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Mathematics
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Mathematics on Automation Control Systems
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Mathematics on Automation Control Systems

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (30 April 2019) | Viewed by 28346

Special Issue Editor

Prof. Dr. Manuel De La Sen

E-Mail Website
Guest Editor
Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country, P.O. Box 644 Bilbao, Spain
Interests: dynamic systems; sampled-data systems ( with an emphasis on non-uniform sampling); stability of dynamic systems and stability of differential and difference equations; epidemic mathematical models
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Automation Control Systems have continued to enjoy a strong interaction with research in stochastic processes. The goal of this Special Issue is to explore such interactions between stochastic processes and mathematical finance. We are inviting submissions in various areas of current interest on dynamic systems and control systems, such as (but not limited to):

  • Control systems: theory and applications
  • Nonlinear dynamic systems, controllability, observability, stability, absolute stability, hyperstability and passivity properties
  • Epidemic models: new aspects of analysis, stability and vaccination controls
  • Biological processes: modelling and related control issues
  • Fractional calculus in dynamic systems and control systems: theoretical aspects and controller designs
  • New trends on discrete and multirate control modelling and designs, non-uniform and adaptive sampling
  • New mathematical results on the various aspects of consensus properties and issues in dynamic and control systems
  • Active and semiactive control designs: modelling and stability. Its usefulness against seismic motions and other pernitious perturbing actions
  • Theoretical aspects of impulsive dynamic systems and controls and their potential applications
  • New mathematical results and trends on the study and development of hybrid continuous- time/digital control systems and       related results on switched systems
  • Probabilistic and stochastic control systems
  • Dynamic systems under time scales
  • New proposals on fuzzy control systems
  • Applications of fixed point theory, Lyapunov theory and other related mathematical techniques to the development of new theoretical aspects of stability of dynamic and control systems

Both theoretical and applied research manuscripts are welcomed, as are papers on emerging areas of control systems and interdisciplinary topics. The submitted manuscripts are required to involve a formal treatment including the use of an acceptable rigor from the mathematical point of view.

Prof. Dr. Manuel De la Sen
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • control systems
  • controllability, observability, stability, consensus, absolute stability, hyperstability, passivity
  • epidemic models
  • vaccination controls
  • fractional calculus multirate , non-uniform and adaptive sampling
  • hybrid systems  and controllers
  • probabilistic and stochastic control systems
  • adaptive control
  • Lyapunov stability
  • Nonlinear dynamic and control systems

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Published Papers (6 papers)

