The MCISCO research group deals with open problems in Mathematical Theory of Control

in a wide sense, including as well related problems of ‘diagnostics’ (detection and/or estimation of features of a complex system), with particular emphasis on Automatic Control and Automatic Decision problems.

The MCISCO group carries out researches in several fields of Mathematics, such as Differential Algebra and Geometry, Mathematical Analysis, Stochastic Processes and Probability Theory, insofar their application in Control is involved.

Besides this theoretical research activity, the group applies (at the computer-simulation level, up to the production of pseudo-codes) the algorithmic results of the research in order to solve real-world problems arising in many fields of application. These real-world problems are both classical problems taken from the literature, as well as commissioned by Industry, or whose solution is demanded by pro-administration and/or private sponsors through research-funds assignment.

The MCISCO group, carries out its activity autonomously, or in collaboration with other groups of IASI, or in collaboration with other international research institutions and Universities.

The activity is performed along three main research topics: Deterministic and stochastic dynamical systems and control theory, Systems identification and filtering, Signal and image processing, and Statistical parameter estimation.

Research topics

DETERMINISTIC AND STOCHASTIC DYNAMIC SYSTEMS AND CONTROL THEORY
The MCISCO group studies dynamical systems described by any mathematical structure, however, most of the research is focused on the more classic structures, such as ordinary differential equations, stochastic differential equations and discrete-time recursive equations (deterministic and stochastic).

Dynamical systems are studied as for their structural properties of controllability and stabilizability, and as for the design of controllers and observers. As far as the performance is concerned, optimality criterion are used (Optimal control), as well as stabilization methods based on achieving a tunable, and exponential, convergence rate to zero of the error.

SYSTEMS IDENTIFICATION AND FILTERING
The MCISCO group studies the state and parameter estimation problem for stochastic systems (filtering, smoothing, identification). Most of the research is devoted to nonlinear stochastic systems. Similarly to control systems the performance criterion is often stated as an optimal one, with respect to various error measures. The latter can be a mean-square (MS), or minimum variance, error measure, as well as a maximum a posteriori (MAP), or a maximum likelihood (ML) one.

SIGNAL, SPEECH AND IMAGE PROCESSING
The MCISCO group studies as well the estimation problem for systems which have not a state-space description, and/or are not dynamic (i.e. evolving in time). For these systems only a probabilistic description is given (typically the a-priori signal distribution). For this class of systems the research goal is finding out computationally efficient estimation algorithms (filters and smoothers). The methods used are indirect, based on the realization of the signal (i.e. finding a state-space description of it) as well as direct, i.e. derived directly from the given a-priori distribution (Bayesian methods). Signals indexed by one parameter are considered, as well as indexed by a graph, and in the latter case methods from Random Field Theory and Machine Learning are extensively used. The application includes target tracking problems, as well as speech and image processing.

STATISTICAL PARAMETER ESTIMATION