Feedback tuning of bifurcations

The present paper studies a feedback regulation problem that arises in at least two different biological applications. The feedback regulation problem under consideration may be interpreted as an adaptive control problem for tuning bifurcation parameters, and it has not been studied in the control literature. The goal of the paper is to formulate this problem and to present some preliminary results.     

A remark on the converging-input converging-state property

Suppose that an equilibrium is asymptotically stable when external inputs vanish. Then, every bounded trajectory which corresponds to a control which approaches zero and which lies in the domain of attraction of the unforced system, must also converge to the equilibrium. This "well-known" but hard-to-cite fact is proved and slightly generalized here.     

Singular Trajectories in Multi-Input Time-Optimal Problems: Application to Controlled Mechanical Systems

This paper deals with the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems have certain special properties. These properties are explored and used in conjunction with the Pontryagin maximum principle to determine the structure of singular extremals and, in particular, time-optimal trajectories. The theory is illustrated by an application to a time-optimal problem for a class of underwater vehicles.     

An example of a GAS system which can be destabilized by an integrable perturbation

A construction of a globally asymptotically stable time-invariant system which can be destabilized by some integrable perturbation is given. Besides its intrinsic interest, this serves to provide counterexamples to an open question regarding Lyapunov functions.     

Cost effectiveness of decentralized energy supply systems taking solar and wind utilization plants into account

In this article, results are presented of annual simulations of a decentralized (regional) plant for the power and heat supply of a residential complex. This complex consists of four houses with 40 flats all in all. The annual power consumption of the complex is 157 MWh and the heat requirement is 325 MWh. The concrete dynamics of the energy demands over the year is taken into consideration. The energy supply system is composed of a power-controlled combined heat and power (CHP) plant (55 kW), a photovoltaic plant (PV array or PV plant) array for power generation as well as a field of solar thermal collectors with a short-term accumulator for water heating and a long-term accumulator for supplying heat for domestic heating purposes. Simulation results demonstrate that synergetic effects result from the combination of a CHP plant with wind power and PV plants of varying sizes, which have an effect on the cost effectiveness of the plant as a whole with the different dynamics of energy sources (wind and solar energies) and of the consumption of power and heat being the decisive factors. The power deficits of wind power and PV plants are compensated through the application of a natural gas-operated CHP plant. In almost all variants, the demand for fossil energy carriers is distinctly less than in conventional energy supply plants.     

A remark on bilinear systems and moduli spaces of instantons

Explicit equations are given for the moduli space of framed instantons as a quasi-affine variety, based on the representation theory of noncommutative power series, or equivalently, the minimal realization theory of bilinear systems.     

Inferring (Biological) Signal Transduction Networks via Transitive Reductions of Directed Graphs

In this paper we consider the p-ary transitive reduction (TR _p ) problem where p>0 is an integer; for p=2 this problem arises in inferring a sparsest possible (biological) signal transduction network consistent with a set of experimental observations with a goal to minimize false positive inferences even if risking false negatives. Special cases of TR _p have been investigated before in different contexts; the best previous results are as follows:

Further results on controllability properties of discrete-time nonlinear systems

Controllability questions for discrete-time nonlinear systems are addressed in this paper. In particular, we continue the search for conditions under which the group-like notion of transitivity implies the stronger and semigroup-like property of forward accessibility. We show that this implication holds, pointwise, for states which have a weak Poisson stability property, and globally, if there exists a global attractor for the system.This research was supported in part by US Air Force Grant AFOSR-91-0346, and also by an INDAM (Istituto Nazionale di Alta Matematica Francesco Severi, Italy) fellowship.     

A learning result for continuous-time recurrent neural networks

The following learning problem is considered, for continuous-time recurrent neural networks having sigmoidal activation functions. Given a “black box” representing an unknown system, measurements of output derivatives are collected, for a set of randomly generated inputs, and a network is used to approximate the observed behavior. It is shown that the number of inputs needed for reliable generalization (the sample complexity of the learning problem) is upper bounded by an expression that grows polynomially with the dimension of the network and logarithmically with the number of output derivatives being matched.