Behavioral Control in the Presence of Disturbances

This paper deals with the issue of control with a constraint that in the controlled system certain variables remain free. By free, we mean that the variables are allowed to assume any trajectory. These variables can be interpreted as disturbances. The question of which controlled behaviors are a priori possible such that the controlled behaviors do not impose any constraints on the disturbance variables is addressed and solved. Certain generalities are imposed on the problem in the sense that a controller can act on only certain variables called control variables, while the performance specification is in terms of a different variable called the tobe- controlled variable. Another issue that we deal with is the notion of compatibility of such controllers. Further, the issue of controllability of the controller itself is dealt with, for the specific control problems of pole placement and stabilization. We use the behavioral approach to address these issues. In this setup control is considered as interconnection of two systems without distinguishing the variables of each system into inputs and outputs

The canonical controller and its regularity

This paper deals with properties of canonical controllers. We first specify the behavior that they implement. It follows that a canonical controller implements the desired controlled behavior if and only if the desired behavior is implementable. We subsequently investigate the regularity of the controlled behavior. We prove that a canonical controller is regular if and only if every controller is regular. In other words, canonical controllers are maximally irregular

Metabolic Networks Analysis using Convex Optimization

Metabolic networks map the biochemical reactions in a living cell to the flow of various chemical substances in the cell, which are called metabolites. A standard model of a metabolic network is given as a linear map from the reaction rates to the change in metabolites concentrations. We study two problems related to the analysis of metabolic networks, the minimal network problem and the minimal knockout problem

From Discrete to Continuous and Back: Abstractions and Mesoscopic Phenomena in Cells

We discuss the interplay between stochasticity and multistability in bio-molecular networks. The resulting cell-level stochastic behavior reflects the fundamentally discrete and random nature of the underlying molecular processes. These ideas are illustrated on the well studied example of the lac operon. We first describe the switching behavior predicted by a differential-equation based model and then show how cell-level stochastic behavior emerges. Finally we point out that the observed macroscopic behavior may not be enough to determine both the dynamic and stochastic parameters