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Research

13 pages, 293 KiB  
Article
Robust H∞ Control For Uncertain Singular Neutral Time-Delay Systems
by Yuhong Huo and Jia-Bao Liu
Mathematics 2019, 7(3), 217; https://doi.org/10.3390/math7030217 - 26 Feb 2019
Cited by 10 | Viewed by 2266
Abstract
The present paper attempts to investigate the problem of robust H ∞ control for a class of uncertain singular neutral time-delay systems. First, a linear matrix inequality (LMI) is proposed to give a generalized asymptotically stability condition and an H ∞ norm condition [...] Read more.
The present paper attempts to investigate the problem of robust H ∞ control for a class of uncertain singular neutral time-delay systems. First, a linear matrix inequality (LMI) is proposed to give a generalized asymptotically stability condition and an H ∞ norm condition for singular neutral time-delay systems. Second, the LMI is utilized to solve the robust H ∞ problem for singular neutral time-delay systems, and a state feedback control law verifies the solution. Finally, four theorems are formulated in terms of a matrix equation and linear matrix inequalities. Full article
(This article belongs to the Special Issue Mathematics on Automation Control Systems)
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19 pages, 3493 KiB  
Article
On a New Discrete SEIADR Model with Mixed Controls: Study of Its Properties
by Raul Nistal, Manuel De la Sen, Santiago Alonso-Quesada and Asier Ibeas
Mathematics 2019, 7(1), 18; https://doi.org/10.3390/math7010018 - 25 Dec 2018
Cited by 16 | Viewed by 2730
Abstract
A new discrete SEIADR epidemic model is built based on previous continuous models. The model considers two extra subpopulation, namely, asymptomatic and lying corpses on the usual SEIR models. It can be of potential interest for diseases where infected corpses are infectious like, [...] Read more.
A new discrete SEIADR epidemic model is built based on previous continuous models. The model considers two extra subpopulation, namely, asymptomatic and lying corpses on the usual SEIR models. It can be of potential interest for diseases where infected corpses are infectious like, for instance, Ebola. The model includes two types of vaccinations, a constant one and another proportional to the susceptible subpopulation, as well as a treatment control applied to the infected subpopulation. We study the positivity of the controlled model and the stability of the equilibrium points. Simulations are made in order to provide allocation and examples to the different possible conditions. The equilibrium point with no infection and its stability is related, via the reproduction number values, to the reachability of the endemic equilibrium point. Full article
(This article belongs to the Special Issue Mathematics on Automation Control Systems)
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11 pages, 1078 KiB  
Article
Adaptive System for Steering a Ship Along the Desired Route
by Piotr Borkowski
Mathematics 2018, 6(10), 196; https://doi.org/10.3390/math6100196 - 10 Oct 2018
Cited by 17 | Viewed by 3609
Abstract
An adaptive ship steering system along a preset track is an example of an intelligent system. An optimal linear quadratic regulator (LQR) regulator with a symmetric indicator of control quality was adopted as the control algorithm. The model identification was based on the [...] Read more.
An adaptive ship steering system along a preset track is an example of an intelligent system. An optimal linear quadratic regulator (LQR) regulator with a symmetric indicator of control quality was adopted as the control algorithm. The model identification was based on the continuous version of the least squares method. A significant part of the article presents the proof of the stability of the proposed system. The results of the calculation experiments are provided to confirm the effective and correct working of the system. Full article
(This article belongs to the Special Issue Mathematics on Automation Control Systems)
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18 pages, 321 KiB  
Article
On Some Sufficiency-Type Stability and Linear State-Feedback Stabilization Conditions for a Class of Multirate Discrete-Time Systems
by M. De la Sen
Mathematics 2018, 6(5), 78; https://doi.org/10.3390/math6050078 - 9 May 2018
Cited by 1 | Viewed by 3081
Abstract
This paper presents and discusses the stability of a discrete multirate sampling system whose sets of sampling rates (or sampling periods) are the integer multiple of those operating on all the preceding substates. Each of such substates is associated with a particular sampling [...] Read more.
This paper presents and discusses the stability of a discrete multirate sampling system whose sets of sampling rates (or sampling periods) are the integer multiple of those operating on all the preceding substates. Each of such substates is associated with a particular sampling rate. The sufficiency-type stability conditions are derived based on simple conditions on the norm, spectral radius and numerical radius of the matrix of the dynamics of a system parameterized at the largest sampling period. Full article
(This article belongs to the Special Issue Mathematics on Automation Control Systems)
15 pages, 6750 KiB  
Article
Singularity Penetration with Unit Delay (SPUD)
by Timothy Sands, Jae Jun Kim and Brij Agrawal
Mathematics 2018, 6(2), 23; https://doi.org/10.3390/math6020023 - 11 Feb 2018
Cited by 11 | Viewed by 4820
Abstract
This manuscript reveals both the full experimental and methodical details of a most-recent patent that demonstrates a much-desired goal of rotational maneuvers via angular exchange momentum, namely extremely high torque without mathematical singularity and accompanying loss of attitude control while the angular momentum [...] Read more.
This manuscript reveals both the full experimental and methodical details of a most-recent patent that demonstrates a much-desired goal of rotational maneuvers via angular exchange momentum, namely extremely high torque without mathematical singularity and accompanying loss of attitude control while the angular momentum trajectory resides in the mathematical singularity. The paper briefly reviews the most recent literature, and then gives theoretical development for implementing the new control methods described in the patent to compute a non-singular steering command to the angular momentum actuators. The theoretical developments are followed by computer simulations used to verify the theoretical computation methodology, and then laboratory experiments are used for validation on a free-floating hardware simulator. A typical 3/4 CMG array skewed at 54.73° yields 0.15H. Utilizing the proposed singularity penetration techniques, 3H momentum is achieved about yaw, 2H about roll, and 1H about pitch representing performance increases of 1900%, 1233%, and 566% respectfully. Full article
(This article belongs to the Special Issue Mathematics on Automation Control Systems)
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2263 KiB  
Article
Controlling Chaos—Forced van der Pol Equation
by Matthew Cooper, Peter Heidlauf and Timothy Sands
Mathematics 2017, 5(4), 70; https://doi.org/10.3390/math5040070 - 24 Nov 2017
Cited by 33 | Viewed by 10286
Abstract
Nonlinear systems are typically linearized to permit linear feedback control design, but, in some systems, the nonlinearities are so strong that their performance is called chaotic, and linear control designs can be rendered ineffective. One famous example is the van der Pol equation [...] Read more.
Nonlinear systems are typically linearized to permit linear feedback control design, but, in some systems, the nonlinearities are so strong that their performance is called chaotic, and linear control designs can be rendered ineffective. One famous example is the van der Pol equation of oscillatory circuits. This study investigates the control design for the forced van der Pol equation using simulations of various control designs for iterated initial conditions. The results of the study highlight that even optimal linear, time-invariant (LTI) control is unable to control the nonlinear van der Pol equation, but idealized nonlinear feedforward control performs quite well after an initial transient effect of the initial conditions. Perhaps the greatest strength of ideal nonlinear control is shown to be the simplicity of analysis. Merely equate coefficients order-of-differentiation insures trajectory tracking in steady-state (following dissipation of transient effects of initial conditions), meanwhile the solution of the time-invariant linear-quadratic optimal control problem with infinite time horizon is needed to reveal constant control gains for a linear-quadratic regulator. Since analytical development is so easy for ideal nonlinear control, this article focuses on numerical demonstrations of trajectory tracking error. Full article
(This article belongs to the Special Issue Mathematics on Automation Control Systems)
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