Control Theory Commons^™

Linearizable Feedforward Systems: A Special Class, Issa Amadou Tall

Miscellaneous (presentations, translations, interviews, etc)

We address the problem of linearizability of systems in feedforward form. In a recent paper [22] we completely solved the linearizability for strict feedforward systems. We extend here those results to a special class of feedforward systems. We provide an algorithm, along with explicit transformations, that linearizes the system by change of coordinates when some easily checkable conditions are met. We also re-analyze type II class of linearizable strict feedforward systems provided by Krstic in [9] and we show that this class is the unique linearizable among the class of quasi-linear strict feedforward systems (see Definition III.1). Our results allow …

Modeling Of Fermentation Processes Using Online Kernel Learning Algorithm, Yi Liu

Dr. Yi Liu

No abstract provided.

Adaptive Control Of A Class Of Nonlinear Discrete-Time Systems With Online Kernel Learning, Yi Liu

Dr. Yi Liu

No abstract provided.

On Linearizability Of Strict Feedforward Systems, Issa Amadou Tall, Witold Respondek

Miscellaneous (presentations, translations, interviews, etc)

In this paper we address the problem of linearizability of systems in strict feedforward form. We provide an algorithm, along with explicit transformations, that linearizes a system by change of coordinates when some easily checkable conditions are met. Those conditions turn out to be necessary and sufficient, that is, if one fails the system is not linearizable. We revisit type I and type II classes of linearizable strict feedforward systems provided by Krstic in [6] and illustrate our algorithm by various examples mostly taken from [5], [6].

Stochastic Differential Equations With Jumps, Jose L. Menaldi

Mathematics Faculty Research Publications

Part I Stochastic Processes with Jumps Chapters: Probability Spaces, Semigroup Theory - Part II Stochastic Differential Equations with Jumps Chapters: Stochastic Calculus, Stochastic Differential Equations - Part III Reflected SDE with Jumps Chapters: Stochastic Differential Equations II, Stochastic Differential Equations III.

Comment: This is last version from 2014-01-07. *This Initial version 15/May/2008 was corrected and augmented to produce the others 5 volumes.

The Adaptability Principle Of Mechanical Law And The Scale-Invariant Principle Of Mechanical Law In Fractal Space, Yang Xiaojun

Xiao-Jun Yang

The adaptability principle of mechanical law and the scale-invariant principle of mechanical law in fractal space are proved by using parameter-space and scale-space transforms in renormalization groups.From the space-transform angle,the transform of mechanical law from fractal space to European space is the scale-invariant transform while the transform of mechanical law from European space to fractal space is the adaptability transform.Their deductions are that law of conservation of energy and vectorial resultant of force and displacement in fractal space hold the line in form and Carpinteri's dimensional formula of fractal space is also proved. Namely,the spilling dimension of volume in fractal …

Fractional Definite Integral, Yang Xiaojun

Xiao-Jun Yang

Fractional definite integral is that a value of the integral calculus over given interva1．Under the circumstance of fractional dimension，fractional definite integral is important to compute some value in given interva1．It is complied with starting introducing definition，the properties，leads into fractional integral function of definition and the properties，and then induces to basic theorems for fractional integral calculus

Optimal Switching Control For Microbial Fed-Batch Culture, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin

Chongyang Liu

In fed-batch culture of glycerol bio-dissimilation to 1,3-propanediol (1,3-PD), the aim of adding glycerol is to obtain as much 1,3-PD as possible. Hence, a proper feed strategy is required during the process. In this paper, we present an optimal switching control model based on our proposed controlled switching system. Some properties of the controlled switching system are obtained. Subsequently, we prove the existence of optimal control. In order to deduce the optimality conditions, we transcribe the optimal switching control model into an equivalent one with fixed switching instants and parameters. Finally, the optimality conditions of the equivalent problem are investigated …

Identification Of Intracellular Kinetic Parameters In Continuous Bioconversion Of Glycerol By Klebsiella Pneumoniae, Enmin Feng, Chongyang Liu, Zhaohua Gong, Yaqin Sun

Chongyang Liu

In this paper, we propose a hybrid nonlinear dynamical system to describe the concentration changes of extracellular and intracellular substances of glycerol bioconversion to 1,3- propanedol (1,3-PD) in microbial continuous cultures. It is proved that the solution to the system exists and is continuous with respect to kinetic parameters. Subsequently, a novel quantitative definition of biological robustness is investigated. We present a performance index based on experiment data of extracellular concentrations and biological robustness. Taking the proposed hybrid nonlinear dynamical system as a constraint, we establish an identification model to determine the most reasonable metabolic pathway and optimal kinetic parameters. …