Adaptive Neural Tracking Control Research Articles

Observer-based adaptive neural tracking control for a class of nonlinear systems with prescribed performance and input dead-zone constraints

This paper investigates the problem of output feedback neural network (NN) learning tracking control for nonlinear strict feedback systems subject to prescribed performance and input dead-zone constraints. First, an NN is utilized to approximate the unknown nonlinear functions, then a state observer is developed to estimate the unmeasurable states. Second, based on the command filter method, an output feedback NN learning backstepping control algorithm is established. Third, a prescribed performance function is employed to ensure the transient performance of the closed-loop systems and forces the tracking error to fall within the prescribed performance boundary. It is rigorously proved mathematically that all the signals in the closed-loop systems are semi-globally uniformly ultimately bounded and the tracking error can converge to an arbitrarily small neighborhood of the origin. Finally, a numerical example and an application example of the electromechanical system are given to show effectiveness of the acquired control algorithm.

Command-filter-based adaptive neural tracking control for a class of nonlinear MIMO state-constrained systems with input delay and saturation

This paper investigates the problem of adaptive tracking control for a class of nonlinear multi-input and multi-output (MIMO) state-constrained systems with input delay and saturation. During the process of the control scheme, neural network is employed to approximate the unknown nonlinear uncertainties and the appropriate barrier Lyapunov function is introduced to prevent violation of the constraint. In addition, for the issue of input saturation with time delay, a smooth non-affine approximate function and a novel auxiliary system are utilized, respectively. Moreover, adaptive neural tracking control is developed by combining the command filtering backstepping approach, which effectively avoids the explosion of differentiation and reduces the computation burden. The introduced filtering error compensating system brings a significant improvement for the system tracking performance. Finally, the simulation result is presented to verify the feasibility of the proposed strategy.

Adaptive practical fixed‐time tracking control for uncertain non‐strict‐feedback systems with input delay and prescribed boundary constraints

SummaryThis article concentrates upon the practical fixed‐time adaptive neural tracking control problem of non‐strict‐feedback nonlinear systems with input delay and prescribed boundary constraints (PBCs). A modified appropriate auxiliary system is introduced to eliminate the complex calculations appeared in the input delay. The unknown nonlinear functions exist in non‐strict‐feedback nonlinear systems, which are approximated by the radial basis function neural networks. The adaptive practical fixed‐time control strategy is developed based on a novel coordinate transformation by utilizing the backstepping algorithm. Under the proposed controller, it can be guaranteed that the tracking error satisfies the PBCs in fixed time and all the signals in the closed‐loop system are bounded. Some numerical simulations verify the effectiveness of the control approach.

Sliding mode differentiator-based event-triggered control for state-constrained nonlinear systems with unknown virtual control coefficients

In this paper, a novel event-triggered (ET) adaptive neural tracking control scheme is proposed for uncertain strict-feedback systems subject to asymmetric time-varying full-state constraints, unknown virtual control coefficients and external disturbances. The lower-order time-varying asymmetric barrier Lyapunov function (TVABLF) is constructed to ensure that state constraints are not transgressed. Then, a simple backstepping-based control procedure is developed to remove the existing restrictions on a high power of piecewise TVABLF and high-order differentiability of virtual laws. In particular, a novel adaptive updating law is constructed to co-design the controller and the ET scheme by the combination of the Nussbaum gain technique, thereby solving the ET controller design difficulty resulting from unknown control coefficients. The proposed scheme can guarantee all states within the time-varying constrained areas, achieve the satisfactory tracking ability and save the communication resource. Finally, the effectiveness of the proposed scheme is testified by numerical and practical examples.

Nussbaum gain adaptive neural asymptotic tracking of nonlinear systems with full-state constraints

The adaptive neural tracking control problem of a class of strict-feedback nonlinear systems with unknown control directions (UCD) and full-state constraints is investigated in this paper. The neural network (NN) is adopted to identify the totally unknown nonlinear functions. In the meanwhile, by resorting to the Nussbaum gain technique, the effects caused by the UCD and output dead zone are counteracted. Given physical limits and safety demands, a novel barrier Lyapunov function (BLF)-based adaptive neural control scheme is devised for the strict-feedback nonlinear systems to ensure that the constraints are not violated during operations. Besides, a rigorous theoretical analysis has been given to indicate that all of the closed-loop signals are bounded and the tracking error achieves asymptotic convergence performance. Finally, the effectiveness and flexibility of our proposed scheme are illustrated by two numerical examples.

