounted cost over an infinite horizon, or an average cost per unit time over an infinite horizon. For each case a sequential decomposition of the global optimization problem is obtained. The results are extended to the case when the sensor makes an imperfect observation of the state of the system.
  3. Aditya Mahajan and Demosthenis Teneketzis On Globally Optimal Encoding, Decoding and Memory Update for Noisy Real-Time Communication Systems IEEE Transactions on Information Theory submitted for publication (Revision May 9, 2008). ( abstract) (paper) (code) (pretty printed code)
    The design of optimal joint source-channel communication strategies for a real-time communication system, i.e., a sequential communication system in which information must be transmitted and decoded withing a fixed-finite delay, is considered. First, a system which runs for a finite horizon and consists of a first-order Markov source, a real-time encoder, a memoryless noisy channel, a real-time decoder with finite memory, and distortion metric that accepts zero delay, is considered. The design of optimal real-time communication strategies is formulated as a decentralized stochastic optimization problem. There is no existing solution methodology to solve general decentralized stochastic optimization problems over finite and infinite horizon. This paper develops a systematic methodology, based on the notions of information structure and information state, to sequentially obtain globally optimal real-time encoding, decoding, and memory update strategies. Such a sequential decomposition results in a set of nested optimality equations whose solution determines an optimal communication strategy. This methodology is extended to two classes of infinite-horizon systems, where optimal communication strategies are determined by the solution of an appropriate functional equation. The methodology is also extended to systems where distortion metric accepts a fixed-finite delay, to systems with higher-order Markov sources, and to systems with channels with memory. Thus, this paper develops a comprehensive method to study different variations of real-time communication.
  4. Aditya Mahajan, Manu Agarwal, and Ajit K. Chaturvedi A novel method for down-conversion of multiple bandpass signals IEEE Transactions on Wireless Communication vol. 5, no. 2, pp. 427–434, February 2006. ( abstract) (paper)
    Simultaneous down-conversion of multiple bandpass signals is desirable for a number of wireless applications. Bandpass sampling technique can be used for this purpose, but it is difficult to implement and has several drawbacks. In this paper we propose a novel front-end technique to directly down-convert multiple frequency division multiplexed (FDM) signals separated by certain minimum frequency. A special down-conversion function is derived to achieve simultaneous down-conversion of the received signals. The technique requires simpler bandpass filters and the ADC has a baseband input as compared to bandpass sampling, which imposes strict requirements on bandpass filters and requires an ADC which can handle RF inputs. The performance of the method has been evaluated by simulating a BPSK receiver employing this technique.
  5. Baquer Mazhari and Aditya Mahajan An improved interpretation of depletion approximation in p-n junctions IEEE Transactions on Education vol. 48, no. 1, pp. 60–62, February 2005. (abstract) (paper)
    The conventional treatment of depletion approximation in p-n-junctions often leaves a student with an erroneous impression that the approximation essentially involves complete neglect of the fraction of the space charge region (SCR) where charge density makes a transition to zero. This work describes a simple analytical model for clarifying the relationship of depletion approximation to the SCR.

Conference Publications

  1. Mahta Moghaddam, Dara Entekhabi, Leila Farhadi, Yuriy Goykhman, Mingyan Liu, Aditya Mahajan, Ashutosh Nayyar, David Shuman, and Demosthenis Teneketzis Initial Analyses and Demonstration of a Soil Moisture Smart Sensor Web Proceedings of the Earth Science Technology Conference (ESTC) East Adelphi, MD, June 24–26, 2008. (paper)
  2. Aditya Mahajan and Demosthenis Teneketzis On-time diagnosis in discrete event systems Proceedings of the 9th International Workshop on Discrete Event Systems (WODES) pp. 382–387, Gothenberg, Sweden, May 28–30, 2008. (paper) (examples) (code)
  3. Aditya Mahajan and Demosthenis Teneketzis Real-Time Communication Systems with Noisy Feedback IEEE Information Theory Workshop pp. 283–287, Lake Tahoe, CA, September 2–6, 2007. (paper)
  4. Aditya Mahajan and Demosthenis Teneketzis Optimal Performance of Feedback Control Systems with Limited Communication over Noisy Channels Proceedings of the 45th IEEE Conference on Decision and Control pp. 3228–3235, San Diego, CA, December 13–15, 2006. (paper)
  5. Aditya Mahajan and Demosthenis Teneketzis Fixed Delay Optimal Joint Source-Channel Coding for Finite-Memory Systems Proceedings of the International Symposium of Information Theory pp. 2319–2323, Seattle, WA, July 9–14, 2006. (paper)
  6. Aditya Mahajan and Demosthenis Teneketzis A decision theoretic approach to real-time communication Proceedings of the 43rd Annual Allerton Conference on Communication, Control and Computing September 2005. (paper).

Thesis

Talks and Presentations