Adaptive Tracking Control Approach Research Articles

Novel adaptive neural networks control with event-triggered for uncertain nonlinear system

In this paper, the issue of developing an event-triggered adaptive tracking controller for a class of uncertain nonlinear system is investigated. The radial basis function neural networks (RBFNN) is employed to approximate the uncertain parts, where the time-varying approximation errors are combined. However, it causes the dimensionality of RBFNN’s weight vector larger, which means more network resources are needed. It is a tough task to develop an adaptive tracking controller for nonlinear systems suffered network resources constraint. To save network resources, an event-triggered scheme is developed. Then, with the aid of adaptive backstepping technique, an event-triggered adaptive tracking control approach is established. With the developed event-triggered adaptive tracking controller, the boundedness of all signals in the closed-loop system can be guaranteed. Moreover, it can achieve the balance of tracking performance and the utilization of network resources. Finally, two simulation examples are given to verify the effectiveness of the proposed control scheme.

Adaptive robust servo constraint tracking control for an underactuated quadrotor UAV with mismatched uncertainties

In this research, to achieve the altitude and attitude tracking control of an underactuated quadrotor UAV with mismatched uncertainties, based upon Udwadia–Kalaba theory, a novel adaptive robust tracking control approach is proposed and which will be designed in two steps. First, aiming at the uncertain and underactuated quadrotor UAV, regardless of initial constraint deviation and mismatched uncertainties, a nominal control is constructed through transforming the desired trajectories into corresponding servo constraints; second, for the mismatched uncertainties, we decompose them into two parts, i.e. the matched part and mismatched part, and the mismatched part will “vanish” during the stability analysis of proposed adaptive robust controller. Eventually, with such a decomposition technique, the large mismatched uncertainties can be addressed properly and the burden of controller design will be reduced to a certain degree. In addition, two deterministic robust control performances are also guaranteed by our proposed approach. The simulation results have shown a good robustness and tracking precision of our proposed scheme for quadrotor UAV.

Adaptive multi-dimensional Taylor network tracking control for a class of switched nonlinear systems with input nonlinearity

In this paper, a multi-dimensional Taylor network (MTN)-based adaptive tracking control approach is proposed for a class of switched nonlinear systems with input nonlinearity. Firstly, the input nonlinearity is assumed to be bounded by a sector interval. Secondly, with the help of MTNs approximating the unknown nonlinear functions, a novel adaptive MTN control scheme has the advantages of low cost, simple structure and real time feature is developed via backstepping technique. It is shown that the tracking error finally converges to a small domain around the origin and all signals in the closed-loop system are bounded. Finally, two examples are given to demonstrate the effectiveness of the proposed control scheme.

Adaptive tracking control for nonlinear time-delay systems with time-varying full state constraints

This paper presents an adaptive tracking control approach for a class of uncertain nonlinear strict-feedback systems subject to time-varying full state constraints and time-delays. To stabilize such systems, an adaptive tracking controller is structured by combining the neural networks and the backstepping technique. To guarantee all states do not violate the time-varying constraint sets, the appropriate time-varying Barrier Lyapunov functions are employed at each stage of the backstepping procedure. By using the Lyapunov-Krasovskii functionals, the effect of time delay is eliminated. It is proved that the output follows the desired signal well without violating any constraints, and all the signals in the closed-loop system are semiglobal uniformly ultimately bounded by using the Lyapunov analysis. Finally, a comparison study simulation is provided to illustrate the effectiveness of the proposed control strategy.

Adaptive neural tracking control for non-affine nonlinear systems with finite-time output constraint

In this paper, an adaptive neural tracking control approach is presented for a class of non-affine nonlinear systems with finite-time output constraint. The non-affine form of the original system is converted to the affine form by means of the mean value theorem. To constraint the output tracking error within a predefined boundary in finite time, a modified performance function, i.e., finite-time performance function, is introduced. During the process of controller design, the dynamic surface control is employed to handle the ‘explosion of complexity’ problem occurred in the conventional backstepping method. According to the approximation of radial basis functions neural networks, an adaptive neural control scheme is developed which guarantees that the output tracking error is preserved within a specified prescribed performance and all the signals in closed-loop system are bounded by appropriately choosing the design parameters. The stability of the closed-loop system is proved by Lyapunov stability analysis and the simulation results are proposed to demonstrate the effectiveness of the developed control approach.