Robust Prescribed Performance Control of Uncertain Vehicle Lateral System under State Constraints

In the study of the zero-error tracking control problem for vehicle lateral control systems under full-state constraints and nonparametric uncertainties, the zero-error tracking control problem is presented in this paper. A neural adaptive tracking control scheme is proposed by combining the error transformation of the vehicle lateral control system with the barrier Lyapunov function, which realizes that the tracking error of the vehicle lateral control converges to a prescribed compact set at a controllable or specified convergence rate in a specified finite time. The scheme has the following significant characteristics: 1) Based on the Nussbaum gain, the preset new energy finite-time control algorithm, the tracking error of the vehicle lateral control system with non-parametric uncertainty and external disturbance decreases to zero with t → ∞. In addition, it also has the control ability to cope with the presence or even unknown moment of inertia of the system. 2) Barrier Lyapunov function (BLF) ensures the bounded input of the neural network during the whole system envelope, and ensures the stable learning and approximation of the neural network. Furthermore, the bounded stability of the closed-loop system is proved by Lyapunov analysis. Finally, the effectiveness and superiority of the proposed control method are verified by simulation.

Adaptive neural tracking control for stochastic nonlinear multi-agent periodic time-varying systems

This paper investigates the design of adaptive tracking neural controllers for first- and second-order nonlinear multi-agent periodic time-varying systems described based on random differential equations, respectively. First, the Fourier series expansion and neural networks are used as the main tools to describe the nonlinear periodic disturbance dynamics of the follower, which transforms the completely nonlinear problem into a partially linearizable problem. Then, the fully distributed adaptive neural controllers are developed based on adaptive estimation, in which new estimation methods are designed to address periodic time-varying perturbations. Furthermore, based on the stochastic Lyapunov stability theory, it is proved that the tracking errors converge asymptotically to a small neighborhood of zero in the sense of mean square. Finally, the efficicency of the proposed controllers is verified using simulations.

Adaptive neural tracking control for high angle of attack maneuver with average dwell time

SummaryThis article attempts to study the high angle of attack maneuver from the perspective of switched system control. In view of the complex aerodynamic characteristics, an improved longitudinal attitude motion model is presented, which is a switched stochastic nonstrict feedback nonlinear system with distributed delays. The significant design difficulty is the completely unknown diffusion and drift terms and distributed delays with all state variables. Based on a technical lemma and neural networks, an improved smooth state feedback control law for nonstrict feedback systems is proposed without any growth assumptions. To eliminate the influence of distributed delays, an improved Lyapunov–Krasovskii function is constructed, which skillfully removes the constraint of the upper bound of the delay change rate. Then, by combining the average dwell‐time scheme and stochastic backstepping technique, an adaptive neural network tracking control law is designed, which extends a newly proposed switched system stability condition to the stochastic switched system. Theoretical analysis and flight control simulation experiments are provided to illustrate the effectiveness of the proposed control method.

Event-triggered fixed-time adaptive neural tracking control for stochastic non-triangular structure nonlinear systems

Event-triggered fixed-time adaptive neural tracking control for stochastic non-triangular structure nonlinear systems

Adaptive neural tracking control of high-order nonlinear systems with quantized input

In this paper, adaptive neural tracking control problem is considered for non-strict-feedback high-order nonlinear systems with quantized input signal. Compared with the logarithmic quantizer, the quantizer introduced in this paper can avoid chattering problem. The dynamic surface control (DSC) technique is introduced to solve the problem of ‘explosion of complexity’, which is appeared in the classic adaptive backstepping control of high-order nonlinear systems. The structural properties of radial basis function neural networks (RBF NNs) are used to simplify the design difficulty from the functions of whole state variables. According to the classic adaptive backstepping technique and neural network algorithm, an output tracking controller is designed, which can guarantee that all the signals of the closed-loop system are semiglobally uniformly bounded and the output of the system can track the reference signal. Finally, a numerical example is presented to verify the effectiveness of the proposed method.

