Adaptive Fuzzy Tracking Control for Nonlinear State Constrained Pure-Feedback Systems With Input Delay via Dynamic Surface Technique

This brief constructs the adaptive backstepping control scheme for a class of pure-feedback systems with input delay and full state constraints. With the help of Mean Value Theorem, the pure-feedback system is transformed into strict-feedback one. Barrier Lyapunov functions are employed to guarantee all of the states remain constrained within predefined sets. By introducing the Pade approximation method and corresponding intermediate, the impact generated by input delay on the output tracking performance of the system can be eliminated. Furthermore, a low-pass filter driven by a newly-defined control input, is employed to generate the actual control input, which facilitates the design of backstepping control. To approximate the unknown functions with a desired level of accuracy, the fuzzy logic systems (FLSs) are utilized by choosing appropriate fuzzy rules, logics and so on. The minimal learning parameter (MLP) technique is employed to decrease the number of nodes and parameters in FLSs, and dynamic surface control (DSC) technique is leveraged to avoid so-called "explosion of complexity". Moreover, smooth robust compensators are introduced to circumvent the influences of external disturbance and approximation errors. By stability analysis, it is proved that all of signals in the closed-loop system are semi-globally ultimately uniform bounded, and the tracking error can be within a arbitrary small neighbor of origin via selecting appropriate parameters of controllers. Finally, the results of numerical illustration are provided to demonstrate the effectiveness of the designed method.Comment: arXiv admin note: text overlap with arXiv:2310.1540

Lyapunov based optimal control of a class of nonlinear systems

Optimal control of nonlinear systems is in fact difficult since it requires the solution to the Hamilton-Jacobi-Bellman (HJB) equation which has no closed-form solution. In contrast to offline and/or online iterative schemes for optimal control, this dissertation in the form of five papers focuses on the design of iteration free, online optimal adaptive controllers for nonlinear discrete and continuous-time systems whose dynamics are completely or partially unknown even when the states not measurable. Thus, in Paper I, motivated by homogeneous charge compression ignition (HCCI) engine dynamics, a neural network-based infinite horizon robust optimal controller is introduced for uncertain nonaffine nonlinear discrete-time systems. First, the nonaffine system is transformed into an affine-like representation while the resulting higher order terms are mitigated by using a robust term. The optimal adaptive controller for the affinelike system solves HJB equation and identifies the system dynamics provided a target set point is given. Since it is difficult to define the set point a priori in Paper II, an extremum seeking control loop is designed while maximizing an uncertain output function. On the other hand, Paper III focuses on the infinite horizon online optimal tracking control of known nonlinear continuous-time systems in strict feedback form by using state and output feedback by relaxing the initial admissible controller requirement. Paper IV applies the optimal controller from Paper III to an underactuated helicopter attitude and position tracking problem. In Paper V, the optimal control of nonlinear continuous-time systems in strict feedback form from Paper III is revisited by using state and output feedback when the internal dynamics are unknown. Closed-loop stability is demonstrated for all the controller designs developed in this dissertation by using Lyapunov analysis --Abstract, page iv

A brief review of neural networks based learning and control and their applications for robots

As an imitation of the biological nervous systems, neural networks (NN), which are characterized with powerful learning ability, have been employed in a wide range of applications, such as control of complex nonlinear systems, optimization, system identification and patterns recognition etc. This article aims to bring a brief review of the state-of-art NN for the complex nonlinear systems. Recent progresses of NNs in both theoretical developments and practical applications are investigated and surveyed. Specifically, NN based robot learning and control applications were further reviewed, including NN based robot manipulator control, NN based human robot interaction and NN based behavior recognition and generation

Fixed-time safe tracking control of uncertain high-order nonlinear pure-feedback systems via unified transformation functions

summary:In this paper, a fixed-time safe control problem is investigated for an uncertain high-order nonlinear pure-feedback system with state constraints. A new nonlinear transformation function is firstly proposed to handle both the constrained and unconstrained cases in a unified way. Further, a radial basis function neural network is constructed to approximate the unknown dynamics in the system and a fixed-time dynamic surface control (FDSC) technique is developed to facilitate the fixed-time control design for the uncertain high-order pure-feedback system. Combined with the proposed unified transformation function and the FDSC technique, an adaptive fixed-time control strategy is proposed to guarantee the fixed-time tracking. The novel original results of the paper allow to design the independent unified flexible fixed-time control strategy taking into account the actual possible constraints, either present or missing. Numerical examples are presented to demonstrate the proposed fixed-time tracking control strategy

