Browsing by Author "Aguila-Camacho, Norelys"

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    Error-Based Switched Fractional Order Model Reference Adaptive Control for MIMO Linear Time Invariant Systems
    (2024) Aguila-Camacho, Norelys; Gallegos, Javier A.
    This paper presents the design and analysis of Switched Fractional Order Model Reference Adaptive Controllers (SFOMRAC) for Multiple Input Multiple Output (MIMO) linear systems with unknown parameters. The proposed controller uses adaptive laws whose derivation order switches between a fractional order and the integer order, according to a certain level of control error. The switching aims to use fractional orders when the control error is larger to improve transient response and system performance during large disturbed states, and to obtain smoother control signals, leading to a better control energy usage. Then, it switches to the integer order when the control error is smaller to improve steady state. Boundedness of all the signals in the scheme is analytically proved, as well as convergence of the control error to zero. Moreover, these properties are extended to the case when system states are affected by a bounded non-parametric disturbance. Simulation studies are carried out using different representative plants to be controlled, showing that fractional orders and switching error levels can be found in most of the cases, such as when SFOMRAC achieves a better balance among control energy and system performance than the non-switched equivalent strategies.
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    Fractional adaptive observer for variable structure high cell density fed-batch cultures
    (ELSEVIER, 2024) Bárzaga-Martell, Lisbel; Aguila-Camacho, Norelys; Ibáñez Espinel, Francisco; Duarte-Mermoud, Manuel; Saa Higuera, Pedro Andrés E.; Pérez C., José Ricardo
    This paper presents the design and application of a fractional order asymptotic adaptive observer coupled to an adaptive controller for the robust operation of high-cell density cultures in fed-batch mode. The control goal is to maximize biomass productivity by controlling the culture's estimated specific growth rate. Since the specific growth rate cannot be measured, a fractional order asymptotic adaptive observer is proposed, based on the equivalent integer order asymptotic observer proposed before. Simulations are performed to validate the observer and controller, under the assumption that the system is in the oxidative regime under aerobic conditions. Obtained results show that, in close loop operation, the fractional adaptive observer behaves better than the integer order observer in the presence of measurement noise. For fractional orders of the observer in the range α G [0.6,0.8], it was observed a 51.71% increase in biomass concentration, compared to the biomass obtained with the classic integer-order observer. Furthermore, the controlled system reaches very low ethanol concentrations (< 1 grams per liter), which is desirable in this process.
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    High-Gain Adaptive Control With Switching Derivation Order and Its Application to a Class of Multiagent Systems
    (2024) Gallegos, Javier; Aguila-Camacho, Norelys; Nunez, Felipe
    This article presents the design and analysis of a switching high-gain adaptive control scheme for a class of nonlinear systems. Adaptation is included in the scheme to estimate the controller gains, using differential equations whose order can switch between 1 (integer order) and some real number (fractional order) in the interval (0,1) , depending on the error level. This switching strategy permits obtaining lower values for controller gains due to fractional orders, resulting in improved robustness, while simultaneously guaranteeing fast convergence of the state to the origin due to the integer order, leading to a better balance between system behavior and control energy efficiency. Applications to multiagent systems are presented to illustrate the potential of the proposed scheme.
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    Pseudo-Lyapunov methods for Grunwald-Letnikov and initialized fractional systems
    (2023) Gallegos, Javier A. A.; Aguila-Camacho, Norelys
    This paper presents reduced-order methods to study the stability of initialized or Grunwald-Letnikov fractional nonlinear systems. It is shown that the initialization procedure must be formalized by introducing a class of systems, and the corresponding stability analysis must be established for each element of that class. The main features obtained using this novel approach are (a) the requirements for stability are imposed directly on the equations of the system and involve only finite-dimensional variables; (b) the conclusions are asserted on the variables of interest; (c) the method can be extended in several ways, including multi-order systems. Illustrative examples, including an application in adaptive control, are finally presented to convey the usefulness of our approach.
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    RELAXED EXCITATION CONDITIONS FOR ROBUST IDENTIFICATION AND ADAPTIVE CONTROL USING ESTIMATION WITH MEMORY
    (2024) Gallegos, Javier; Aguila-Camacho, Norelys
    In this paper, adaptive controllers are designed to track a given trajectory for linear and nonlinear systems. No condition on the tracked trajectory, other than continuity and boundedness, is needed to simultaneously ensure exponential convergence to the tracking reference, exponential convergence to the identification of the plant, and robustness to nonparametric uncertainties. To achieve this, the formulation of the excitation condition associated with the identification part of the adaptive scheme is proposed without employing closed -loop signals, allowing the use of a transient enrichment of the reference. The effect of this transient modification is attenuated by using relaxed requirements for the identification, obtained through a generalization of several estimation algorithms found in recent literature that use memory mechanisms. Consequently, no spectral content of the tracked trajectory ---a classic requirement in adaptive theory ---is needed to guarantee the mentioned features when the proposed scheme is used. A numerical example is given to illustrate the design aspects involved and the distinctive features of the proposed strategy.