Backstepping Scheme Research Articles

Reinforcement Learning-Based Predefined-Time Tracking Control for Nonlinear Systems Under Identifier-Critic-Actor Structure.

A novel reinforcement learning-based predefined-time tracking control scheme with prescribed performance is presented in this article for nonlinear systems in the presence of external disturbances. First, by employing the backstepping strategy, an adaptive optimized controller is developed under the identifier-critic-actor framework. Therein, the unknown nonlinear dynamics and the system control behavior can be learned effectively through neural networks. Moreover, aiming at obtaining the preset tracking performance, the prescribed performance control is integrated with the predefined-time control. In contrast to previous studies, the proposed scheme can not only constrain the tracking error rapidly to a prearranged vicinity of origin, but also ensure that the upper bound of convergence time can be adjusted in advance via a separate control parameter. In terms of the predefined-time stability theory, the boundedness of all system states can be proven within a predefined time. Finally, the availability and improved performances of the proposed control scheme are demonstrated by a numerical example and a single-link manipulator example.

Nonlinear Adaptive Neural Control of Power Converter‐Driven DC Motor System: Design and Experimental Validation

ABSTRACTThis article presents an intelligent adaptive neural control scheme to track the output speed trajectory in power converter‐driven DC motor system. The proposed technique integrates an adaptive polynomial‐neural network with a backstepping strategy to yield a robust control system for output tracking in DC motor. Such a unification of online neural network‐based estimation and adaptive control, results in effective regulation of the output across a wide load torque uncertainties, besides yielding a promising transient and steady‐state performance. The stability of the entire closed‐loop system is ensured through Lyapunov stability criterion. The efficacy of the proposed strategy is revealed through an extensive experimental investigation under various operating points during start‐up, step‐reference tracking, and external step‐load torque disturbances. The real‐time experimentation is conducted on a laboratory prototype of power converter‐driven DC motor of 200 W, using dspace DS1104 control board with MPC8240 processor. The results obtained confirm an improvement in the transient response of the output speed by significantly reducing the settling time to and yielding a steady state behavior with no peak over/undershoots during load disturbances, in contrast to other similar works presented in the literature intended for same the application.

Flight Control Based on Adaptive Output Feedback for Quadrotors Using Quaternions

Quadrotors are expected to play an active role in out-of-sight areas such as equipment inspection and transportation of supplies to disaster areas. However, ensuring stable and highly accurate automatic flights has become a significant challenge. Trajectory tracking control methods that combine adaptive output feedback control based on almost strictly positive real characteristics and backstepping strategy have been proposed for a quadrotor control system with nonlinearities. These methods have simple structures and are robust. However, existing adaptive control methods have the problem of singularities, owing to the use of Euler angles in the modeling of quadrotors. In this paper, we propose an adaptive control method that enables a wider range of attitude changes using quaternions. The effectiveness of the proposed method is validated through numerical simulations.

Adaptive fuzzy quantized prescribed performance synchronization of uncertain non-strict feedback chaotic systems with time-varying actuator failure

This paper addresses an adaptive fuzzy prescribed performance synchronization for a class of uncertain non-strict feedback chaotic systems subject to input quantization and time-varying actuator faults. The proposed approach utilizes fuzzy logic systems to estimate uncertainties. In addition, multiplicative and additive faults are considered simultaneously, which may occur either separately or simultaneously. To address the challenge, based on the backstepping scheme and a filter, an intermediate controller is conducted to compensate for the interference between actuator faults and quantification, in which a damping term and a positive time-varying function are introduced. Moreover, treating the error system as a constrained system, a simplified nonlinear mapping is employed to achieve asymmetric prescribed performance synchronization. Unlike traditional methods that rely on barrier Lyapunov functions and switch functions, the proposed approach eliminates the need for a switch function and extends the action scope to cover all synchronization errors. The analysis demonstrates that even if actuator faults and input quantization coexist, all signals in the closed-loop system remain bounded, and synchronization errors remain within the prescribed performance range. Finally, synchronization simulations are conducted on a nonlinear gyroscope system and a Non-autonomous chaotic Micro-Electro-Mechanical-System to reveal the validity of the proposed scheme.

