There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

System Identification I

Computer and Robot Vision Vol. 1, by R.M. Haralick and Linda G. Shapiro, Addison-Wesley, 1992, ISBN 0-201-10887-1.

Computer and Robot Vision

The Biometry of Plant Growth

This paper presents a set of realistic simulations conducted to demonstrate the applicability of the partial state reference model (PSRM) control approach to automotive control. Particular emphasis is put on those engineering design features as the tracking capability and the stability robustness and performances in the presence of state disturbance and modelling errors.

Automotive control: the PSRM control approach

ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE)

An MR damper is a device that exhibits a high nonlinear and complex behavior with a hysteresis phenomenon. A comparison between different state-of-the-art and a Linear Parameter Varying (LPV) models for Magneto-Rheological (MR) dampers is presented. Several experimental datasets validate that Linear Parameter Varying (LPV)-based model outperforms the classical MR damper models for 51 % than any structures considering the Error to Signal Ratio index and 37 % better considering the Squared root of Sum of Squared Errors index.

/pdf/lpv-based-mr-damper-modelling-exqz8um0dx.pdf

LPV-based MR damper modelling


Purpose
The purpose of this paper extends the authors’ previous contributions on aircraft system identification, such as open loop identification or closed loop identification, to cascade system identification. Because the cascade system is one special network system, existing in lots of practical engineers, more unknown systems are needed to identify simultaneously within the statistical environment with the probabilistic noises. Consider this problem of cascade system identification, prediction error method is proposed to identify three unknown systems, which are parameterized by three unknown parameter vectors. Then the cascade system identification is transferred as one parameter identification problem, being solved by the online subgradient descent algorithm. Furthermore, the nonparametric estimation is proposed to consider the general case without any parameterized process. To make up the identification mission, model validation process is given to show the asymptotic interval of the identified parameter. Finally, simulation example confirms the proposed theoretical results.


Design/methodology/approach
Firstly, aircraft system identification is reviewed through the understanding about system identification and advances in control theory, then cascade system identification is introduced to be one special network system. Secondly, for the problem of cascade system identification, prediction error method and online subgradient decent algorithm are combined together to identify the cascade system with the parameterized systems. Thirdly from the point of more general completeness, another way is proposed to identify the nonparametric estimation, then model validation process is added to complete the whole identification mission.


Findings
This cascade system corresponds to one network system, existing in lots of practice, such as aircraft, ship and robot, so it is necessary to identify this cascade system, paving a way for latter network system identification. Parametric and nonparametric estimations are all studied within the statistical environment. Then research on bounded noise is an ongoing work.


Originality/value
To the best of the authors’ knowledge, research on aircraft system identification only concern on open loop and closed loop system identification, no any identification results about network system identification. This paper considers cascade system identification, being one special case on network system identification, so this paper paves a basic way for latter more advanced system identification and control theory.


Synthesis cascade estimation for aircraft system identification

Based on our recent contributions on direct data driven control scheme, this paper continues to do some new research on direct data driven control, paving another way for latter future work on advanced control theory. Firstly, adaptive idea is combined with direct data driven control, one parameter adjustment mechanism is constructed to design the parameterized controller online. Secondly, to show the input-output property for the considered closed loop system, passive analysis is studied to be similar with stability. Thirdly, to validate whether the designed controller is better or not, another safety controller modular is added to achieve the designed or expected control input with the essence of model predictive control. Finally, one simulation example confirms our proposed theories. More generally, this paper studies not only the controller design and passive analysis, but also some online algorithm, such as recursive parameter identification and online subgradient descent algorithm. Furthermore, safety controller modular is firstly introduced in direct data driven control scheme.

https://ieeexplore.ieee.org/ielx7/6287639/6514899/09895228.pdf

Ricardo A. Ramirez-Mendoza

Papers

Automotive control: the PSRM control approach

ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE)

LPV-based MR damper modelling

Synthesis cascade estimation for aircraft system identification

On Online Adaptive Direct Data Driven Control