Synthesis of multivariable regulators: The internal model principle

For the multivariable control system described by \(\dot x = Ax + Bu,y = Cx,z = Dx\) (wherey is the measured output andz the output to be regulated) conditions are given for the existence of a controller which preserves output regulation and loop stability, in the presence of small parameter variations in controller and plant. Under mild conditions, such a “strong” synthesis is shown to exist if and only if the regulator problem with internal stability (RPIS) is well-posed. Synthesis is achieved by means of a feedback configuration which in general incorporates an invariant, and suitably redundant, copy of the dynamic model adopted for the exogenous disturbance and reference signals which the system is required to process.     

On the lewis acid catalyzed diels-alder reaction of furan. regio- and stereospecific synthesis of substituted cyclohexenols and cyclohexadienols.

The [4+2] cycloaddition between furan and some dienophiles can be greatly accelerated in the presence of a Lewis-Acid (i.e. ZnI₂. The 7-oxabicyclo [2.2.1] heptyl system readily undergoes a base promoted β-elimination of the heteroatom bridge leading to substituted cyclohexenols and cyclohexadienols.     

The sub master equation

Three postulates are proposed concerning the probabilistic dynamics of chemically reactive systems: the occurrence of the elementary event is a random variable characterized by a Poisson process; the state of the chemical system is a multivariate random variable characterized by a Markov process; the identity of any chemical species in the system is an independent random variable. These postulates when applied to chemically reactive systems in a uniform manner lead to a hierarchy of equations describing in detail how eachk subpopulation varies with time. By summing over all permutations of the equation forf _n ⁽ⁿ⁾ (e ₁, ...,e _n ;t) we obtain the usual master equation. This paper focuses on the simple isomerization reaction.     

The synthesis of oximes containing the ferroin group

A series of oximes of substituted 2-pyridylmethyl and phenyl ketones has been prepared. These all contain the ferroin group (?N? C? C? N?). The 4-substituted pyridyl-syn-methyl and phenyl ketoximes form chelates with Fe(II).     

Stochastic invariant imbedding

We study stochastic differential equations of the type: