Robust Adaptive Tracking Research Articles

Adaptive Robust Motion Control of Quadrotor Systems Using Artificial Neural Networks and Particle Swarm Optimization

Most of the mechanical dynamic systems are subjected to parametric uncertainty, unmodeled dynamics, and undesired external vibrating disturbances while are motion controlled. In this regard, new adaptive and robust, advanced control theories have been developed to efficiently regulate the motion trajectories of these dynamic systems while dealing with several kinds of variable disturbances. In this work, a novel adaptive robust neural control design approach for efficient motion trajectory tracking control tasks for a considerably disturbed non-linear under-actuated quadrotor system is introduced. Self-adaptive disturbance signal modeling based on Taylor-series expansions to handle dynamic uncertainty is adopted. Dynamic compensators of planned motion tracking errors are then used for designing a baseline controller with adaptive capabilities provided by three layers B-spline artificial neural networks (Bs-ANN). In the presented adaptive robust control scheme, measurements of position signals are only required. Moreover, real-time accurate estimation of time-varying disturbances and time derivatives of error signals are unnecessary. Integral reconstructors of velocity error signals are properly integrated in the output error signal feedback control scheme. In addition, the appropriate combination of several mathematical tools, such as particle swarm optimization (PSO), Bézier polynomials, artificial neural networks, and Taylor-series expansions, are advantageously exploited in the proposed control design perspective. In this fashion, the present contribution introduces a new adaptive desired motion tracking control solution based on B-spline neural networks, along with dynamic tracking error compensators for quadrotor non-linear systems. Several numeric experiments were performed to assess and highlight the effectiveness of the adaptive robust motion tracking control for a quadrotor unmanned aerial vehicle while subjected to undesired vibrating disturbances. Experiments include important scenarios that commonly face the quadrotors as path and trajectory tracking, take-off and landing, variations of the quadrotor nominal mass and basic navigation. Obtained results evidence a satisfactory quadrotor motion control while acceptable attenuation levels of vibrating disturbances are exhibited.

Disturbance observer-based robust adaptive control for uncertain actuated nonlinear systemwith disturbances

PurposeThe aim of this research paper is to design a disturbance observer (DO)-based robust adaptive tracking control of uncertain nonlinear system subject to unknown nonlinear disturbance.Design/methodology/approachTo achieve desired control objectives, i.e. nonlinear trajectory tracking and disturbance attenuation, firstly, a control scheme is designed based on the adaptive criteria integrated in sliding mode control (SMC). In the second step, the disturbance estimation criterion is designed followed by patching with the controller obtained in the first step. Following the control development, using the Lyapunov candidate function, the stability criterion is ensured by designing appropriate adaptive gains.FindingsIn this paper, a robust adaptive nonlinear tracking method is presented. The findings includes the design of adaptive gains for the control parameters involved in the robust SMC technique, i.e. adaptive criterion is designed for the switching gain as well as for the gain used in sliding mode surface. Furthermore, a disturbance estimation criterion is developed to attenuate nonlinear disturbances with variable frequency and magnitude. Finally, the disturbance estimation scheme is combined with the control technique to obtain DO-based control (DOBC) algorithm.Practical implicationsSliding mode control is a powerful robust control method. And, combining it with the DO achieves the control objectives of plants subject to disturbances and uncertainties. However, usually the uncertainties and disturbances are unknown and time varying. Thus, during practical implementation, designing the standard SMC is a challenging task due to the constant gains involved in the control design. Hence, it is important to have a criterion which adapts to the varying dynamics of plants due to the uncertainties and disturbances for achieving practical implementation of the control system.Originality/valueSliding mode control has been widely used for achieving the desired control objectives and robustness in the close-loop nonlinear systems. Besides, the SMC technique has been combined with the DOs as well. However, mostly the ideal conditions were considered during these developments, which required the control gains to be designed simply by manual tuning appropriately. However, by considering the real-time dynamics, uncertainties and disturbances, the constant control gain criteria can fail. Furthermore, due to external and internal disturbances, the model plant can vary with time. Thus, it is important to design the adaptive criteria for the control gains in DOBC schemes.

