Arunabha Bagchi

Parameter identification in infinite dimensional linear systems

Parameter identification is studied for infinite dimensional linear systems. An almost sure characterization of sample path-wise limit sets of maximum likelihood estimates is given.

Team decision theory for linear continuous-time systems

This paper develops a team decision theory for linear-quadratic (LQ) continuous-time systems. First, a counterpart of the well-known result of Radner on quadratic static teams is obtained for two-member continuous-time LQ static team problems when the statistics of the random variables involved are not necessarily Gaussian. An iterative convergent scheme is developed, which in the limit yields the optimal team strategies. For the special case of Gaussian distributions, the team-optimal solution is affine in the information available to each DM, and for the further special case when the team cost function does not penalize the intermediate values of state, the optimal strategies can be obtained by solving a Liapunov type time-invariant matrix equation. This static theory is then extended to LQG continuous-time dynamic teams with sampled observations under the one-step-delay observation sharing pattern. The unique solution is again affine in the information available to each DM, and further, it features a certainty-equivalence property.

Modeling and feedback control of a flexible arm of a robot for prescribed frequency-domain tolerances

In this article we solve the problem of achieving quantitative specifications for the tip of a rotating flexible beam with uncertainty in some of its physical and geometric parameters. The frequency-domain design method used here is also helpful in clarifying some limitations on the feedback loop capabilities due to the distributed nature of the problem. Finally, time domain simulations, while proving the validity of the design method suggested in this work, pointed to some interesting mathematical problems concerning the influence of some of the parameters on the plant dynamics with possible physical consequences on the design of flexible beams.

A martingale approach to state estimation in delay-differential systems

A rigorous derivation of filtering arid smoothing equations for linear stochastic systems with time delay is presented. The estimation equations are obtained in term of the innovation process of the problem under consideration. The method used is based on a representation theorem on Gaussian martingales.

Modeling Stochastic Hybrid Systems

Stochastic hybrid systems arise in numerous applications of systems with multiple models; e.g., air traffc management, flexible manufacturing systems, fault tolerant control systems etc. In a typical hybrid system, the state space is hybrid in the sense that some components take values in a Euclidean space, while some other components are discrete. In this paper we propose two stochastic hybrid models, both of which permit diffusion and hybrid jump. Such models are essential for studying air traffic management in a stochastic framework.

Stackelberg strategies in linear-quadratic stochastic differential games

This paper obtains the Stackelberg solution to a class of two-player stochastic differential games described by linear state dynamics and quadratic objective functionals. The information structure of the problem is such that the players make independent noisy measurements of the initial state and are permitted to utilize only this information in constructing their controls. Furthermore, by the very nature of the Stackelberg solution concept, one of the players is assumed to know, in advance, the strategy of the other player (the leader). For this class of problems, we first establish existence and uniqueness of the Stackelberg solution and then relate the derivation of the leaders Stackelberg solution to the optimal solution of a nonstandard stochastic control problem. This stochastic control problem is solved in a more general context, and its solution is utilized in constructing the Stackelberg strategy of the leader. For the special case Gaussian statistics, it is shown that this optimal strategy is affine in observation of the leader. The paper also discusses numerical aspects of the Stackelberg solution under general statistics and develops algorithms which converge to the unique Stackelberg solution.

Continuous time systems identification with unknown noise covariance

In identifying parameters of a continuous-time dynamical system, a difficulty arises when the observation noise covariance is unknown. The present paper solves this problem in the case of a linear time-invariant system with white noise affecting additively both the state and the observation. The problem is that the likelihood functional cannot be obtained when the observation noise covariance is unknown. A related procedure is suggested, however, and the estimates are obtained by finding roots of an appropriate functional. It is shown that the estimates obtained are consistent.In identifying parameters of a continuous-time dynamical system, a difficulty arises when the observation noise covariance is unknown. The present paper solves this problem in the case of a linear time-invariant system with white noise affecting additively both the state and the observation. The problem is that the likelihood functional cannot be obtained when the observation noise covariance is unknown. A related procedure is suggested, however, and the estimates are obtained by finding roots of an appropriate functional. It is shown that the estimates obtained are consistent.

Linear-quadratic stochastic pursuit-evasion games

A linear-quadratic differential game in which the system state is affected by disturbance and both players have access to different measurements is solved. The problem is first converted to an optimization problem in infinite-dimensional state space and then solved using standard techniques. For convenience, “L2-white noise” instead of “Wiener process” setup is used.

Parameter identification in infinte dimensional linear systems

Parameter identification is studied for infinite dimensional linear systems. An almost sure characterization of sample path-wise limit sets of maximum likelihood estimates is given.

Smoothing and likelihood ratio for Gaussian boundary value processes

A new derivation, which does not need the invertibility assumption of the covariance matrix of the boundary data, is given for the smoothing of Gaussian two-point boundary value processes (TPBVP). The likelihood ratio for TPBV processes is then derived in terms of the system parameters by using the Krein factorization. The likelihood ratio involves the smoother of the process. An alternate expression for the likelihood ratio based on the filtered estimate of the state is also given. >