The surveillance or monitoring of places is crucial to ensuring security, protecting people and assets, preventing crimes, and detecting emergencies, to mention some. Unmanned Aerial Vehicles (UAVs) ...play a vital role in these applications, offering versatility, agility, and aerial vision. A crucial step for such tasks is to protect the UAV path ahead. This paper focuses on a methodology harnessing the unpredictable nature of chaotic systems to generate trajectories around a closed area or contour. However, although a vast quantity of research papers mention the use of chaotic path generation, they have yet to learn about the control system and the dynamics affecting the UAV, where developing the control theory is challenging. In this paper, we design controllers based on predetermined-time stability, ensuring the achievement of the desired trajectory before a specified time. Additionally, adjusting control parameters is a crucial step during the control design, impacting the control performance. Hence, we present a method to optimize and adapt controller parameters through evolutionary optimization, demonstrating precision enhancement. We validate the proposed system’s performance and the controllers through numerical simulations, indicating that the UAV effectively and accurately follows some types of chaotic trajectories like a square contour, aiming at the feasibility of this methodology in real UAV surveillance applications.
•Design of Predefined-Time Control (PTC) for chaotic trajectory tracking with UAVs.•Generation of complex and unpredictable trajectories based on chaotic systems.•Optimization of controller parameters by Differential Evolution metaheuristic.•Lyapunov analysis for the design and convergence of Predefined-Time Controllers.
Stability analysis plays an essential role in control systems design. This analysis can be done using different techniques that show the equilibrium points are stable (or unstable). This paper ...focuses on fractional systems of order 0 < α < 1 modeled by the Atangana–Baleanu derivative of Riemann–Liouville type (ABR), which allows consistent modeling of a large class of physical systems with complex dynamics. The main contribution of the paper consists of some novel inequalities for the Atangana–Baleanu derivative of the Riemann–Liouville type. Furthermore, the proposed study allows considering both quadratic and convex Lyapunov functions to analyze stability in ABR systems by applying the Direct Lyapunov Method.
ABSTRACT This article describes a control approach for obtaining predefined‐time robust tracking in multiplicative systems despite positive, bounded, and unknown multiplicative disturbances. The ...proposed approach is distinguished by imposing predefined‐time convergence, a topic previously studied in conventional calculus in the context of multiplicative systems. Multiplicative calculus is recognized as a beneficial tool that complements standard calculus by simplifying the modeling and comprehension of numerous processes. Simulations are carried out to illustrate that the given control strategy enforces convergence before a predefined time instant and, while inducing robustness against system uncertainties. The findings of this article pave the way for further research into predefined‐time synchronization of multiplicative oscillator systems, which would bring promising implications for data encryption and secure communication.
In this article, the estimation problem in a class of nonlinear fractional-order systems is solved by a stable estimator that generalizes the classical exponential observers, establishing a new class ...called Mittag–Leffler observers. The solution to the linear quadratic regulator problem is proposed to design optimal control laws for fractional-order linear systems and its applications. All the results are based on the Caputo derivative for commensurate fractional-order systems. Numerical simulations validate the proposed theory.
This paper proposes the study of a newer class of integro-differential operators, which allow analysing a more general family of dynamical systems, with not necessarily integer-order differentiable ...solutions, and based on Volterra integral equations of the second kind. One of the main advantages of the present study is that the proposed operators include, in particular cases, some classical and modern formulations of fractional- and distributed-order derivatives. In contrast to conventional methodologies, the integer-order differentiability of the solution is not assumed, allowing to deem on a more general class of dynamical systems and non-smooth techniques for robust stabilisation. The formal presentation of novel tools could result in high interest for robust control of more varied dynamical processes. Representative simulations are also presented in order to highlight the feasibility of the proposed methods.
In this work, a class of chaotic nonlinear fractional systems of commensurate order called Liouvillian systems is considered to solve the problem of generalized synchronization. To solve this ...problem, the master and the slave systems are expressed in the Fractional Generalized Observability Canonical Form (FGOCF), then a fractional-order dynamical control law is designed to achieve the generalized synchronization. The encryption of color images is presented as an application to the proposed synchronization method, the encryption algorithm allows to decrypt data without loss. The synchronization and its applications are then illustrated with numerical examples.
In the context of different applications demanding fast, secure, and accurate chaotic systems synchronization, this article is concerned with improving the security and timeliness of chaotic ...synchronization schemes in chaotic secure information transmission. Firstly, we introduce five control laws designed to achieve predefined-time chaotic synchronization within a master–slave scheme, employing a generalized Lorenz-type systems family as the chaotic model, guaranteeing that the chaotic systems achieve synchronization before a known predefined time. We apply the synchronization scheme in a practical application to validate its performance by implementing a secure communication system for image encryption on Raspberry Pi, using the MQTT protocol for transmission. We present system experimental results and evaluate its performance using diverse metrics, including errors, correlation, variance, and statistical tests like entropy, NPCR, and UACI.
•A family of predefined-time controllers (PTC) to synchronize Lorenz-type systems.•Lyapunov analysis gives conditions for the design and convergence of PTC algorithms.•MQTT protocol for predefined-time transmission is implemented on Raspberry Pi.•Numerical and experimental results show the feasibility of the theory.
In control theory, there are many proposals to solve the problem of observer design. This paper studies the Mittag-Leffler stability of a class of dynamic observers for nonlinear fractional-order ...systems, given in the observable canonical form and defined by the Caputo fractional derivative. We prove that the Riemann–Liouville integral could be employed to provide robustness against noisy measurements during the estimation problem. Based on this advantage, the main result of this paper consists of the design of a family of high-gain proportional
ρ
-integral observers employed to estimate unmeasured state variables of nonlinear fractional systems of commensurate order. Three illustrative numerical examples of mechanical systems are provided, which corroborate the effectiveness of the proposed algorithms.
This paper presents a generalization of existing control methods. The proposal stands for a novel control structure that enforces the robust stabilization of a large class of physical and engineering ...systems, which are subject to the effect of nonlinearities, disturbances and uncertainties. The proposed scheme results as a state feedback plus a generalized proportional–integral (PI) controller. The state feedback compensates vanishing uncertainties, while the generalized PI control term gets rid of the effect of matched uncertainties, where the assumption on the regularity of the disturbance is relaxed. The proposed contribution is the generalization of conventional PI structures to account for the case of more variate closed-loop responses. Although the usefulness of the studied generalization in real applications deserves further investigation, some numerical simulations show the pertinence of the proposed scheme.
In this paper, we study the recently proposed fractional-order operators with general analytic kernels. The kernel of these operators is a locally uniformly convergent power series that can be chosen ...adequately to obtain a family of fractional operators and, in particular, the main existing fractional derivatives. Based on the conditions for the Laplace transform of these operators, in this paper, some new results are obtained—for example, relationships between Riemann–Liouville and Caputo derivatives and inverse operators. Later, employing a representation for the product of two functions, we determine a form of calculating its fractional derivative; this result is essential due to its connection to the fractional derivative of Lyapunov functions. In addition, some other new results are developed, leading to Lyapunov-like theorems and a Lyapunov direct method that serves to prove asymptotic stability in the sense of the operators with general analytic kernels. The FOB-stability concept is introduced, which generalizes the classical Mittag–Leffler stability for a wide class of systems. Some inequalities are established for operators with general analytic kernels, which generalize others in the literature. Finally, some new stability results via convex Lyapunov functions are presented, whose importance lies in avoiding the calculation of fractional derivatives for the stability analysis of dynamical systems. Some illustrative examples are given.
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