Hybrid Neural Adaptive Control for Practical Tracking of Markovian Switching Networks.

While neural adaptive control is widely used for dealing with continuous- or discrete-time dynamical systems, less is known about its mechanism and performance in hybrid dynamical systems. This article develops analytical tools to investigate the neural adaptive tracking control of the hybrid Markovian switching networks with heterogeneous nonlinear dynamics and randomly switched topologies. A gradient-descent adaptation law built on neural networks (NNs) is presented for efficient distributed adaptive control. It is shown that the proposed control scheme can guarantee a stable closed-loop error system for any positive control gain and tuning gain. The tracking error is demonstrated to be practically uniformly exponentially stable with a threshold in the mean-square sense. This study further reveals how the topological structure affects the NN function, by measuring the influence of the switched topologies on the learning performance.

Fixed-time adaptive neural tracking control of output constrained nonlinear pure-feedback system with input saturation

This paper considers the fixed-time tracking control problem for system-constrained nonlinear pure-feedback systems involving input saturation and output constraints. A sequence of auxiliary virtual and actual input signals is designed to obtain an expression for the system tracking error and stabilize the system. A combination of the fixed-time stability theory, barrier Lyapunov function, and radial basis function neural network is employed to develop the proposed method for obtaining the expected performance from the considered system. Further, a theorem is proposed to ensure that the designed controller allows the system output to track the reference signal within a fixed time, ensuring that the tracking error is limited to a small neighborhood of origin within a fixed time and that all the signals in the system are bounded. The aforementioned problem can be solved using the proposed control method, and the simulation experiments indicate the effectiveness of the designed controller.

Adaptive output-feedback neural tracking control for uncertain switched MIMO nonlinear systems with time delays

This paper investigates the problem of adaptive output-feedback neural tracking control for a class of uncertain switched multiple-input multiple-output (MIMO) nonstrict-feedback nonlinear systems with time delays. It should be emphasised that the design for the considered system is quite difficult due to its unknown factors caused by the unknown system coefficients and the unknown functions. In our proposed design procedure, neural networks (NNs) are introduced to identify the unknown nonlinear functions and a valid hypothesis is used to deal with the unknown system coefficients. Then, the developed switched filter can be utilised to estimate the unmeasured system states. On the basis of the backstepping technique and the common Lyapunov function (CLF) approach, an adaptive neural controller is constructed for each subsystem. It is proved that all signals existing in the switched closed-loop system are ultimately bounded under arbitrary switching and each system output can track the corresponding target trajectory within a small bounded error. Finally, simulation results are presented to illustrate the efficiency of the proposed control method.

Adaptive neural tracking control for switched nonlinear systems with state quantization

In this study, an adaptive neural tracking control problem for uncertain switched nonlinear systems with state quantization under arbitrary switching is investigated. A command-filtered backstepping control design strategy is implemented to overcome the difficulty that the time derivate of common virtual control signals cannot be well defined. By deriving the closed-loop system quantized errors bounded, quantized states can be used to the control design and unquantized states can be applied to the stability analysis. And then, an adaptive neural tracking control approach for switched nonlinear systems with state quantization via common Lyapunov function is proposed, which guarantees that all the signals in the closed-loop system remain semiglobal uniform ultimate boundedness and the genuine output of system can well track the reference trajectory. Finally, the proposed method is demonstrated by two simulation results.

Command-filter-based adaptive neural tracking control for strict-feedback stochastic nonlinear systems with input dead-zone

The problem of command-filter-based adaptive tracking control is investigated for a class of stochastic nonlinear systems with strict-feedback structure with input dead-zone in this paper. Radial basis function neural network (RBF NN) is employed to approximate the packaged unknown nonlinearities. In order to eliminate the influence of ‘the explosion of complexity’ which will exist in the conventional controller design process via backstepping technique, the control method of the command-filter is introduced. For the problem of input dead-zone which appears in the stochastic nonlinear systems, which will be dealt by a reasonable method, namely, the dead-zone nonlinearity can be regarded as a combination for a linear term and bounded disturbance-like term. Combined adaptive backstepping design algorithm and Lyapunov stability theorem, an adaptive neural command-filter controller is developed. The proposed control scheme reduces the calculation burden due to the repeated differentiation for the virtual control laws and guarantees all the closed-loop signals remain semi-globally uniformly ultimately bounded (SGUUB) in the sense of the four moment. And the tracking error converges to a small area near zero. Meanwhile, the effectiveness of the presented approach is proved by simulation results.

