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

Data Driven Strategies

In this paper, interval prediction model is studied for model predictive control (MPC) strategy with unknown but bounded noise. After introducing the family of models and some basic information, some computational results are presented to construct interval predictor model, using linear regression structure whose regression parameters are included in a sphere parameter set. A size measure is used to scale the average amplitude of the predictor interval, then one optimal model that minimizes this size measure is efficiently computed by solving a linear programming problem. The active set approach is applied to solve the linear programming problem, and based on these optimization variables, the predictor interval of the considered model with sphere parameter set can be directly constructed. As for choosing a fixed non-negative number in our given size measure, a better choice is proposed by using the Karush-Kuhn-Tucker (KKT) optimality conditions. In order to apply interval prediction model into model predictive control, the midpoint of that interval is substituted in a quadratic optimization problem with inequality constrained condition to obtain the optimal control input. After formulating it as a standard quadratic optimization and deriving its dual form, the Gauss-Seidel algorithm is applied to solve the dual problem and convergence of Gauss-Seidel algorithm is provided too. Finally simulation examples confirm our theoretical results.

Application of Interval Predictor Model Into Model Predictive Control

This paper studies one identification problem for a piecewise affine system which is a special nonlinear system. As the difficulty in identifying the piecewise affine system is to determine each se...

https://www.tandfonline.com/doi/pdf/10.1080/21642583.2020.1737845

Zonotope parameter identification for piecewise affine system

Engineering education requires learning strategies to engage students and improve the development of disciplinary and transversal competencies. Additionally, as economic resources are generally limited, it is sought to avoid investing large sums of money in software and hardware, as well as in fitting out laboratories. This work presents a didactic proposal within the framework of active and collaborative learning that includes the flipped classroom technique to be applied in the curriculum of undergraduate engineering programs and inside a massive flexible digital master class. The activity is the mathematical modeling, simulation, and control system of a direct current motor where simulation work is carried out in open license computational packages. Students understand the physical phenomena involved in the motor’s modeling and the input–output variables’ relations. Moreover, an analogy between an electromechanical and a pure electrical model is carried out, where the relevant variables respond in an agile and reliable manner. To validate the modeling, the differential equations are solved by applying numerical methods, and tested for control purposes. The activity has been validated with a rule-based system applied to a Likert scale survey data. This type of human–computer interaction, in the context of active learning, could engage students and motivate them to develop competencies that are highly appreciated by industry practitioners.

/pdf/an-active-learning-didactic-proposal-with-human-computer-mapufubh.pdf

An Active Learning Didactic Proposal with Human-Computer Interaction in Engineering Education: A Direct Current Motor Case Study

We present a direct data driven model reference control framework for flight simulation table from both the theoretical analysis and engineering application. Sate of the art direct driven model reference control designs the unknown controller based on the input-output data and guarantees the actual model converge to the reference model, under a case of no any priori knowledge for the unknown plant. We improve this direct data driven model reference control strategy by considering its stability validation and synthesis analysis for nonlinear controller. The resulting direct data driven model reference control scheme can be implemented to ensure flight simulation table rotate accuracy, resulting in improved performance index. As the main technical contribution, we show that the proposed direct data driven model reference control framework also ensures closed loop stability and suitable extension for nonlinear controller.

https://ieeexplore.ieee.org/ielx7/6287639/6514899/09741737.pdf

Ricardo A. Ramirez-Mendoza

Papers

Data Driven Strategies

Application of Interval Predictor Model Into Model Predictive Control

Zonotope parameter identification for piecewise affine system

An Active Learning Didactic Proposal with Human-Computer Interaction in Engineering Education: A Direct Current Motor Case Study

Direct Data Driven Model Reference Control for Flight Simulation Table