Composite‐observer‐based asynchronous control for hidden Markov nonlinear systems with disturbances

SummaryIn this article, an asynchronous adaptive tracking control approach is presented for a type of hidden Markov jump nonlinear systems with external disturbances. In this joint jump process model, hidden Markov model signifies the dynamics of the actual system, whereas the signal emits from the detector symbolizes the transmitted information. This leads to the phenomenon of asynchronization between the modes of the system and that of the controller. Accordingly, an asynchronous observer is developed by using the mode information from the detector to develop an asynchronous control approach. The observer contains a disturbance estimation part, to compensate the unknown external inputs. Utilizing the backstepping scheme, a strict‐feedback asynchronous tracking controller is formulated, guaranteeing that all signals within the closed‐loop system are semi‐globally uniformly ultimately bounded in probability. Finally, the validity of the presented methodology is illustrated by means of a simulation example.

Trajectory tracking of a mobile robot manipulator using fractional backstepping sliding mode and neural network control methods

ABSTRACT In this paper, a fractional adaptive backstepping sliding mode control system based on the Caputo-Fabrizio derivative for a 2-DoF mobile robot manipulator is designed and described. The fractional dynamics of the system are obtained using the Atangana-Baleanu derivative and the Euler-LaGrange formalism, which include external disturbances, parametric uncertainties, and nonholonomic constraints. A fractional sliding mode control strategy is designed for trajectory tracking tasks. In order to compensate for the chattering phenomenon, the proposed controller is combined with a fractional backstepping strategy. Additionally, the Caputo-Fabrizio derivative is introduced to further reduce the chattering effects and improve the driver performance. A fractional adaptive control law is used to cope with the parametric uncertainties, while adding robustness to external disturbances. To further improve system performance, a tracking control strategy based on a fractional neural network is added. For a comparative analysis, the conventional adaptive neural network backstepping sliding mode control is implemented. Numerical simulations are described and discussed to validate the effectiveness of our control system for trajectory tracking tasks under different operating conditions such as trajectory changes and external disturbances. Our proposed control system and its traditional counterpart were tuned using the Cuckoo optimization approach.

Reinforcement learning‐based finite‐time cross‐media tracking control for a cross‐media vehicle under unknown dynamics and disturbances

AbstractThis study proposes a reinforcement learning‐based finite‐time cross‐media tracking control approach for a slender body cross‐media vehicle encountering unknown hydrodynamics, wind, and wave disturbances. Initially, a reinforcement learning framework consisting of the actor neural network and critic neural network is constructed. The critic neural network monitors the actions of the actor neural network and approximates the cost function, while the actor neural network estimates the unknown hydrodynamics and disturbances, minimising the cost function to optimise performance. Subsequently, the command filter featuring finite‐time convergence is formulated, effectively managing the corresponding filter error through a proposed error compensating signal. By integrating these techniques, a reinforcement learning‐based finite‐time control strategy is developed, circumventing the singularity issue inherent in traditional finite‐time backstepping strategies. Comparative analysis with existing methods demonstrates the strong robustness of the proposed scheme against unknown hydrodynamics and disturbances, ensuring finite‐time convergence of the system's states and optimising controller performance. Finally, simulations confirm the effectiveness and superiority of the presented approach.

Optimised backstepping control for the nonlinear strict-feedback system having unknown control dead-zone

In this article, the optimised backstepping (OB) strategy is extended to deal with the dead-zone control problem for a class of the nonlinear strict feedback systems. Since the dead-zone phenomenon is frequently encountered in the control of nonlinear strict feedback system, it is very necessary to consider the effect of dead-zone in the OB control. However, the published OB control methods are to rarely deal with the dead-zone problem because of the complex algorithm of reinforcement learning (RL). In this OB control, the dead-zone problem is effectively solved by utilising a simplified RL algorithm. For effective eliminating the effect of dead-zone, an adaptive compensation of dead-zone function's remainder is added to this RL. Since the RL under identifier-critic-actor architecture is implemented in every backstepping step, the requirement of complete dynamic acknowledge is released. Ultimately, the validity of this OB method is certified both theory and simulation.

