Mithun Chakraborty

Tuning PID and PI /λ D δ Controllers using the Integral Time Absolute Error Criterion

Particle swarm optimization (PSO) is extensively used for real parameter optimization in diverse fields of study. This paper describes an application of PSO to the problem of designing a fractional-order proportional-integral-derivative (PIlambdaDdelta) controller whose parameters comprise proportionality constant, integral constant, derivative constant, integral order (lambda) and derivative order (delta). The presence of five optimizable parameters makes the task of designing a PIiquestDiquest controller more challenging than conventional PID controller design. Our design method focuses on minimizing the integral time absolute error (ITAE) criterion. The digital realization of the deigned system utilizes the Tustin operator-based continued fraction expansion scheme. We carry out a simulation that illustrates the effectiveness of the proposed approach especially for realizing fractional-order plants. This paper also attempts to study the behavior of fractional PID controller vis-a-vis that of its integer-order counterpart and demonstrates the superiority of the former to the latter.

Implementation of Basic Arithmetic Operations Using Cellular Automaton

This paper presents hardware architecture to perform the basic arithmetic operation addition using cellular automata (CA). This age old problem of addition were previously solved by ripple circuit or carry look ahead circuit or by using a combination of them. Each of these circuits is purely combinational in nature and their complexity is centered on the number of logic gates and the associated gate delays. On the contrary, in our CA based design the complexity is mainly centered on the number of clock cycles required to finish the computation instead of the gate delays.

A bayesian market maker

Ensuring sufficient liquidity is one of the key challenges for designers of prediction markets. Variants of the logarithmic market scoring rule (LMSR) have emerged as the standard. LMSR market makers are loss-making in general and need to be subsidized. Proposed variants, including liquidity sensitive market makers, suffer from an inability to react rapidly to jumps in population beliefs. In this paper we propose a Bayesian Market Maker for binary outcome (or continuous 0-1) markets that learns from the informational content of trades. By sacrificing the guarantee of bounded loss, the Bayesian Market Maker can simultaneously offer: (1) significantly lower expected loss at the same level of liquidity, and, (2) rapid convergence when there is a jump in the underlying true value of the security. We present extensive evaluations of the algorithm in experiments with intelligent trading agents and in human subject experiments. Our investigation also elucidates some general properties of market makers in prediction markets. In particular, there is an inherent tradeoff between adaptability to market shocks and convergence during market equilibrium.

Investigation of the global dynamics of cellular automata using Boolean derivatives

Global dynamics of a non-linear Cellular Automaton (CA), is, in general irregular, asymmetric and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable. In this paper, efforts have been made to systematize non-linear CA evolutions in the light of Boolean derivatives and Jacobian matrices. A few new theorems on Hamming Distance between Boolean functions as well as on Jacobian matrices of cellular automata are proposed and proved. Moreover, a classification of Boolean functions based on the nature of deviation from linearity has been suggested with a view to grouping them together to classes/subclasses such that the members of a class/subclass satisfy certain similar properties. Next, an error vector, which cannot be captured by the Jacobian matrix, is identified and systematically classified. This leads us to the concept of modified Jacobian matrix whereby a quasi-affine representation of a non-linear cellular automaton is introduced.

Instructor rating markets

We describe the design of Instructor Rating Markets (IRMs) where human participants interact through intelligent automated market-makers in order to provide dynamic collective feedback to instructors on the progress of their classes. The markets are among the first to enable the empirical study of prediction markets where traders can affect the very outcomes they are trading on. More than 200 students across the Rensselaer campus participated in markets for ten classes in the Fall 2010 semester. In this paper, we describe how we designed these markets in order to elicit useful information, and analyze data from the deployment. We show that market prices convey useful information on future instructor ratings and contain significantly more information than do past ratings. The bulk of useful information contained in the price of a particular class is provided by students who are in that class, showing that the markets are serving to disseminate insider information. At the same time, we find little evidence of attempted manipulation by raters. The markets are also a laboratory for comparing different market designs and the resulting price dynamics, and we show how they can be used to compare market making algorithms.

Design of a fractional-order self-tuning regulator using optimization algorithms

The self-tuning regulators form an important sub-class of adaptive controllers. This paper introduces a novel scheme for designing a fractional order self-tuning regulator. Original designs for all the sub-modules of the self-tuning regulator are proposed. The particle swarm optimization algorithm is utilized for online identification of the parameters of the dynamic fractional order process while the subsequent tuning of the controller parameters is performed by differential evolution. Results show that the proposed self-tuning regulator is both precise and robust.

A Study of the Grunwald-Letnikov Definition for Minimizing the Effects of Random Noise on Fractional Order Differential Equations

Of the many definitions for fractional order differintegral, the Grunwald-Letnikov definition is arguably the most important one. The necessity of this definition for the description and analysis of fractional order systems cannot be overstated. Unfortunately, the Fractional Order Differential Equation (FODE) describing such a systems, in its original form, highly sensitive to the effects of random noise components inevitable in a natural environment. Thus direct application of the definition in a real-life problem can yield erroneous results. In this article, we perform an in-depth mathematical analysis the Grunwald-Letnikov definition in depth and, as far as we know, we are the first to do so. Based on our analysis, we present a transformation scheme which will allow us to accurately analyze generalized fractional order systems in presence of significant quantities of random errors. Finally, by a simple experiment, we demonstrate the high degree of robustness to noise offered by the said transformation and thus validate our scheme.

A novel approach for complete identification of dynamic fractional order systems using stochastic optimization algorithms and fractional calculus

This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as opposed to the ideal integral order models. A simple and elegant scheme of estimating the parameters for such a fractional order process is proposed. This method employs fractional calculus theory to find equations relating the parameters that are to be estimated, and then estimates the process parameters after solving the simultaneous equations. The said simultaneous equations are generated and updated using particle swarm optimization (PSO) technique, the fitness function being the sum of squared deviations from the actual set of observations. The data used for the calculations are intentionally corrupted to simulate real-life conditions. Results show that the proposed scheme offers a very high degree of accuracy even for erroneous data.

A particle swarm optimization-based approach towards the solution of the dynamic channel assignment problem in mobile cellular networks

The limited availability of channel resources offers a bottleneck on the allocation of channels to subscribers in wireless mobile communication systems. This paper provides a novel technique for dynamic channel assignment in mobile cellular networks by constructing a suitable objective function, the optimization of which yields a solution to the problem. The objective function has been optimized using particle swarm optimization (PSO) algorithm. The proposed channel allocation scheme has been studied with six typical benchmarks, available in the literature, and the results are promising. For instance, call rejection probability evaluated in the present context is as low as 20% even for the busiest network considered.

Coordinated Versus Decentralized Exploration In Multi-Agent Multi-Armed Bandits

In this paper, we introduce a multi-agent multiarmed bandit-based model for ad hoc teamwork with expensive communication. The goal of the team is to maximize the total reward gained from pulling arms of a bandit over a number of epochs. In each epoch, each agent decides whether to pull an arm, or to broadcast the reward it obtained in the previous epoch to the team and forgo pulling an arm. These decisions must be made only on the basis of the agent’s private information and the public information broadcast prior to that epoch. We first benchmark the achievable utility by analyzing an idealized version of this problem where a central authority has complete knowledge of rewards acquired from all arms in all epochs and uses a multiplicative weights update algorithm for allocating arms to agents. We then introduce an algorithm for the decentralized setting that uses a value-ofinformation based communication strategy and an exploration-exploitation strategy based on the centralized algorithm, and show experimentally that it converges rapidly to the performance of the centralized method.