Adaptive Backstepping Approach Research Articles

A non-identification adaptive backstepping approach to global output feedback tracking control of nonlinear systems with input quantization

A non-identification adaptive backstepping approach to global output feedback tracking control of nonlinear systems with input quantization

Observer-based adaptive neutral network inverse optimal containment control for nonlinear multiagent systems with input quantization

This article focuses on the issue of addressing an adaptive neural network (NN) inverse optimal containment control for nonlinear multiagent systems (MASs), which are subject to immeasurable states and quantized input signals simultaneously. To tackle this problem, we utilize a NN to model unknown agents and design a NN observer to estimate the immeasurable states. Additionally, we decompose the hysteretic quantized input into two bounded nonlinear functions. By employing the adaptive backstepping approach and inverse optimal principle, we formulate an adaptive NN inverse optimal containment control method. The developed inverse optimal containment control scheme guarantees that the controlled system is input-to-state stabilizable (ISS). Finally, we validate the effectiveness of our proposed control scheme through simulation results.

Robust fractional-order sliding mode tracker for quad-rotor UAVs: Event-triggered adaptive backstepping approach under disturbance and uncertainty

In this paper, tracking control of the quad-rotor UAVs in the presence of exterior perturbations and dynamical uncertainties is accomplished using an event-triggered adaptive backstepping fractional-order sliding mode control scheme. For this reason, tracking errors are considered as the difference between the actual and desired states of the quad-rotor system. Moreover, event-triggering errors are defined as the difference between tracking errors at time ti and tracking errors at time t. Afterward, a dynamical model of the quad-rotor system under external disturbance and model uncertainty is obtained based on the tracking errors’ states. Then, the fractional-order sliding mode surface based on the tracking errors and virtual control inputs is proposed to guarantee the convergence of desired tracking errors. Hence, to avoid the complexity in the control process, the virtual control inputs are presented as fractional-order integral-type laws to avoid high derivatives of virtual control inputs. In addition, the event-triggering condition is applied for backstepping fractional-order sliding mode control to prevent frequent periodic action of control inputs. Moreover, employing the backstepping control procedure and the Lyapunov stability concept, the convergence of fractional-order sliding surfaces is guaranteed. Later, the fractional-order adaptive laws are designed to estimate the unknown upper bounds of perturbations and uncertainties. Finally, to demonstrate the efficiency of the control algorithm recommended in this paper, the simulation results on MATLAB/Simulink environment are presented. A comparison between the control method in this paper and another existing technique is prepared to prove the productivity of performance of the offered control method on the quad-rotor system.

Adaptive tracking control for stochastic nonlinear state-constrained systems with input delay based on multi-dimensional Taylor network

In this paper, an adaptive tracking control strategy based on multi-dimensional Taylor network (MTN) is proposed for a class of stochastic nonlinear state-constrained systems with input delay. Firstly, to avoid constraint violation, the adaptive backstepping approach and barrier Lyapunov function (BLF) are combined in a unified framework. Then, a suitable auxiliary system with the same order as the considered system is constructed to deal with the effect of input delay. In addition, MTN is used to estimate unknown nonlinear functions during the design of the controller. Furthermore, with the help of the Lyapunov stability theorem, the controller presented in this paper can guarantee that all the closed-loop signals are bounded in probability, the system states remain in the defined compact sets, the output signal can track the reference signal successfully, and the tracking error is bounded by the expected bound. Finally, two examples are given to verify the effectiveness of the designed scheme.

A novel Lyapunov-based robust controller design for LCL-type shunt active power filters using adaptive sliding-mode backstepping approach

In this paper, a novel hybrid two-loop nonlinear controller is designed for stabilization and robust control of the LCL-type shunt active power filter (SAPF). To cope with the instability issue of the closed-loop system and the inherent resonance of the LCL coupling, backstepping, sliding mode and adaptive controllers are combined. DC link voltage of the grid-connected inverter is regulated in an outer control loop by determining a proper reference value for an inner loop. In addition to DC link voltage control, a major objective of the proposed closed-loop system is to make the grid current in phase with the grid voltage directly. Hence, active power filtering of the grid-connected inverter can be achieved without any current feedback from the local load. To stabilize the LCL-type SAPF in a wide range of changes, all uncertain parameters of the model including the DC link capacitor and equivalent impedances of the LCL coupling network are estimated by employing a proper Lyapunov function. For practical evaluation of the developed approach, the closed-loop system is implemented by using Texas Instruments’ digital signal processor (DSP-TMS28F335). Considering the application of an adaptive-robust nonlinear controller, it is proved that the system enjoys a stable and robust performance over the whole range of utilization, and it doesn't suffer from resonance issues of the LCL-type SAPFs. Moreover, considering the experimental results, it is observed that the steady-state error of the proposed nonlinear controller is zero in a wide range of operations.