Nonlinear robust sliding mode - Backstepping hybrid control for WECS -theoretical design and experimental evaluation

This paper proposes a new contribution in the field of optimizing control techniques for wind systems to enhance the quality of the energy produced in the grid. Although the Sliding Mode control technique, whether classical or involving the use of artificial intelligence, has shown interesting results, its main drawback lies in the oscillation phenomenon commonly referred to as “chattering.” This phenomenon affects the accuracy and robustness of the system, as well as the parametric variation of the system. In this work, we propose a solution that combines two nonlinear techniques based on the Lyapunov theorem to eliminate the chattering phenomenon. It is a hybrid approach between the Backstepping strategy and the Sliding Mode, aiming to control the active and reactive powers of the doubly fed induction generator (DFIG) connected to the electrical grid by two converters (grid side and machine side). This hybrid technique aims to improve the performance of the wind system in terms of precision errors, stability, as well as active and reactive power. The proposed solution has been validated in the Matlab & Simulink environment to assess the performance and robustness of the proposed model, as well as experimentally validated on a test bench using the DSPACE 1104 card. The obtained results are then compared with other techniques, demonstrating a significant improvement in performance.

Controlling the unpredictable: bifurcation and backstepping strategies in supply chain dynamics

Controlling the unpredictable: bifurcation and backstepping strategies in supply chain dynamics

Saturated stabilization of feed‐forward systems subject to lower‐order perturbations

AbstractThis article revisits saturated stabilization of the feed‐forward systems that are subject to lower‐order perturbations, with the purpose of providing new analysis approaches. To carry out the saturation reduction analysis, we do not use the existing time‐interval based contradiction approach, but propose a Lyapunov function method; to deal with the reduced system (the closed‐loop system that does not contain saturation any longer), we do not use the “adding a power integrator” backstepping scheme, but propose an approach which is established by jointly using the vector Lyapunov function theory, a matrix measure stability theory and the switching systems theory. As a result, a quite number of inequality computations can be avoided, and the stability conditions summarized in two analysis procedures can be expressed by directly using the system parameters. This article also shows that the established approaches are applicable to the uncertain feedforward systems subject to linear input perturbation and consequently, allows to present new stabilizing control laws for several intractable under‐actuated systems.

Event-Triggered Adaptive Neural Network Control for State-Constrained Pure-Feedback Fractional-Order Nonlinear Systems with Input Delay and Saturation

In this research, the adaptive event-triggered neural network controller design problem is investigated for a class of state-constrained pure-feedback fractional-order nonlinear systems (FONSs) with external disturbances, unknown actuator saturation, and input delay. An auxiliary compensation function based on the integral function of the input signal is presented to handle input delay. The barrier Lyapunov function (BLF) is utilized to deal with state constraints, and the event-triggered strategy is applied to overcome the communication burden from the limited communication resources. By the utilization of a backstepping scheme and radial basis function neural network, an adaptive event-triggered neural state-feedback stabilization controller is constructed, in which the fractional-order dynamic surface filters are employed to reduce the computational burden from the recursive procedure. It is proven that with the fractional-order Lyapunov analysis, all the solutions of the closed-loop system are bounded, and the tracking error can converge to a small interval around the zero, while the state constraint is satisfied and the Zeno behavior can be strictly ruled out. Two examples are finally given to show the effectiveness of the proposed control strategy.

Finite-Time Adaptive Event-Triggered Control for Full States Constrained FONSs with Uncertain Parameters and Disturbances

This article focuses the event-triggered adaptive finite-time control scheme for the states constrained fractional-order nonlinear systems (FONSs) under uncertain parameters and external disturbances. The backstepping scheme is employed to construct the finite-time controller via a series of barrier Lyapunov function (BLF) to solve that all the state constraints are not violated. Different from the trigger condition with fixed value, the event-triggered strategy is applied to overcome the communication burden of controller caused by the limited communication resources. By utilizing fractional-order Lyapunov analysis, all variables in the resulted system are proven to be bounded, and the tracking error converges to the small neighborhood around origin in finite time and without the Zeno behavior. Finally, the effectiveness of the proposed control scheme is verified by the simulation analysis of a bus power system.