Robust adaptive formation tracking of autonomous surface vehicles with guaranteed performance and actuator faults

This paper investigates a performance-guaranteed formation tracking problem of autonomous surface vehicles (ASVs) under uncertain environments. Especially, model uncertainties, external disturbances and actuator faults exist simultaneously. Based on graph theory and adaptive techniques, a novel two-layer robust adaptive fault-tolerant formation scheme is developed. In kinematic layer, a transformation is made to get a performance unconstrained problem and an adaptive control strategy is incorporated to stabilize transformed errors. In kinetic layer, two types of robust adaptive fault-tolerant formation controllers, i.e. the fault-based one and the fault-unknown one, are designed for different fault scenarios. These controllers share the same structure of single-parameter updating laws to adjust adaptive parameters. It is shown that: 1) using the proposed formation scheme with either designed fault-tolerant controller, desired formation configurations of ASVs are achieved if the interaction topology is connected and control parameters satisfy given conditions; 2) prescribed formation tracking performance can be ensured and all error signals are guaranteed to be uniformly ultimately bounded; 3) a trade-off between two designed controllers exists, that is although the assumption for fault-unknown controller is weaker, larger control parameters are required to behave like fault-based one. Simulations and comparisons are provided to illustrate the effectiveness of theoretical results.

Robust adaptive asymptotic trajectory tracking control for underactuated surface vessels subject to unknown dynamics and input saturation

Robust adaptive asymptotic trajectory tracking control for underactuated surface vessels subject to unknown dynamics and input saturation

Quantized-states-based adaptive control against unknown slippage effects of uncertain mobile robots with input and state quantization

An adaptive tracking design strategy based on quantized state feedback is developed for uncertain nonholonomic mobile robots with unknown wheel slippage effects. All state variables and control torques are assumed to be quantized by the state and input quantizers, respectively, in a network control environment. Thus, the quantized state feedback information is only available for the tracking control design. An approximation-based adaptive controller using quantized states is recursively designed to ensure the robust adaptive tracking against unknown wheel slippage effects where the quantized-states-based adaptive mechanism is derived to compensate for unknown wheel slippage effects, system nonlinearities, and quantization errors. The boundedness of the quantization errors and estimated parameters in the closed-loop system is analyzed by presenting some theoretical lemmas. Based on these lemmas, we prove the uniform ultimate boundedness of closed-loop signals and the convergence of the trajectory tracking error in the presence of wheel slippage effects. Simulations verify the effectiveness of the resulting tracking scheme.

Robust adaptive tracking control of UMSVs under input saturation: A single-parameter learning approach

This paper investigates the robust adaptive trajectory tracking control problem for unmanned marine surface vessels (UMSVs) subject to nonparametric uncertainties and external disturbances under input saturation. The non-smooth saturation nonlinearity is replaced by the Gaussian error function. The lumped uncertain term including nonparametric uncertainties, external disturbances and approximation error is formulated by the linear parameterization-like form with a single unknown parameter. Combining the parameter adaptive technique with backstepping design tool, single parameter learning-based tracking control schemes are developed, which involves both full state feedback and output feedback control. The theoretical analysis indicates that under our proposed schemes, all signals in the closed-loop trajectory tracking control system are bounded. Simulation results and comparison illustrate the effectiveness of the developed schemes.

Robust Adaptive Tracking Control for Hypersonic Vehicle Based on Interval Type-2 Fuzzy Logic System and Small-Gain Approach.

This paper presents a novel robust adaptive tracking control method for a hypersonic vehicle in a cruise flight stage based on interval type-2 fuzzy-logic system (IT2-FLS) and small-gain approach. After the input-output linearization, the vehicle model can be decomposed into two uncertain subsystems by considering matching disturbances and parametric uncertainties. For each subsystem, an interval type-2 Takagi-Sugeno-Kang fuzzy logic system (IT2-TSK-FLS) is then employed to approximate the unavailable model information. Following the idea of a small-gain approach, a composite feedback form for each subsystem is constructed, based on which the final robust adaptive tracking control law is developed. Rigorous stability analysis shows that all signals in the derived closed-loop system are kept uniformly ultimately bounded (UUB). The main contribution of this paper is that the proposed control law for the hypersonic vehicle is with only two adaptive parameters in total which can greatly alleviate the computation and storage burden in practice; meanwhile its superiority over the conventional minimal-learning-parameter (MLP)-based one is specifically illustrated. Comparative numerical simulations of three cases demonstrate the effectiveness of our proposed control method with respect to complicated uncertainties.

