Advances in Mathematical Methods in Optimal Control and Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 30 September 2024 | Viewed by 1881

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Department of Mathematics, ISTA, Instituto Universitário de Lisboa (ISCTE-IUL), Av. das Forças Armadas, 1649-026 Lisbon, Portugal
Interests: optimal control theory; mathematical modeling; optimization methods; applications to biology and epidemiology
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Special Issue Information

Dear Colleagues,

Optimal control theory is a mathematical research area of great development with a wide range of applications across various fields. Optimal control problems aim to find the optimal control strategy that minimizes an objective (also called cost) function, while satisfying control system dynamics and a set of constraints (e.g., boundary, state, and control). The mathematical framework of the control system, cost function, and constraints can be very different, and for each of them, distinct mathematical methods must be applied.

This Special Issue focuses on recent advances in mathematical methods for the optimal control of different types of control systems, state and control constraints, and boundary conditions. We welcome papers on new mathematical methods for optimal control problems with applications in biology, ecology, population dynamics, epidemiology, economy, etc. 

Prof. Dr. Cristiana J. Silva
Guest Editor

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 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

  • optimal control problems
  • optimality conditions
  • control system
  • mathematical methods
  • applications

Published Papers (2 papers)

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17 pages, 2691 KiB  
Article
Combined Observer-Based State Feedback and Optimized P/PI Control for a Robust Operation of Quadrotors
by Oussama Benzinane and Andreas Rauh
Axioms 2024, 13(5), 285; https://doi.org/10.3390/axioms13050285 - 23 Apr 2024
Viewed by 601
Abstract
This paper deals with a discrete-time observer-based state feedback control design by taking into consideration bounded parameter uncertainty, actuator faults, and stochastic noise in an inner control loop which is extended in a cascaded manner by outer PI- and P-control loops for velocity [...] Read more.
This paper deals with a discrete-time observer-based state feedback control design by taking into consideration bounded parameter uncertainty, actuator faults, and stochastic noise in an inner control loop which is extended in a cascaded manner by outer PI- and P-control loops for velocity and position regulation. The aim of the corresponding subdivision of the quadrotor model is the treatment of the control design in a systematic manner. In the inner loop, linear matrix inequality techniques are employed for the placement of poles into a desired area within the complex z-plane. A robustification of the design towards noise is achieved by optimizing both control and observer gains simultaneously guaranteeing stability in a predefined bounded state domain. This procedure helps to reduce the sensitivity of the inner control loop towards changes induced by the outer one. Finally, a model-based optimization process is employed to tune the parameters of the outer P/PI controllers. To allow for the validation of accurate trajectory tracking, a comparison of the novel approach with the use of a standard extended Kalman filter-based linear-quadratic regulator synthesis is presented to demonstrate the superiority of the new design. Full article
(This article belongs to the Special Issue Advances in Mathematical Methods in Optimal Control and Applications)
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16 pages, 830 KiB  
Article
Robustness Analysis for Sundry Disturbed Open Loop Dynamics Using Robust Right Coprime Factorization
by Yuanhong Xu and Mingcong Deng
Axioms 2024, 13(2), 116; https://doi.org/10.3390/axioms13020116 - 9 Feb 2024
Viewed by 874
Abstract
In this paper, the robustness of a system with sundry disturbed open loop dynamics is investigated by employing robust right coprime factorization (RRCF). These sundry disturbed open loop dynamics are present not only in the feed forward path, but also within the feedback [...] Read more.
In this paper, the robustness of a system with sundry disturbed open loop dynamics is investigated by employing robust right coprime factorization (RRCF). These sundry disturbed open loop dynamics are present not only in the feed forward path, but also within the feedback loop. In such a control framework, the nominal plant is firstly right coprime factorized and a feed forward and a feedback controllers are designed based on Bezout identity to ensure the overall stability. Subsequently, considering the sundry disturbed open loop dynamics, a new condition formulated as a disturbed Bezout identity is put forward to achieve the closed loop stability of the system, even in the presence of disturbances existing in sundry open loops, where in the feedback loop a disturbed identity operator is defined. This approach guarantees the system robustness if a specific inequality condition is satisfied. And, it should be noted that the proposed approach is applicable to both linear and nonlinear systems with sundry disturbed open loop dynamics. Simulations demonstrate the effectiveness of our methodology. Full article
(This article belongs to the Special Issue Advances in Mathematical Methods in Optimal Control and Applications)
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