Entirely Coupled Recurrent Neural Network-Based Backstepping Control for Global Stability of Power System Networks

In an interconnected power system network, global performance is affected by various unknown power system parameters subjected to system uncertainties. These unknown parameters in the control expression deteriorate the performance of the power system network. Therefore, these terms associated with the control expression must be estimated precisely. This paper proposes an adaptive backstepping scheme using an entirely coupled recurrent neural network (ECRNN) to estimate these control terms. Three continuous differentiable functions are used to design control input, virtual signals, and adaptive control laws to achieve global performance. The objective of ECRNN is to reduce the control complexity by estimating the associated nonlinear term in the control expression. It will facilitate the complex formulation of the controller and improve system performance. The robust functional estimation ability of ECRNN will make the system immune to uncertainties that may appear due to external disturbances. In ECRNN, feedback loops are added to each neuron layer to achieve additional estimation accuracy. The proposed adaptive law enhances the online weight update speed and accuracy. Verification of the proposed scheme is carried out in MATLAB/Simulink. It is also verified in the real-time digital simulator (RTDS) platform using the IEEE standard New England 39-bus, 10-machine power system model. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the existing limitations in the global performance of a multimachine power system network due to uncertainty in the system parameters. Uncertainties in the power system network primarily appeared due to penetration of renewable power sources, load uncertainty, or occurrence of an uncertain fault in the network. As power system networks are complex nonlinear interconnected systems, these perturbations in the generator states may cause economic losses, load demand uncertainty, or electric scarcity. Thus, a control scheme is required to address the global performance of such networks. This article proposes uniform ultimate bounded stability of synchronous generators in a multimachine power system network with a robust ECRNN-based backstepping control design. The other available technique has not adequately addressed the global performance under uncertainties. The efficacy of the proposed scheme is verified in a real-time environment via a real-time digital simulator which may be a feasible solution for designing excitation control for the synchronous machine in an extensive industrial network.

Multi-Channel Phase-Compensated Active Disturbance Rejection Control with an Improved Backstepping Strategy for Electro-Optical Tracking Systems

A multi-channel phase-compensated active disturbance rejection control (MPADRC) incorporating an improved backstepping strategy is proposed in this paper to handle the phase lag in the extended state observer (ESO) and the residual uncertainty in the system. Firstly, a multi-channel phase-compensated ESO (MPESO) is constructed by adding phase-advanced networks to all output channels of the ESO, which allows disturbances and system states to be compensated and feedback in a more timely manner, respectively. Then, to estimate and offset the residual uncertainty in the system, an improved backstepping control method is employed and a Lyapunov function is designed to verify the convergence of the error between the estimated and actual values of the residual uncertainty. After that, the improved backstepping control is combined with MPADRC, and comparisons with the conventional linear active disturbance rejection control (LADRC) are conducted for a range of cases. Finally, on an inertial stabilization platform in the electro-optical tracking system (ETS), simulation and experimental results verified the effectiveness of the proposed method.

Sensorless AC Current Control with Backstepping Design for a PWM AC-DC Converter

In this paper, a novel sensorless AC current control scheme is proposed for the design of PWM AC-DC converter. This design strategy deals with nonlinear backstepping controllers and AC current observer to achieve the purpose of current following. In general, PWM AC-DC converter design requires AC current measurement to achieve control goals, the backstepping observer employed estimates the AC current, and then nonlinear controllers based on backstepping design algorithm are developed to realize the sensorless AC current for the PWM AC-DC converter system. The proposed control scheme is not only to stabilize the PWM AC-DC converter system, but also to drive the current tracking error to converge to zero asymptotically. Furthermore, some simulation results are shown to illustrate excellent performances of the nonlinear backstepping control design scheme applied to a PWM AC-DC converter

Control of Uncertain High-Order Fully Actuated Strict-Feedback Systems: A Backstepping Approach With High-Gain Observer-Based Derivative Approximation.