Robust adaptive estimation and tracking control for perturbed cyber-physical systems against denial of service

This paper is concerned with the adaptive state observation and resilient control problem for a class of perturbed cyber-physical system against denial of service (DoS) attacks. An adaptive observer is firstly constructed to observe the compromised states under DoS attacks. Then based on the estimated sates, a resilient control strategy is developed to remedy the negative influence of DoS attacks and perturbations. By employing linear matrix inequality and Lyapunov stability theory, one can guarantee that the system states can track the desired signals of reference systems with time going to infinity. Furthermore, the state observation errors are guaranteed to remain a high accuracy. An aircraft system with different attack forms and attack modes is given to verify the effectiveness of designed adaptive observer and control methods.

Adaptive robust dynamic surface asymptotic tracking for uncertain strict-feedback nonlinear systems with unknown control direction

For strict-feedback nonlinear systems (SFNSs) with unknown control direction, this paper synthesizes an asymptotic tracking controller by a combination of the dynamic surface control (DSC) technique, the Nussbaum gain technique (NGT) and fuzzy logic systems (FLSs). The SFNSs under study feature unknown nonlinear uncertainties and external disturbances. By utilizing the DSC technique with nonlinear filters, the issue of ‘differential explosion’ is obviated, in which the adaptive laws are constructed to conquer the effect of unknown functions. The FLSs are exploited to cope with uncertainties without any prior conditions of the ideal weight vectors and the approximation errors. In addition, by introducing the NGT, the unknown control direction problem is solved. Compared with the existing results, the proposed design procedure is able to simultaneously overcome the ‘differential explosion’ and the unknown control direction problems, and asymptotic tracking is accomplished. At the end, a second-order numerical system and a more realistic Norrbin nonlinear mathematical model are applied to confirm the feasibility of the design procedure.

Adaptive Robust Tracking Control for Hybrid Models of Three-Dimensional Bipedal Robotic Walking Under Uncertainties

Abstract This paper introduces an adaptive robust trajectory tracking controller design to provably realize stable bipedal robotic walking under parametric and unmodeled uncertainties. Deriving such a controller is challenging mainly because of the highly complex bipedal walking dynamics that are hybrid and involve nonlinear, uncontrolled state-triggered jumps. The main contribution of the study is the synthesis of a continuous-phase adaptive robust tracking control law for hybrid models of bipedal robotic walking by incorporating the construction of multiple Lyapunov functions into the control Lyapunov function. The evolution of the Lyapunov function across the state-triggered jumps is explicitly analyzed to construct sufficient conditions that guide the proposed control design for provably guaranteeing the stability and tracking the performance of the hybrid system in the presence of uncertainties. Simulation results on fully actuated bipedal robotic walking validate the effectiveness of the proposed approach in walking stabilization under uncertainties.

Robust adaptive radial‐basis function neural network‐based backstepping control of a class of perturbed nonlinear systems with unknown system parameters

SummaryIn this article, the robust adaptive output tracking control problem is addressed for a class of nonlinear systems with nonlinear dynamics and unknown system parameters. The nonlinear dynamics including internal parameter uncertainties and external disturbances are formulated as time‐varying state/input‐dependent perturbations. Radial‐basis function neural networks (RBFNNs) are developed to approximate the perturbations. A robust adaptive RBFNN‐based output feedback control strategy against the perturbations is developed by using backstepping technique with immeasurable states and without knowing any system parameter. Based on Lyapunov stability theorem, the asymptotic output tracking results of the closed‐loop nonlinear system are obtained in the presence of perturbations, immeasurable states, and unknown system parameters. The efficacy of the proposed adaptive RBFNN‐based output feedback control strategy is validated by simulation in a DC–DC buck converter system.

Adaptive Robust Trajectory Tracking Control of Multiple Quad-Rotor UAVs with Parametric Uncertainties and Disturbances.