Observer-based adaptive neural tracking control for a class of stochastic nonlinear systems

In this paper, an observer-based adaptive neural tracking control approach is proposed for a class of stochastic nonlinear systems with immeasurable states. The radial basis function neural networks (RBFNNs) are used to approximate the unknown nonlinear functions, and a linear reduced-order state observer is designed for estimating the unmeasured states. Based on the designed the state observer, an adaptive neural output feedback control approach is developed via backstepping control design. It is shown that the proposed controller ensures that all signals of the closed-loop system remain bounded in probability, and the tracking error converges to an arbitrarily small neighbourhood around the origin in the sense of mean quartic value. Finally, two examples are given to illustrate the effectiveness of the proposed design approach.

Adaptive neural tracking control for a class of non‐lower triangular non‐linear systems with dead zone and unmodelled dynamics

This study presents the disturbance observer-based adaptive neural tracking control approach for non-linear systems in non-strict-feedback form. The design difficulties including unmodelled dynamics and non-strict-feedback form are handled by resorting to a dynamic signal and the variable separation approach, respectively. A disturbance observer is constructed to cope with the effect of time varying disturbance. Neural networks are directly utilised to cope with the completely unknown non-linear functions and stochastic disturbances existing in systems. It is shown that the designed adaptive controller can guarantee that all the signals remain bounded and the desired signal can be tracked with a small domain of the origin. A numerical example is presented to illustrate the effectiveness of the proposed approach and an example of a real plant for one-link manipulator is provided to show the feasibility of the newly designed controller scheme.

Decentralized adaptive multi‐dimensional Taylor network tracking control for a class of large‐scale stochastic nonlinear systems

SummaryThis paper investigates the problem of adaptive multi‐dimensional Taylor network (MTN) decentralized tracking control for large‐scale stochastic nonlinear systems. Minimizing the influence of randomness and complex nonlinearity, which increases computational complexity, and improving the controller's real‐time performance for the stochastic nonlinear system are of great significance. With combining adaptive backstepping with dynamic surface control, a decentralized adaptive MTN tracking control approach is developed. In the controller design, MTNs are used to approximate nonlinearities, the backstepping technique is employed to construct the decentralized adaptive MTN controller, and the dynamic surface control technique is adopted to avoid the “explosion of computational complexity” in the backstepping design. It is proven that all the signals in the closed‐loop system remain bounded in probability, and the tracking errors converge to a small residual set around the origin in the sense of a mean quartic value. As the MTN contains only addition and multiplication, the proposed control method is more simplified and of good real‐time performance, compared with the existing control methods for large‐scale stochastic nonlinear systems. Finally, a numerical example is presented to illustrate the effectiveness of the proposed design approach, and simulation results demonstrate that the method presented in this paper has good real‐time performance and control quality, and the dynamic performance of the closed‐loop system is satisfactory.

Bounded adaptive output feedback tracking control for flexible-joint robot manipulators

This paper presents a bounded adaptive output feedback tracking control approach for flexible-joint robot manipulators with parametric uncertainties and bounded torque inputs, from a systematic perspective of different (weak or strong) joint flexibilities. The singular perturbation theory and integral manifold concept are applied to decouple the dynamics of flexible-joint robot manipulators into a slow subsystem and a fast subsystem. A class of saturation functions is used to make the control law bounded, ensuring the torque control inputs are within the output limitation of the joint actuators. An adaptive control law of the projection type is adopted to handle the feed-forward term of the slow sub-controller with parametric uncertainties. Meanwhile, an approximate differential filter and a high-gain observer are utilized in the slow and fast subsystems, respectively, to estimate the unmeasurable states, making the complete closed-loop control with only position measurements of motors and links. Importantly, a corrective control scheme is proposed to break through the traditional singular perturbation approach and to make it feasible for robot manipulators with strong joint flexibility. Furthermore, an all-round and strict stability analysis of the whole control system is given. Finally, simulation results verify the superior dynamic performance of the proposed approach.

Adaptive tracking control for nonlinear time-varying delay systems with full state constraints and unknown control coefficients

This paper proposes an adaptive tracking control approach for a class of nonlinear state-constrained and time-varying delay systems with unknown time-varying control coefficients. As far as we know, there is no control method for such systems at present. To stabilize such a class of systems, the neural networks and a backstepping technique are utilized to structure an adaptive tracking controller. The Nussbaum gain technique is utilized to solve the problem of unknown time-varying control coefficients, and the Lyapunov–Krasovskii functionals (LKFs) are employed to eliminate the effect of unknown time-varying delays. In addition, the states are guaranteed to remain within their constraint sets based on the Barrier Lyapunov functions (BLFs). Finally, it can be proved that all signals in the closed-loop systems are bounded, the state constraints are never violated and the tracking errors fluctuate within the predetermined compact range around the zero. The simulation results are provided to illustrate the effectiveness of the proposed control strategy.