Adaptive Output Consensus of Heterogeneous Nonlinear Multiagent Systems: A Distributed Dynamic Compensator Approach

Distributed dynamic compensators play a key role in the output consensus problem of heterogeneous nonlinear multi-agent systems. The existing distributed dynamic compensators require the compensators' information to be exchanged through communication networks, and to satisfy additional stability conditions in the controller design. This note proposes a distributed dynamic compensator to address the adaptive output consensus problem of heterogeneous nonlinear multi-agent systems with unknown parameters. The distributed dynamic compensator only requires the output information to be exchanged through communication networks. In addition, the distributed dynamic compensator converts the original consensus problem into asymptotic tracking problem of nonlinear systems, without requiring extra stability conditions in the literature. Then, well-established and standard control approaches are used to design tracking controllers and solve the standard tracking problems. The current work adopts the standard adaptive backstepping approach as an example to design an adaptive tracking controllers. It is further proved that all signals in the closed-loop system are globally uniformly bounded, and the proposed scheme enables the outputs of all agents to track the leader's signal asymptotically. A simulation is presented to illustrate the effectiveness of the design methodology.

Fixed-Time Anti-Synchronization of Unified Chaotic Systems via Adaptive Backstepping Approach

In this brief, the fixed-time anti-synchronization control problem is considered for two unified chaotic systems with uncertain parameters. In the process of controller design, adaptive technique is applied to approximate the uncertain constants occurred in the original systems and the piecewise functional approach is introduced to overcome the singularity problem appeared in the virtual control signals. Based on the Lyapunov theory and fixed-time control method, an adaptive fixed-time control scheme is designed. The designed controller achieves the anti-synchronization of two unified chaotic systems in a fixed-time. Theoretical analysis and simulation results demonstrate that the effectiveness of the control method.

Adaptive Interaction Control of Compliant Robots Using Impedance Learning

This paper presents an impedance learning-based adaptive control strategy for series elastic actuator (SEA)-driven compliant robots without the measurement of the robot-environment interaction force. The adaptive controller is designed based on the command filter-based adaptive backstepping approach, where a command filter is used to decrease computational complexity and avoid the requirement of high derivatives of the robot position. In the controller, environmental impedance profiles and robotic parameter uncertainties are estimated using adaptive learning laws. Through a Lyapunov-based theoretical analysis, the tracking error and estimation errors are proven to be semiglobally uniformly ultimately bounded. The control effectiveness is illustrated through simulations on a compliant robot arm.

Accurate Parking Control for Urban Rail Trains via Robust Adaptive Backstepping Approach

Nowadays, precise train parking has become a key technology of automatic train operation. Due to the high nonlinearities and various uncertainties existing in the dynamics of urban rail trains (URTs), it is challenging to develop an effective parking controller to achieve high-precision parking. To address this issue, a novel robust adaptive backstepping controller is proposed in the paper, where a robust term is employed to compensate for the system uncertainties caused by the brake shoe, and meanwhile several parametric adaption laws are equipped to estimate the uncertain system parameters as well as the external disturbances. The closed-loop stability of the controlled system is analyzed rigorously by virtue of the Lyapunov theory, and the effectiveness of the proposed control scheme in precise parking of URTs is demonstrated through numerical simulations.

A nonlinear adaptive excitation controller design for two‐axis models of synchronous generators in multimachine power systems to augment the transient stability during severe faults

This paper presents an excitation controller design process for multimachine power systems with synchronous generators using an adaptive backstepping approach to ensure robust performance against parametric uncertainties as well as to improve the transient stability during large disturbances. In this work, electrical dynamics of synchronous generators are described using two-axis models while excitations systems are represented as the IEEE Type II exciter which mainly captures electrical dynamics while swing equations are used to capture mechanical dynamics. The proposed adaptive backstepping control approach is then employed to derive the excitation control law. The proposed adaptive backstepping scheme uses all nonlinearities, which are mainly due to the interconnections and rotations of rotors in synchronous generators, within the dynamical models to improve the transient stability during severe disturbances. Furthermore, this excitation control scheme uses estimated values of parameters appearing in the dynamical models of power system which are estimated using adaptation laws based on real-time measurements and hence, it provides robustness against parametric uncertainties. The theoretical stability of the proposed scheme is assessed using the Lyapunov stability theory, that is, by checking the negative definiteness or semi-definiteness of the derivative of control Lyapunov functions (CLFs). Rigorous simulations are conducted on an IEEE 39-bus 10-machine test power system for evaluating the performance of the proposed scheme under different operating conditions. Simulation results clearly demonstrate the superiority of the adaptive backstepping excitation controller over existing nonlinear controllers including an existing adaptive backstepping excitation controller that is designed using the classical model of synchronous generators.