An improved adaptive online neural control for robot manipulator systems using integral Barrier Lyapunov functions

Conventional Neural Network (NN) control for robots uses radial basis function (RBF) and for n-link robot with online control, the number of nodes and weighting matrix increases exponentially, which requires a number of calculations to be performed within a very short duration of time. This consumes a large amount of computational memory and may subsequently result in system failure. To avoid this problem, this paper proposes an innovative NN robot control using a dimension compressed RBF (DCRBF) for a class of n-degree of freedom (DOF) robot with full-state constraints. The proposed DCRBF NN control scheme can compress the nodes and weighting matrix greatly and provide an output that meets the prescribed tracking performance. Additionally, adaption laws are designed to compensate for the internal and external uncertainties. Finally, the effectiveness of the proposed method has been verified by simulations. The results indicate that the proposed method, integral Barrier Lyapunov Functions (iBLF), avoids the existing defects of Barrier Lyapunov Functions (BLF) and prevents the constraint violations

Simultaneous identification, tracking control and disturbance rejection of uncertain nonlinear dynamics systems: A unified neural approach

Previous works of traditional zeroing neural networks (or termed Zhang neural networks, ZNN) show great success for solving specific time-variant problems of known systems in an ideal environment. However, it is still a challenging issue for the ZNN to effectively solve time-variant problems for uncertain systems without the prior knowledge. Simultaneously, the involvement of external disturbances in the neural network model makes it even hard for time-variant problem solving due to the intensively computational burden and low accuracy. In this paper, a unified neural approach of simultaneous identification, tracking control and disturbance rejection in the framework of the ZNN is proposed to address the time-variant tracking control of uncertain nonlinear dynamics systems (UNDS). The neural network model derived by the proposed approach captures hidden relations between inputs and outputs of the UNDS. The proposed model shows outstanding tracking performance even under the influences of uncertainties and disturbances. Then, the continuous-time model is discretized via Euler forward formula (EFF). The corresponding discrete algorithm and block diagram are also presented for the convenience of implementation. Theoretical analyses on the convergence property and discretization accuracy are presented to verify the performance of the neural network model. Finally, numerical studies, robot applications, performance comparisons and tests demonstrate the effectiveness and advantages of the proposed neural network model for the time-variant tracking control of UNDS

Adaptive fuzzy control for coordinated multiple robots with constraint using impedance learning

In this paper, we investigate fuzzy neural network (FNN) control using impedance learning for coordinated multiple constrained robots carrying a common object in the presence of the unknown robotic dynamics and the unknown environment with which the robot comes into contact. First, an FNN learning algorithm is developed to identify the unknown plant model. Second, impedance learning is introduced to regulate the control input in order to improve the environment-robot interaction, and the robot can track the desired trajectory generated by impedance learning. Third, in light of the condition requiring the robot to move in a finite space or to move at a limited velocity in a finite space, the algorithm based on the position constraint and the velocity constraint are proposed, respectively. To guarantee the position constraint and the velocity constraint, an integral barrier Lyapunov function is introduced to avoid the violation of the constraint. According to Lyapunov's stability theory, it can be proved that the tracking errors are uniformly bounded ultimately. At last, some simulation examples are carried out to verify the effectiveness of the designed control

Unknown dynamics estimator-based output-feedback control for nonlinear pure-feedback systems

Most existing adaptive control designs for nonlinear pure-feedback systems have been derived based on backstepping or dynamic surface control (DSC) methods, requiring full system states to be measurable. The neural networks (NNs) or fuzzy logic systems (FLSs) used to accommodate uncertainties also impose demanding computational cost and sluggish convergence. To address these issues, this paper proposes a new output-feedback control for uncertain pure-feedback systems without using backstepping and function approximator. A coordinate transform is first used to represent the pure-feedback system in a canonical form to evade using the backstepping or DSC scheme. Then the Levant's differentiator is used to reconstruct the unknown states of the derived canonical system. Finally, a new unknown system dynamics estimator with only one tuning parameter is developed to compensate for the lumped unknown dynamics in the feedback control. This leads to an alternative, simple approximation-free control method for pure-feedback systems, where only the system output needs to be measured. The stability of the closed-loop control system, including the unknown dynamics estimator and the feedback control is proved. Comparative simulations and experiments based on a PMSM test-rig are carried out to test and validate the effectiveness of the proposed method