Direct Adaptive Control Scheme Research Articles

Generalization of Direct Adaptive Control Using Fractional Calculus Applied to Nonlinear Systems

This paper presents a new direct adaptive control (DAC) technique using Caputo’s definition of the fractional-order derivative. This is the first time a fractional-order adaptive law is introduced to work together with an integer-order stable manifold for approximating the uncertainty of a class of nonlinear systems. The DAC approach uses universal function approximators such as multi-layer perceptrons with one hidden layer or fuzzy systems to approximate the controller. This paper presents a new lemma, which elucidates and clarifies the link between the Caputo and the Riemann–Liouville definitions. The introduced lemma is useful in developing a Lyapunov candidate to prove the stability of using the proposed fractional-order adaptive law. This is further explained by a numerical example, which is provided to elucidate the practicality of using the fractional-order derivative for updating the approximator parameters. The main novelty of the results in this paper is a rigorous stability proof of the fractional DAC approach for a class of nonlinear systems that is subjected to unstructured uncertainty and deals with the adaptation mechanism using a traditional integer-order stable manifold. This makes the control scheme easier to implement in practice. The fractional-order adaptation law provides greater degrees of freedom and a potentially larger functional control structure than the conventional adaptive control. Finally, the paper demonstrates that traditional integer-order DAC is a special case of the more general fractional-order DAC scheme introduced here.

Deadzone-adapted disturbance suppression control for global practical IOS and zero asymptotic gain to matched uncertainties

For control-affine nonlinear systems with a disturbance and unknown parameters satisfying a matching condition but not having a known bound, we introduce a direct adaptive control scheme with three design elements: (a) nonlinear damping, (b) single-gain adjustment, and (c) deadzone in the update law. Combining these three ingredients for the first time, we guarantee the following previously unattained property: an attenuation of the plant state to an assignable small level, despite unknown bounds on the parameters and disturbance, without a drift of the gain, state, and input. Given the tools and results, we refer to the proposed scheme as a Deadzone-Adapted Disturbance Suppression (DADS) Controller.

Direct Adaptive Fuzzy Control with Prescribed Tracking Accuracy for Orbit Adjustment of Satellites

In this paper, we investigate the orbit-adjustment problem of satellite systems in the presence of nonlinear uncertainties in kinematics and dynamics. We propose a novel direct adaptive fuzzy control scheme with prescribed tracking accuracy to address uncertain nonlinear dynamics by employing advanced fuzzy logic systems and integrating a class of sophisticated smooth functions, thereby ensuring convergence of the tracking error within a precisely defined interval. The ingeniously designed control scheme guarantees negative semi-definiteness of the Lyapunov function, ensuring boundedness for all variables. Moreover, our groundbreaking control approach requires only one adaptive law, completely eliminating any direct correlation with the number of nonlinear functions. Simulation results unequivocally validate the remarkable effectiveness and superiority of our innovative control approach.

Robust synchronization of four-dimensional chaotic finance systems with unknown parametric uncertainties

ABSTRACT The inherent randomness in economic factors causes complex and irregular behaviour that affects financial system stability and economic growth. Such chaotic behaviour can make it difficult to synchronize financial systems. The chaotic finance system synchronization precision maintains financial stability and economic growth. In this paper, the controller design procedure assumes that the financial system is exposed to unknown bounded exogenous disturbances and model uncertainties. This research proposes a novel direct adaptive control strategy that achieves robust synchronization of two identical four-dimensional finance chaotic (FDFC) systems. The proposed controller establishes a faster, smoother synchronization error vector convergence to zero. The controller design procedure does not eliminate the closed-loop's nonlinear terms and is independent of the financial system parameters. These controller's attributes accomplish the closed-loop robust performance. Further, this controller uses real-time estimates of unknown model uncertainties and bounds to compensate for unknown exogenous disturbances. Computer simulation results and proofs of theoretical analysis based on the Lyapunov stability theory confirm that the proposed control technique compels the error vector trajectories to the origin in a short transient time with less active oscillations for all signals. The paper includes comparative computer simulations for verifying the theoretical findings.