An Advanced Nonlinear Controller for the LCL-Type Three-Phase Grid-Connected Solar Photovoltaic System With a DC–DC Converter

In this article, an advanced nonlinear control scheme is proposed for a three-phase grid-connected inverter and a solar photovoltaic (PV) system connected dc–dc converter. The proposed control scheme is based on a nonlinear adaptive integral backstepping approach. The robustness of the proposed control scheme is achieved through maintaining stability of the overall system, extacting maximum power from the solar PV, and controlling active power. Moreover, the injection of less harmonic components into the grid, the superior performance against different atmospheric conditions, and external disturbances enduring capability are also key features of the controller. The stability of the overall system is achieved through the negative-definite control Lyapunov functions of the proposed control scheme. An adaptive law of the proposed control scheme on external disturbances provides the undergoing capability against the external disturbances. Maximum dc power from the solar PV system is obtained using the proposed control scheme on the dc–dc converter along with the incremental conductance algorithm. The proposed control scheme embedded in the three-phase grid-connected inverter with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> -type filter provides maximum active power in the presence of external disturbances, controls reactive power, and injects less harmonic current into the grid. The simulation results under different atmospheric conditions further demonstrate the robustness of the proposed control scheme. The laboratory scale experiments validate the superiority of the proposed control scheme.

Adaptive backstepping for distributed optimization

This paper presents an adaptive backstepping approach to distributed optimization for a class of nonlinear multi-agent systems with each agent represented by the parametric strict-feedback form. In particular, this paper does not assume known gradient functions of the local objective functions, and uses the measured gradient values depending on the agents’ real-time outputs instead. A stepwise method is presented to derive novel distributed adaptive optimization algorithms that steer the outputs of all the agents to the optimal solution of the total objective function. First, a novel distributed adaptive optimization algorithm is developed for first-order nonlinear uncertain multi-agent systems, supported by stability analysis and convergence proofs using Lyapunov arguments. Second, by means of Lyapunov arguments in the spirit of backstepping, a distributed adaptive optimization algorithm is presented for high-order strict-feedback systems with parametric uncertainty. Interesting extensions of the main result to practically important classes of systems with unknown virtual control coefficients, output feedback, and relative-measurement feedback are also discussed.

Event-triggered adaptive backstepping admittance control for cooperative manipulation

This paper proposes an adaptive control strategy for multiple uncertain manipulators handling an object cooperatively in the presence of environmental forces and limited communication. To address the same, external and internal admittance models are imposed between the object/environment and manipulators/object to limit the excess interaction and internal forces. Thereafter, an adaptive backstepping approach is dedicated to follow the admittance-generated trajectory and deal with the dynamic uncertainties of the manipulators. Based on the Lyapunov analysis, an event-triggered (ET) mechanism is further designed to alleviate the controller-to-robot communication burden and preserve the system stability in the cooperative task. The performance of the proposed controller is compared with two admittance-based control strategies while manipulating the object through circular and lemniscate trajectories. The well-known triggering conditions, fixed and relative thresholds, are utilized further to investigate the effectiveness of the designed triggering condition. The obtained results prove the superiority of the proposed controller over the different time-triggered and even-triggered control strategies.

Erratum to: “On position/force tracking control problem of cooperative robot manipulators using adaptive fuzzy backstepping approach” [ISA Trans. 70 (2017) 432-446

Erratum to: “On position/force tracking control problem of cooperative robot manipulators using adaptive fuzzy backstepping approach” [ISA Trans. 70 (2017) 432-446

Neuro‐adaptive distributed output‐feedback containment control for multiagent systems with nonstrict‐feedback nonlinear dynamics and input constraints

AbstractIn this article, distributed adaptive controllers are designed for containment control of multiagent systems (MASs) with high‐order nonlinear dynamics in nonstrict‐feedback form. To broaden the application horizon, the agents' dynamics are considered heterogeneous, and the control saturation is taken into account. Moreover, the agents' dynamics, as well as their full state information, are assumed unknown. An adaptive observer is designed in the first step for each agent to estimate the agents' states using available output measurements. An adaptive backstepping controller is then integrated with the observer to solve the containment control problem. The computational complexity of the controller is reduced by adopting the command filtered adaptive backstepping approach to the containment control of MASs. The effect of the input saturation is also compensated by employing an auxiliary system throughout the design procedure. The proposed control approach guarantees that the states of all agents are cooperatively semiglobally uniformly ultimately bounded and containment errors converge to a small neighborhood of the origin. Finally, the effectiveness of the presented control algorithm is confirmed by a simulation example.