Adaptive tracking control of nonlinear systems with dynamic uncertainties using neural network

ABSTRACTIn this paper, an adaptive neural tracking control approach is proposed for a class of nonlinear systems with dynamic uncertainties. The radial basis function neural networks (RBFNNs) are used to estimate the unknown nonlinear uncertainties, and then a novel adaptive neural scheme is developed, via backstepping technique. In the controller design, instead of using RBFNN to approximate each unknown function, we lump all unknown functions into a suitable unknown function that is approximated by only a RBFNN in each step of the backstepping. It is shown that the designed controller can guarantee that all signals in the closed-loop system are semi-globally bounded and the tracking error finally converges to a small domain around the origin. Two examples are given to demonstrate the effectiveness of the proposed control scheme.

Adaptive control of a 7-DOF exoskeleton robot with uncertainties on kinematics and dynamics

In this paper, we propose a new adaptive visual tracking control approach based on sliding mode control in Cartesian space applied to an exoskeleton robot with uncertain kinematics and dynamics, taking into account uncertainties in visual system (camera) parameters. The adaptation of kinematic uncertainties is based on a filtered regressor kinematic matrix, whereas, the adaptation of dynamic uncertainties is based on a Time Delay Estimation approach. This is performed considering the Time Delay Error (TDR) to provide a control action capable of following the designed functional therapy tasks. A new recursive controller is combined with TDE in order to estimate the TDR and limit its effect. The proposed strategy does not need the accurate dynamic and kinematic models of the exoskeleton. The update laws are designed using Lyapunov theory to solve the adaptation problem methodically and to show the stability of the robot system. Experimental results confirm the effectiveness and feasibility of the designed approach.

(1606-3017) ADAPTIVE FUZZY TRACKING CONTROL FOR A CLASS OF PERTURBED NONLINEARLY PARAMETERIZED SYSTEMS USING MINIMAL LEARNING PARAMETERS ALGORITHM

In this paper, an adaptive fuzzy tracking control approach is proposed for a class of single-inputsingle-output (SISO) nonlinear systems in which the unknown continuous functions may be nonlinearlyparameterized. During the controller design procedure, the fuzzy logic systems (FLS) in Mamdani type are applied to approximate the unknown continuous functions, and then, based on the minimal learning parameters (MLP) algorithm and the adaptive backstepping dynamic surface control (DSC) technique, a new adaptive fuzzy backstepping control scheme is developed. The main advantages of our approach include: (i) unlike the existing results which deal with the nonlinearlyparameterized functions by using the separation principle, the nonlinearly parameterized functions are lumped into the continuous functions which can be approximated by using the FLS, (ii) only one parameter needs to be adjusted online in controller design procedure, which reduces the online computation burden greatly, and our development is able to eliminate the problem of ''explosion of complexity inherent in the existing backstepping-based methods. It is proven thatthe proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error is smaller than a prescribed error bound. Finally, two examples are used to show the effectiveness of the proposed approach.

Adaptive Neural Dynamic Surface Control for Stochastic Nonlinear Time‐Delay Systems with Input and Output Constraints

AbstractThis paper presents an adaptive neural tracking control approach for uncertain stochastic nonlinear time‐delay systems with input and output constraints. Firstly, the dynamic surface control (DSC) technique is incorporated into adaptive neural control framework to overcome the problem of ‘explosion of complexity’ in the control design. By employing a continuous differentiable asymmetric saturation model, the input constraint problem is solved. Secondly, the appropriate Lyapunov‐Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown time‐delay terms, RBF neural network is utilized to identify the unknown systems functions, and barrier Lyapunov functions (BLFs) are designed to avoid the violation of the output constraint. Finally, based on adaptive backstepping technique, an adaptive neural control method is proposed, and it decreases the number of learning parameters. Using Lyapunov stability theory, it is proved that the designed controller can ensure that all the signals in the closed‐loop system are 4‐Moment (or 2 Moment) semi‐globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of the origin. Two simulation examples are provided to further illustrate the effectiveness of the proposed approach.

Observer-Based Adaptive NN Control for a Class of Uncertain Nonlinear Systems With Nonsymmetric Input Saturation.

This paper is concerned with the problem of adaptive tracking control for a class of uncertain nonlinear systems with nonsymmetric input saturation and immeasurable states. The radial basis function of neural network (NN) is employed to approximate unknown functions, and an NN state observer is designed to estimate the immeasurable states. To analyze the effect of input saturation, an auxiliary system is employed. By the aid of adaptive backstepping technique, an adaptive tracking control approach is developed. Under the proposed adaptive tracking controller, the boundedness of all the signals in the closed-loop system is achieved. Moreover, distinct from most of the existing references, the tracking error can be bounded by an explicit function of design parameters and saturation input error. Finally, an example is given to show the effectiveness of the proposed method.