Practical adaptive robust tracking control of the dual-valve parallel electro-hydraulic servo system with reduced-order model

To meet the increasing demand for trajectory tracking accuracy and high-efficiency requirements in modern mobile machinery, this paper proposes a practical adaptive robust control method based on the dual-valve parallel electro-hydraulic servo system. Existing tracking control strategies for such servo systems rely on a backstepping method and assume that full states are known, which is stringent in practice. To cope with the problem, we reduce the mathematical model order of the studied system using singular perturbation theory in this paper, and only the position feedback is required for the control implementation. Then, to achieve high accuracy tracking control, a direct adaptive robust control scheme combing with a dynamic flow allocation layer is adopted to synthesize the controller. With this method, parameter uncertainties and load disturbance are rejected, and valve characteristics are considered in the dynamic flow allocation layer to solve the flow redundancy problem, respectively. Convergence of the simplified system tracking results is proved theoretically. Extensive co-simulations and experimental tests are carried out to illustrate the effectiveness of the proposed strategy, both tracking precision and flow distribution can be achieved efficiently by simple parameter adjustments in the field.

Decentralized direct adaptive fuzzy control scheme for state-constrained interconnected systems

This paper focuses on the problem of decentralized adaptive fuzzy tracking control for state-constrained interconnected systems. However, feasibility conditions on virtual controllers are imposed by barrier Lyapunov function (BLF) based approaches. To remove it, a nonlinear state-dependent barrier function (NSBF) is proposed, based on which the constrained interconnected system is equivalently transformed into a non-constrained one. Nonlinear interactions and uncertainties are approximated by fuzzy logic systems (FLS). A decentralized direct adaptive fuzzy control (DAFC) scheme is developed, in which a class of reduced-order smooth functions is fused with backstepping control design procedures, and only one adaptive law is used in each decentralized controller. With the proposed control scheme, not only the feasibility conditions but also the partial-derivative terms are not involved in virtual controllers, and the time derivative of the Lyapunov function is ensured negative semi-definite. It is shown that the proposed control scheme guarantees that the state constraints are not violated, and the tracking error converges to a predefined interval asymptotically. Two simulation examples confirm the effectiveness of the proposed control scheme.

A Hybrid Robust Adaptive Sliding Mode Controller for partially modelled systems: Discrete-time Lyapunov stability analysis and application

This work presents a new discrete-time Hybrid Robust Adaptive Sliding Mode Controller, developed from the union of a Robust Model Reference Adaptive Controller, an Adaptive Sliding Mode Controller, and an Adaptive One Sample Ahead Preview Controller in an unique control structure. Robust Model Reference Adaptive Controller is an adequate direct adaptive control strategy to control partially known plants, but can present slow closed-loop response to ensure global stability. Therefore, an adaptive One Sample Ahead Preview controller is incorporated to accelerate transient regimes, once it tries to track reference signal in one sample. Furthermore, an adaptive Sliding Mode Controller is also merged in the controller structure to help controller performance in transient regime and it also improves relevantly the steady state response in a scenario of several unmodelled dynamics Stability analysis of this controller using Lyapunov criterion and its robustness proof are provided, considering the plant subjected to unmodelled dynamics, which provides controller design constraints. These proofs show the controller is globally stable, and the tracking error tends to a residual set in steady state, even in the presence of matched and unmatched dynamics. Numerical simulations of the Hybrid Robust Adaptive Sliding Mode Controller applied on an unstable nonminimum-phase plant are presented, where only part of the overall plant is take into consideration for controller design. Results corroborate the feasibility and robustness of the developed control strategy and the performance superiority when compared to an adaptive One Sample Ahead Preview controller, with a 75% tracking error reduction in a scenario of several unmodelled dynamics.

Indirect adaptive control of multi-input-multi-output nonlinear singularly perturbed systems with model uncertainties

In this paper, two indirect adaptive control schemes for a class of multi-input-multi-output nonlinear singularly perturbed systems with partially unknown models and parameters are presented. Firstly, the original system dynamic equation is reformulated into a new form with identity control gain matrices, and a new multi-time-scale singularity-free neural network is employed to represent the new dynamic equation. Subsequently, an online identification scheme is proposed to update neural network weights where a set of auxiliary weight error vectors are used such that better convergence property can be achieved. Based on identification results, a singularity-free singular perturbation controller is developed to control the unknown nonlinear system. By using the singularity-free neural network and singular perturbation technique, the complexity in controller design for a singularly perturbed system is reduced, and the potential singularity problem is avoided. Moreover, a singularity-free dynamic surface control scheme is also proposed, and the “explosion of complexity” issue is relieved. Compared to conventional direct adaptive dynamic surface control schemes which use gradient-like updating laws and tracking errors to train the neural networks, the singularity-free dynamic surface controller is designed indirectly and the neural networks are updated using the identification errors. Therefore, better identification and control performance is achieved, and the potential singularity problem is also circumvented. The stability of the closed-loop system is rigorously proved via the Lyapunov approach, and the effectiveness of proposed identification and control schemes is demonstrated by simulations.