Motion Planning and Adaptive Neural Tracking Control of an Uncertain Two-Link Rigid–Flexible Manipulator With Vibration Amplitude Constraint

This article deals with an uncertain two-link rigid-flexible manipulator with vibration amplitude constraint, intending to achieve its position control via motion planning and adaptive tracking approach. In motion planning, the motion trajectories for the two links of the manipulator are planned based on virtual damping and online trajectories correction techniques. The planned trajectories can not only guarantee that the two links can reach their desired angles, but also have the ability to suppress vibration, which can be adjusted to meet the vibration amplitude constraint by limiting the parameters of the planned trajectories. Then, the adaptive tracking controller is designed using the radial basis function neural network and the sliding mode control technique. The developed controller makes the two links of the manipulator track the planned trajectories under the uncertainties including unmodeled dynamics, parameter perturbations, and persistent external disturbances acting on the joint motors. The simulation results verify the effectiveness of the proposed control strategy and also demonstrate the superior performance of the motion planning and the tracking controller.

Adaptive Neural Tracking Control Scheme of Switched Stochastic Nonlinear Pure-Feedback Nonlower Triangular Systems

In this paper, we address the adaptive neural tracking control problem for a class of uncertain switched stochastic nonlinear pure-feedback systems with nonlower triangular form. The significant design difficulty is the completely unknown nonlinear functions with all state variables that can neither be directly estimated by radial basis function (RBF) neural networks (NNs) nor be eliminated by the traditional backstepping technique. To achieve the control objective of this paper, a common state-feedback controller for all subsystems is first systematically constructed by using the common coordinate transformation, the variable separation technique, and the universal approximation capability of RBF NNs. Then the stability analysis shows that the semi-global bounded in probability of the whole closed-loop switched system can be obtained and the desired tracking performance can also be insured under a class of switching signals with the average dwell time property. Finally, simulation results are given to demonstrate the effectiveness of the obtained control scheme.

Adaptive neural tracking control of strict-feedback nonlinear systems with event-triggered state measurement

This paper investigates the adaptive neural tracking control of the strict-feedback nonlinear systems, where the states are measured in an event-triggered manner so as to save the communication resources. As the neural networks (NNs) account for the unknown dynamics of the system, the minimum learning parameters (MLPs) are extracted from the weights of the NNs and the upper bounds of the disturbances. The estimates of the MLPs are updated in an event-triggered manner to ensure the approximation ability of the NNs and the stability of the closed-loop system. An adaptive neural model is established to substitute for the original strict-feedback system and direct the design of the backstepping-based control laws. The states of this adaptive model are reset to the measured states of the original system when the triggering condition is violated. The triggering condition is constructed in the compound form and with the adaptive threshold. The dead-zone operator is involved to avoid the accumulation of triggering instants. In this paper, we notice the problem of “jumps of virtual control laws” for the event-triggered control (ETC) in the backstepping frame, and a detailed formulaic definition is given in section 2.2. To solve this problem, the first-order filters are fabricated to provide the continuous substitutes for virtual control laws. In addition, the “complexity explosion” generated by direct differentiating of virtual control laws can be averted. Through the proposed scheme, the closed-loop system can be viewed as an impulsive dynamic system, and the semi-globally uniformly ultimate boundedness (SGUUB) of all the errors is proved. Finally, two examples validate the feasibility of the proposed control scheme.

Adaptive deep neural network tracking controller augmented using only one-neuron hidden layers for nonlinear systems subject to high constraints and unknown uncertainties

Adaptive deep neural network tracking controller augmented using only one-neuron hidden layers for nonlinear systems subject to high constraints and unknown uncertainties

Adaptive deep neural network tracking controller augmented using only one-neuron hidden layers for nonlinear systems subject to high constraints and unknown uncertainties

Adaptive deep neural network tracking controller augmented using only one-neuron hidden layers for nonlinear systems subject to high constraints and unknown uncertainties