Robust adaptive fault-tolerant control of nonlinear uncertain systems tracking uncertain target trajectory

The problem of enabling nonlinear uncertain dynamic systems to track a moving target with uncertain trajectory is of theoretical and practical importance. The underlying problem becomes further complicated if there involve unexpected actuation failures. In this paper, a robust adaptive fault-tolerant tracking control approach is proposed for unknown multi-input multi-output (MIMO) nonlinear systems without a priori precise knowledge of the desired target trajectory. To account for the impact of the uncertain desired trajectory, a mathematical model based on the extended Kalman filter (EKF) for reconstructing desired trajectory is proposed, which is then integrated into the development of tracking control algorithms to cope with modelling uncertainties and actuation faults. The matrix decomposition technique and the concept of deep-rooted information are used to facilitate the control design and stability analysis. The effectiveness of the proposed method is verified via computer simulation.

Adaptive Tracking Control for a Class of Stochastic Uncertain Nonlinear Systems With Input Saturation

In this technical note, the problem of adaptive tracking control is investigated for a class of stochastic uncertain nonlinear systems in the presence of input saturation. To analyze the effect of input saturation, an auxiliary system is employed. With the help of backstepping technique, an adaptive stochastic tracking control approach is developed. Under the proposed adaptive tracking controller, the boundedness of all the signals in the closed-loop system is achieved almost surely. Moreover, distinct from most of the existing results, the ultimate tracking error can be bounded by an explicit function of design parameters and input saturation error (the error between the control input and saturated input) in the mean quartic sense. Finally, an example is given to show the effectiveness of the proposed scheme.

Observer-based adaptive fuzzy quantized tracking DSC design for MIMO nonstrict-feedback nonlinear systems

This paper concerned with the problem of observer-based adaptive fuzzy quantized tracking dynamic surface control (DSC) is investigated for the uncertain multi-input and multi-output (MIMO) nonstrict-feedback nonlinear systems, which contain unknown nonlinear functions, input quantization, and unmeasured states. By using fuzzy logic systems to identify the uncertain MIMO nonstrict-feedback nonlinear systems, a fuzzy state observer is introduced to estimate the immeasurable states. By transforming the hysteretic quantized input into a new nonlinear decomposition, and utilizing the DSC backstepping design method, a novel and less conservative fuzzy adaptive quantized tracking control approach is developed. It is shown that the proposed control scheme can guarantee the stability of the closed-loop system, and also that the system outputs can track the given desired trajectories. The simulation results are provided to verify the effectiveness of the proposed control strategy.

Robust adaptive neural network-based trajectory tracking control approach for nonholonomic electrically driven mobile robots

This paper presents a robust intelligent controller to be applied to a class of nonholonomic electrically driven mobile robots. This class of robotic systems has an inherent sensitivity to high degree time-varying parametric uncertainties, unmodeled dynamics, and external disturbances. Furthermore, the effects of coupling terms between the mechanical subsystem and the electrical subsystem may cause severe degradations due to the time-varying variations of DC motors and mechanical structure components around their nominal values. To overcome the effects of all these quantities, the robust adaptive neural network tracking controller developed here introduces adaptive laws to estimate a local upper bound of each subsystem of the nonholonomic mobile robot, then, these laws are used on-line as controller gain parameters in order to robustly improve the transient response of the closed-loop system and reduce conservative, in the sense that the local upper bounds to characterize the corresponding uncertainties dynamics for each subsystem, initially computed based on the worse-case scenario, are not updated during the effective control of the mobile robot. In fact, even if more data become available, then they are avoided when estimating local upper bounds, and hence, the level of uncertainty is considerably decreased. According to the universal approximation theorem and the Lyapunov stability theory, the proposed intelligent controller guarantees global stability in the sense that all the states and signals of the closed-loop system, and the trajectory tracking errors are all bounded. Simulation results on two typical examples of nonholonomic electrically driven mobile robots show the effectiveness and robustness of the proposed controller.

Adaptive tracking control for uncertain switched stochastic nonlinear pure-feedback systems with unknown backlash-like hysteresis

In this paper, an adaptive tracking control problem is studied for a class of switched stochastic nonlinear pure-feedback systems with unknown backlash-like hysteresis under arbitrary switching. The mean-value theorem is used to overcome the difficulty arising from the pure-feedback structure. Based on neural networks’ approximation capability, an adaptive tracking control approach is developed via the adaptive backstepping technique and common Lyapunov function method. It is proved that the proposed control scheme can guarantee that all signals in the closed-loop system are semi-globally uniformly ultimately bounded in probability and the tracking error converges to an adjustable neighborhood of the origin. Finally, a simulation example further shows the effectiveness of the presented control scheme.