The concept of direct adaptive control for improving voltage and frequency regulation loops in several power system applications

This article presents the idea of direct adaptive control for several power system applications such as the Egyptian power system (EPS), a three-zone interconnected microgrid (MG), and a single machine connected to the grid (SMIB). The main concept of the proposed adaptive method is built on the tuning of the controller gains using Harris hawks optimizer (HHO). In order to maintain the frequency and voltage at their nominal values, a modified virtual rotor (virtual inertia + virtual damping) is investigated as a tertiary control loop within the proposed EPS and the 3-area MG system. For SMIB application, a secondary automatic voltage regulator (AVR) has been added to the primary AVR within the excitation system to offer more adequate damping characteristics for the synchronous generator of the studied system. Where the proportional-integral-derivative power system stabilizer (PID-PSS) is connected to the excitation system for a single machine tied to the grid to significantly mitigate low-frequency oscillations due to various expected faults and undesirable operating conditions. The proposed direct adaptive control strategy has been used to tune the integral controller of the secondary AVR and PID for SMIB application, and also to adjust the virtual rotor in the EPS and the 3-area MG applications. The operative performance of the introduced adaptive secondary AVR is assessed against the conventional system (no PSS), Lead-Lag PSS, and PSS type 2 based PSO and WECC standard under the effect of a 3-φ short-circuit fault subjected at the grid bus considering solar photovoltaic (PV) farm-based grid. Moreover, the EPS system and 3-area MG are evaluated under the effect of load change conditions and partial injection of PV and random loads. The final findings prove that the direct adaptive concept can provide robust performance and effectively maintain the dynamic stability of the main grid against fluctuations.

Neuroadaptive asymptotic consensus tracking control for a class of uncertain nonlinear multiagent systems with sensor faults

This paper proposes an adaptive neural consensus tracking control approach for a class of leader–follower uncertain multiagent systems with sensor faults. Based on backstepping technique, a new direct adaptive neural control scheme is proposed to adaptively approximate the sensor faults. In order to improve the stability of the system and transient performance, a series of smooth functions are incorporated into control design and Lyapunov analysis. In addition, a class of reduced-order smooth functions is introduced to achieve a simpler virtual controller implementation. It is proved that the closed-loop signals are bounded and the synchronization errors can converge to a preset interval. Besides the asymptotic performance, a tunable L2-norm transient performance is achieved. Finally, numerical and physical example are presented to validate the effectiveness of the proposed control scheme.

Direct adaptive control for nonlinear systems using a TSK fuzzy echo state network based on fractional-order learning algorithm

This paper presents a new Takagi-Sugeno-Kang fuzzy Echo State Neural Network (TSKFESN) structure to design a direct adaptive control for uncertain SISO nonlinear systems. The proposed TSKFESN structure is based on the echo state neural network framework containing multiple sub-reservoirs. Each sub-reservoir is weighted with a TSK fuzzy rule. The adaptive law of the TSKFESN-based direct adaptive controller is derived by using a fractional-order sliding mode learning algorithm. Moreover, the Lyapunov stability criterion is employed to verify the convergence of the fractional-order adaptive law of the controller parameters. The evaluation of the proposed direct adaptive control scheme is verified using two case studies, the regulation problem of a torsional pendulum and the speed control of a direct current (DC) machine as a real-time application. The simulation and the experimental results show the effectiveness of the proposed control scheme.