Recently, formation flying of multiple unmanned aerial vehicles (UAVs) found numerous applications in various areas such as surveillance, industrial automation and disaster management. The accuracy and reliability for performing group tasks by multiple UAVs is highly dependent on the applied control strategy. The formation and trajectories of multiple UAVs are governed by two separate controllers, namely formation and trajectory tracking controllers respectively. In presence of environmental effects, disturbances due to wind and parametric uncertainties, the controller design process is a challenging task. This article proposes a robust adaptive formation and trajectory tacking control of multiple quad-rotor UAVs using super twisting sliding mode control method. In the proposed design, Lyapunov function-based adaptive disturbance estimators are used to compensate for the effects of external disturbances and parametric uncertainties. The stability of the proposed controllers is guaranteed using Lyapunov theorems. Two variants of the control schemes, namely fixed gain super twisting SMC (STSMC) and adaptive super twisting SMC (ASTSMC) are tested using numerical simulations performed in MATLAB/Simulink. From the results presented, it is verified that in presence of disturbances, the proposed ASTSMC controller exhibits enhanced robustness as compared to the fixed gain STSMC.

High-order fully actuated system approaches: Part V. Robust adaptive control

A type of high-order fully actuated (HOFA) systems with both nonlinear uncertainties and time-varying unknown parameters is considered, and a direct approach for the designs of robust adaptive stabilising controllers and robust adaptive tracking controllers is proposed based on the Lyapunov stability theory. The established controller is composed of three parts, the basic part cancels the known nonlinearities in the system and simultaneously assigns the linear dominant term in the closed-loop system, the robustness part overcomes the effects of the nonlinear uncertainties in the system, and the adaptation part adjusts online the controller to suit the effect of the unknown time-varying parameter vector. The proposed controller guarantees that the tracking error of the state to a given signal and the estimation error of the parameter vector finally converge globally into a bounded ellipsoid. Particularly, in the case that the unknown parameter vector is constant, an adaptive scheme that enables global asymptotical tracking is presented. An example demonstrates the effect of the proposed approach.

Robust Adaptive Trajectory Tracking Control Based on Sliding Mode of Electrical Wheeled Mobile Robot

Robust Adaptive Trajectory Tracking Control Based on Sliding Mode of Electrical Wheeled Mobile Robot

Robust adaptive trajectory tracking of nonlinear systems based on input-to-state stability tracking control Lyapunov functions

Abstract In this paper, we propose a trajectory-tracking controller for input-affine nonlinear systems, which guarantees robustness in the presence of both input uncertainties and external disturbances. The framework of input-to-state stability tracking control Lyapunov function(ISS-TCLF) is employed to construct a disturbance attenuation tracking controller. Then, we introduce a Lyapunov-based adaptive compensator to mitigate the effect of input uncertainties. The proposed controller guarantees that (i) the closed-loop system is input-to-state stable, and (ii) the tracking error converges to zero if the disturbance is a constant signal. Simulation results of a wheeled mobile robot validate the effectiveness of the proposed controller.

Trajectory tracking of a quadrotor using a robust adaptive type-2 fuzzy neural controller optimized by cuckoo algorithm

This paper proposes an adaptive and robust adaptive control strategy based on type-2 fuzzy neural network (T2FNN) for tracking the desired trajectories of a quadrotor. The designed methods can control both the position and the orientation of a quadrotor. Contrary to common sliding mode controllers (SMCs), the robust adaptive trajectory tracking scheme presented here is based on SMC with exponential reaching law; which helps reduce the phenomenon of chattering. Moreover, parameters including the gains of sliding surfaces, are optimized by cuckoo optimization algorithm (COA), and the results are compared with those obtained by genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization (ACO). The designed methods in this study are called adaptive T2FNN controller and the exponential SMC (ESMC)-T2FNN. The law for updating the T2FNN is obtained online by using the Lyapunov stability theory. Considering undesired factors such as uncertainties, external disturbances and control signal saturation, the results of our controllers are compared with those of the adaptive type-1 fuzzy neural network controller (T1FNN) and ESMC-T1FNN. The extensive simulations demonstrate the effectiveness of the proposed COA-based ESMC-AT2FNN approach compared to the other tested techniques (i.e. GA, PSO and ACO) in terms of the improved transient and steady-state trajectory-tracking performance. The mean and standard deviation values concerning the COA are obtained through statistical analyses at 0.00006173 and 0.000092, respectively. This paper also examines the complexity of COA in optimizing the trajectory tracking control of quadrotor and investigates the effects of COA parameters on optimization results. The stable performance of the cuckoo algorithm is demonstrated by varying its parameters and analyzing the obtained results. These results also show the convergence of COA for the considered problem.