Command Filtering and Barrier Lyapunov Function-Based Adaptive Control for PMSMs with Core Losses and All-State Restrictions

With the troubles of core losses and all-state confined to certain limitations which are the innate traits of permanent magnet synchronous motors (PMSMs), this article develops a command filtered adaptive backstepping approach to follow the track of PMSM’s desired rotor position. To begin with, the RBF neural network technique is utilized to get close to the uncharted nonlinear terms which existed in PMSM’s mathematical model. Meanwhile, an advanced adaptive command filter control methodology is constructed to avoid the computing explosion during the process of backstepping design. Furthermore, to make sure that all the state variables are confined into certain ranges, we employed the barrier Lyapunov function (BLF) at every step of the controllers construction. In addition, an error compensating mechanism is proposed to neutralize filtering errors and only one adaptive law is required. At last, simulation results bear out the superiority of the aforementioned control scheme.

Cascaded H-Bridge Inverters for UPS Applications: Adaptive Backstepping Control and Formal Stability Analysis

In this letter, an advanced adaptive controller is designed for N-cascaded H-bridge multilevel inverters, each fed by a DC voltage source. The studied system provides an added-value to Uninterruptable Power Supply applications, and is able to generate a precise sinusoidal voltage using a low dimensional LC filter. The main objectives of this letter are: i. generating a low THD sinusoidal voltage, ii. developing adaptive control laws able to regulate the system even with the presence of parameters' variations, and iii. proving the stability of the designed system using some tools from Lyapunov stability, Lasalle's invariance principle and persistency of excitation. This latter proves that the closed-loop control system is uniformly exponentially stable. To achieve these objectives, the adaptive backstepping approach is used. The performance of the system is checked with the use of MATLAB/SIMULINK/ SimPowerSystems environment, where the synthesized regulator meets its objectives.

Neural network adaptive backstepping fault tolerant control for unmanned airships with multi-vectored thrusters

This paper presents the fault tolerant control (FTC) of an unmanned airship with multiple vectored thrusters in the presence of model parameter uncertainties and unknown wind disturbances. A fault tolerant control based on constrained adaptive backstepping (CAB) approach, combined with a radial basis function neural network (RBFNN) approximation, is proposed for the airship with thruster faults. A wind observer is designed to estimate the bounded wind disturbances. An adaptive fault estimator is proposed to estimate the unknown actuator faults. A weighted pseudo inverse based control allocation is incorporated to reconstruct and optimize the practical control inputs of the failed airship under constraints of actuator saturation. Rigorous stability analysis shows that trajectory tracking errors of the airship position and attitude converge to the desired set through Lyapunov theory. Numerical simulations demonstrate the fault tolerant trajectory tracking capability of the proposed NN-CAB controller under the actuator faults, even in the presence of aerodynamic coefficient uncertainties, and unknown wind disturbances.

Finite Time Fractional-order Adaptive Backstepping Fault Tolerant Control of Robotic Manipulator

In this paper, fractional calculus theory is employed to inspect a finite time fault tolerant controller for robotic manipulators in the presence of uncertainties, unknown external load disturbances, and actuator faults, using fractional-order adaptive backstepping approach in order to achieve, fast response and high-precision tracking performance. Knowing the advantages of adaptive controllers an adaptive form of the above controller is then established to deal with the overall uncertainties in the system. The most important property of the proposed controller is that we do not need to have knowledge about the actuator fault, external disturbances and system uncertainties exist in system. In this study two important achievements are made. The first one is that the finite time convergence of closed-loop system is ensured irrespective of initial states values. The second one is that the effects of the actuator faults and other uncertainties are attenuated by the suggested controller. The performance of the suggested controller is then tested for a PUMA560 robot in which the first three joints are used. The simulation results validate the usefulness of the suggested finite-time fractional-order adaptive backstepping fault-tolerant (FOAB-FTC) controller in terms of accuracy of tracking, and convergent speed.

Comparative Analysis of Three Non-Linear Control Strategies for Grid-Connected PV System

This paper examines the limits of power injected to the grid for the photovoltaic (PV) system. Usually, the PV system injects to the grid active power with reactive power equal to zero. However, it can inject/absorb both powers according to the grid demand and maintain the stability of the grid characteristics (voltage and frequency). The proposed system consists of two main controllers: the DC/DC boost converter to track the possible maximum power from the PV panels and the grid-tied three-phase inverter. The controllers are designed based on a nonlinear adaptive backstepping approach, sliding mode control and the vector control strategy. The robustness of the proposed techniques is ensured by considering parametric uncertainties as well as external disturbances. In the proposed control strategies, the sliding mode control presents a small number of parameters than the other strategies. The reactive power is proposed by the grid manager which is controlled via the inverter. The simulation results indicate clearly the robustness of the sliding mode control in terms of injecting active and reactive power into the grid and improving power quality as compared to a backstepping controller and vector control.