Enhancing the performance of a deregulated nonlinear integrated power system utilizing a redox flow battery with a self-tuning fractional-order fuzzy controller

Load frequency regulation is one of the most vital and complex ancillary services in a deregulated power system. Increasing penetration from renewable energy sources in an integrated power system (IPS) further escalates the related control complexity due to a considerable decrement in IPS’s effective inertia. This may incur additional costs and can even lead to the destabilization of IPS. To overcome these problems in frequency regulation, this work proposes and investigates the use of an intelligent, direct adaptive control scheme, i.e., self-tuning fractional order fuzzy PID (STFOFPID) controller with and without the presence of a recently devised energy storage unit, i.e., the redox flow battery. The IPS’ efficacy with the STFOFPID controller is validated for various contracts in a deregulated operation mode for considered three area IPS. Extensive simulation studies are carried out, and detailed comparative studies have been drawn with conventional PID and fractional order PID controllers for load frequency regulation in Poolco, bilateral, and contract-violation mode of operation. Robustness analysis in terms of parametric variations in different nonlinearities present in a reheated thermal power plant is also carried out, and the efficacy of the STFOFPID controller is established using a thorough quantitative comparative analysis. The real-time digital simulation validation of the investigated control structure has been carried out on OPAL-RT 4150 based on Xilinx Kintex-7 FPGA board with INTEL multi-core processor.

Gradient Descent Algorithm-Based Adaptive NN Control Design for an Induction Motor

This paper investigates the position tracking control problem for an induction motor with completely unknown nonlinearities. A novel control scheme is presented by using the gradient descent algorithm, adaptive backstepping technique, neural networks (NNs), and extended differentiators. Differing from some existing results which only designed the adaption of weights of NNs, our proposed control strategy provides training for all the parameters of NNs, including the basis functions' widths and centers. With the help of the gradient descent algorithm and Lyapunov stability criterion, the convergence of both the NN approximation error and the system tracking error can be guaranteed. Finally, a simulation example shows the advantages of our proposed method compared with direct adaptive NN control strategy.

Direct Adaptive Fuzzy Control Scheme With Guaranteed Tracking Performances for Uncertain Canonical Nonlinear Systems

In our recent work, we propose an indirect adaptive fuzzy control scheme for uncertain unparametrizable nonlinear systems, which ensures that the number of adaptive laws does not increase with the number of fuzzy rules, and the time derivative of the chosen Lyapunov function is negative semidefinite. However, the scheme involves a class of high-order smooth functions and their time derivatives, which can make the controller structure become sophisticated especially when the relative degree of system is quite large. To overcome this problem, in the article, we propose a new direct adaptive fuzzy control scheme based on a class of reduced-order smooth functions. With the scheme, no partial-derivative term is involved in controller and virtual controllers, only one adaptive law is used regardless of the increase of fuzzy rules, and also the time derivative of Lyapunov function can be ensured negative semidefinite. It is proved that all closed-loop signals are bounded, and the output tracking error converges to a prescribed interval asymptotically. The transient tracking performance and robustness of the proposed control scheme are also considered. The effectiveness of the obtained results is illustrated by two practical control systems.

Distributed model reference adaptive containment control of heterogeneous multi-agent systems with unknown uncertainties and directed topologies

In this paper, the containment control problem of heterogeneous uncertain high-order linear Multi-Agent Systems (MASs) is addressed and solved via a novel fully-Distributed Model Reference Adaptive Control (DMRAC) approach, where each follower computes its adaptive control action on the basis of local measurements, information shared with neighbors (within the communication range) and the matching errors w.r.t. its own reference model, without requiring any previous knowledge of the global directed communication topology structure. The approach inherits the robustness of the direct model reference adaptive control (MRAC) scheme and allows all agents converging towards the convex hull spanned by leaders while fulfilling at the same time local additional performance requirements at single-agent level, such as prescribed settling time, overshoot, etc. The asymptotic stability of the whole closed-loop network is analytically derived by exploiting the Lyapunov theory and the Barbalat lemma, hence proving that each follower converges to the convex hull spanned by the leaders, as well as the boundedness of the adaptive gains. Extensive numerical analysis for heterogeneous MAS composed of stable, unstable and oscillating agent dynamics are presented to validate the theoretical framework and to confirm the effectiveness of the proposed approach.