In this article, a high-gain observer (HGO)-based differentiator is proposed to approximate the derivatives of the virtual control to ease the "explosion of complexity" problem in backstepping for the second-order strict-feedback systems (SOSFSs) and high-order strict-feedback systems (HOSFSs). Unlike the existing high-order command-filtered backstepping or extended dynamic surface control that needs to tune a large number of parameters, this proposed high-order HGO-based backstepping (HOHGOB) scheme can improve the derivative approximation performance by only tuning a single parameter, i.e., the observer gain. A further advantage of the proposed HOHGOB scheme, in addition to its simplicity and ease of implementation, is that the estimation error of the derivatives shrinks to zero as the observer gain grows to infinity. We have also rigorously established that the states of the closed-loop system achieve uniform ultimate boundedness under the designed high-order backstepping controller. Additionally, the output tracking error can be made arbitrarily small by the designer. The efficacy of the proposed scheme is numerically validated through a benchmark application to a single-link robot arm.

Nonlinear Control of a Wind Turbine System Connected to the Grid

This paper addresses the control problem of interconnecting a wind system based on a Permanent Magnet Synchronous Generator (PMSG) with the electrical grid. The control objectives include: (i) Regulating the PMSG speed to extract maximum power; (ii) Controlling the machine-side currents; (iii) Regulating the DC bus voltage; (iv) Ensuring Power Factor Correction (PFC) at the grid connection. The resolution of this control problem is based on the control of two loops on each side (machine and grid). This nonlinear control uses the Backstepping strategy for the inner loop on the machine side to regulate the currents, while the outer loop is for the speed regulation of the machine. On the grid side, the inner loop is for the current regulation to control the PFC, and the outer loop is for the regulation of the DC bus voltage. Simulation results demonstrate the effectiveness of this control strategy under various conditions, showing precise regulation and high-quality energy production.

Adaptive Fuzzy Nonsingular Fixed-Time Control for a Class of MIMO Nonstrict Feedback System

This paper studies the adaptive fuzzy practical fixed-time control design for MIMO nonlinear systems with non-strict feedback. The extant practical fixed-time stability criterion cannot obtain an accurate settling time upper bound or exists some constraints on parameters that lead to a conservative result. Thus a novel practical fixed-time stability criterion is proved in this paper to resolve the above problem and can obtain the precise value of the settling time upper bound. The control singular issue caused by the fixed-time stability criterion form is avoided by introducing adding power integration method. Compared with other approaches, this method is easy to apply in control design, and it's convenient to prove its effectiveness. And fuzzy logic system is adopted to approximate the unknown nonlinear items. Combining the proposed fixed-time stability criterion, traditional backstepping scheme, and fuzzy logic system, an adaptive practical fixed-time controller is proposed. The simulation of the actual physical system demonstrates the effectiveness of the controller and practical fixed-time criterion.

Dynamic Event-Triggered Reinforcement Learning Control of Stochastic Nonlinear Systems

This article investigates the event-triggered optimized tracking control problem for stochastic nonlinear systems based on reinforcement learning (RL). By using the backstepping strategy, an adaptive RL algorithm is performed under the identifier-critic-actor architecture to achieve event-triggered optimized control (ETOC). Moreover, a novel dynamically adjustable event-triggered mechanism is delicately designed, which adjusts the triggering threshold online to economize communication resources and reduce the computation burden. To overcome the difficulty that the virtual control signals are discontinuous due to the state-triggering, the virtual controllers are designed with the continuous sampling states signals, and the actual optimal controller is redesigned by using the triggered states in the last step. Furthermore, the proposed ETOC in this paper has significant advantages in terms of saving network resources because the event-triggered mechanism is employed in the sensor-to-controller channel and the event-sampled states are utilized to directly activate the control actions. Finally, it can be guaranteed that all signals of the stochastic system are bounded under the presented ETOC method. A simulation example is carried out to illustrate the effectiveness of the proposed ETOC algorithm.