Adaptive Asymptotic Tracking Control of Uncertain Nonlinear Systems Based on Taylor Decoupling and Event-Trigger

This article studies the robust adaptive asymptotic tracking control problem for uncertain nonlinear systems with event-triggered inputs. Contrary to the existing results, a novel nonaffine nonlinear control input separated design scheme is developed based on the Taylor decoupling technique instead of the previous approximation ways. Correspondingly, the augmented dimension parameter updated laws and the unknown bound estimation of the compounded disturbance with a positive continuous integrable function are skillfully introduced. Also, by introducing a suitable decreasing function of tracking error variables, an improved adaptive event-triggered mechanism is constructed to achieve the asymptotic tracking and the communication load can be effectively alleviated. Moreover, it is shown that all the signals in the closed-loop system are uniformly bounded and the tracking errors converge to zero in a preset compact set. Finally, the validity of the proposed method is illustrated by simulation on an inverted pendulum model.

Geometric robust adaptive control for satellite attitude tracking with reaction wheels

This study proposes a new robust adaptive tracking controller for satellite attitude dynamics with reaction wheel assembly. With the attitude kinematics represented by rotation matrix, the attitude control system is formulated to accommodate bounded disturbances and uncertain moment of inertia. The associated error dynamics are developed directly in SO(3) from geometric mechanics. Almost global asymptotic stability is formally proved in the sense of Lyapunov by using the geometry. The proposed controller is then applied to both numerical simulations and hardware experiments. It works well for our own developed spacecraft testbed for three experimental scenarios, even with disturbances/uncertainties caused by offsets of the center of mass and air-bearing. The selection of proportional gain dominantly affects the characteristics of attitude tracking. According to numerical simulations and hardware experiments, the proposed controller performs well, even when the measurement accuracy of angular velocity is low.

Robust adaptive motion tracking of piezoelectric actuated stages using online neural-network-based sliding mode control

Robust and precise motion tracking for micro-electro-mechanical systems in the presence of inherent nonlinearity and external disturbance is of great importance in many applications. Due to high sensitivity to environmental variations, the entire model or some parameters of the system tend to change unexpectedly. Existing offline nonlinearity models are computationally intensive and may be not suitable under system perturbations. In this work, for a class of piezoelectric actuated (PEA) system, a new online neural-network-based sliding mode control (OLNN-SMC) scheme is developed to obtain robust adaptive precision motions. The nonlinearity of the PEA system is identified online and compensated using singularity-free neural networks (NNs). To alleviate the residual NN approximation errors and meanwhile maintain robust stability under external disturbance, a feedback sliding-mode is synthesized into the control law. Considering unknown and varying disturbances, an adaptive mechanism is designed to achieve robust adaptive motion tracking. The controller is implemented and evaluated through experiments on a PEA platform. Results show that the proposed OLNN-SMC is superior to existing proportional-integral-derivative control with disturbance observer (PID+DOB) and adaptive sliding mode control (ASMC) in terms of sinusoidal tracking and disturbance rejection. In particular, the root-mean-square (RMS) errors for sinusoidal tracking at 0.1–10 Hz using the proposed OLNN-SMC are reduced by 83.5% compared with the cases using PID+DOB or ASMC.

Robust adaptive finite-time attitude tracking control of a 3D pendulum with external disturbance: numerical simulations and hardware experiments

The three-degree-of-freedom (3D) pendulum has been used as a benchmark in the field of nonlinear dynamics and control. Nonetheless, the attitude control of 3D pendulum is still an open problem presently since some issues remain not well addressed. In this paper, a robust adaptive finite-time attitude control method is proposed for the attitude tracking control of a 3D pendulum with external disturbance. First, a baseline finite-time attitude controller is designed based on the adding a power integrator technique. Then, a finite-time disturbance observer is designed to exactly estimate the unknown external disturbance. Finally, a robust adaptive finite-time attitude controller is constructed by integrating the baseline finite-time attitude controller with the finite-time disturbance observer. The proposed robust adaptive finite-time attitude controller can guarantee the global finite-time stability of the whole closed-loop system even in the presence of external disturbance owing to the feedforward dynamic compensation. Numerical simulations and hardware experiments are both performed to illustrate the effectiveness and superiority of the proposed control method.