A novel disturbance rejection factor based stable direct adaptive fuzzy control strategy for a class of nonlinear systems

AbstractThis paper proposes a unique disturbance rejection factor (DRF) based design of direct stable adaptive fuzzy logic controllers (AFLCs) for a class of non‐linear systems with large and fast disturbances. The proposed AFLCs are realized by employing hybrid combinations of Lyapunov theory based local adaptation and harmony search algorithm based global optimization technique. These hybrid AFLCs are designed with the objective of optimizing both the structure and free parameters of it with guaranteed stability and, at the same time, simultaneously achieving satisfactory tracking performance and disturbance rejection. The novelty of the proposed work lies in the fact that, in a bid to perform the disturbance rejection, the nature of the disturbance itself is used in designing the tracking control law. The proposed DRF based hybrid stable AFLCs are implemented for several benchmark case studies and extensive performance evaluations demonstrate their usefulness.

Backstepping-based adaptive control of a quadrotor UAV with guaranteed tracking performance

In this paper, a backstepping based indirect adaptive control design and an alternative direct adaptive control scheme, both with guaranteed transient and steady-state tracking performances, are proposed for trajectory tracking of a quadrotor unmanned aerial vehicle (UAV). Backstepping techniques, combined with a prescribed performance function based error transformation, are employed in both designs to achieve the bounded transient and steady-state tracking errors of the strict-feedback position system which comprises both lateral position and altitude dynamics. The effects of parametric inertia and drag uncertainties on attitude regulation are compensated using a least squares based parameter identification algorithm in the indirect adaptive control design, and using a constructive Lyapunov analysis approach in the direct adaptive control scheme. The stability of the closed-loop system for both designs is proven via Lyapunov analysis. Simulation and experimental test results are provided to verify the effectiveness of the proposed control designs.

Adaptive neural control for switched nonlinear systems with unmodeled dynamics and unknown output hysteresis

This paper aims at addressing the adaptive neural control problem for switched nonlinear systems with output hysteresis and unmodeled dynamics. The switching law in this study is arbitrary. In our model, the unmodeled dynamics are assumed to be of input-to-state practical stability (ISpS). With the help of this assumption, a dynamic normalizing signal is constructed to dominate the unmodeled dynamics. And then, a direct adaptive neural state-feedback control scheme is developed with the help of approximation-based backstepping. The stability analysis shows that the system output is convergent to an adjustable small region of zero asymptotically, and furthermore, all the closed-loop signals are bounded. Finally, we further present two simulation examples to verify the effectiveness of our control scheme.

Synchronization and identification of nonlinear systems by using a novel self-evolving interval type-2 fuzzy LSTM-neural network

Nonlinear systems widely exist in the real world. Researches on the synchronization and identification of nonlinear systems have both theoretical and practical interests. However, since the pseudo-random and parameter sensitivity, some nonlinear dynamics, such as chaotic systems, are difficult to achieve the required regression approximation. By means of the fuzzy-neural structure and long short-term memory (LSTM) mechanism, this paper proposes a novel inference structure of the self-evolving interval type-2 fuzzy LSTM-neural network (eIT2FNN-LSTM) for the synchronization and identification of nonlinear dynamics. In order to tackle with the time-dependency data generated by nonlinear systems, recurrent neural fuzzy systems with LSTM structure is introduced into type-2 fuzzy neural networks, where, by means of gate mechanism, a recurrent structure in the time dimension by feeding the rule firing strength of each rule back to itself is implemented. Besides, an online rule generation algorithm based on dynamic density clustering is utilized to achieve structural updates, which can meet the need of high frequency data process in reality. By incorporating direct adaptive interval type-2 LSTM fuzzy control scheme and sliding mode approach, two chaotic systems with external disturbance noise or/and random-varying parameters can be synchronized based on Lyapunov stability criterion, where two methods, i.e., the gradient training and particle swarm optimization (PSO) algorithm are used. In order to further verify the universality of the proposed scheme, besides nonlinear system, real-life datasets are also utilized to verify the effectiveness of the proposed fuzzy-neural inference system.

Blood glucose regulation in type 1 diabetic patients: an adaptive parametric compensation control-based approach.

Here, a direct adaptive control strategy with parametric compensation is adopted for an uncertain non‐linear model representing blood glucose regulation in type 1 diabetes mellitus patients. The uncertain parameters of the model are updated by appropriate design of adaptation laws using the Lyapunov method. The closed‐loop response of the plasma glucose concentration as well as external insulin infusion rate is analysed for a wide range of variation of the model parameters through extensive simulation studies. The result indicates that the proposed adaptive control scheme avoids severe hypoglycaemia and gives satisfactory performance under parametric uncertainty highlighting its ability to address the issue of inter‐patient variability.