Adaptive Control of Unknown Pure Feedback Systems with Pure State Constraints

This paper deals with the tracking control problem for a class of unknown pure feedback system with pure state constraints on the state variables and unknown time-varying bounded disturbances. An adaptive controller is presented for such systems for the very first time. The controller is designed using the backstepping method. While designing it, Barrier Lyapunov Functions is used so that the state variables do not contravene its constraints. In order to cope with the unknown dynamics of the system, an online approximator is designed using a neural network with a novel adaptive law for its weight update. In the stability analysis of the system, the time derivative of Lyapunov function involves known virtual control coefficient with unknown direction and to deal with such problem Nussbaum gain is used to design the control law. Furthermore, to make the controller robust and computationally inexpensive, a novel disturbance observer is designed to estimate the disturbance along with neural network approximation error and the time derivative of virtual control input. The effectiveness of the proposed approach is demonstrated through a simulation study on the third-order nonlinear system

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

Finite-Time Adaptive Fuzzy Tracking Control for Nonlinear State Constrained Pure-Feedback Systems

This paper investigates the finite-time adaptive fuzzy tracking control problem for a class of pure-feedback system with full-state constraints. With the help of Mean-Value Theorem, the pure-feedback nonlinear system is transformed into strict-feedback case. By employing finite-time-stable like function and state transformation for output tracking error, the output tracking error converges to a predefined set in a fixed finite interval. To tackle the problem of state constraints, integral Barrier Lyapunov functions are utilized to guarantee that the state variables remain within the prescribed constraints with feasibility check. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions. In addition, all the signals in the closed-loop system are guaranteed to be semi-global ultimately uniformly bounded. Finally, two simulation examples are given to show the effectiveness of the proposed control strategy

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

New control strategies for neuroprosthetic systems

The availability of techniques to artificially excite paralyzed muscles opens enormous potential for restoring both upper and lower extremity movements with\ud neuroprostheses. Neuroprostheses must stimulate muscle, and control and regulate the artificial movements produced. Control methods to accomplish these tasks include feedforward (open-loop), feedback, and adaptive control. Feedforward control requires a great deal of information about the biomechanical behavior of the limb. For the upper extremity, an artificial motor program was developed to provide such movement program input to a neuroprosthesis. In lower extremity control, one group achieved their best results by attempting to meet naturally perceived gait objectives rather than to follow an exact joint angle trajectory. Adaptive feedforward control, as implemented in the cycleto-cycle controller, gave good compensation for the gradual decrease in performance observed with open-loop control. A neural network controller was able to control its system to customize stimulation parameters in order to generate a desired output trajectory in a given individual and to maintain tracking performance in the presence of muscle fatigue. The authors believe that practical FNS control systems must\ud exhibit many of these features of neurophysiological systems

Lifelong Learning-Based Multilayer Neural Network Control of Nonlinear Continuous-Time Strict-Feedback Systems

In This Paper, We Investigate Lifelong Learning (LL)-Based Tracking Control for Partially Uncertain Strict Feedback Nonlinear Systems with State Constraints, employing a Singular Value Decomposition (SVD) of the Multilayer Neural Networks (MNNs) Activation Function based Weight Tuning Scheme. the Novel SVD-Based Approach Extends the MNN Weight Tuning to (Formula Presented.) Layers. a Unique Online LL Method, based on Tracking Error, is Integrated into the MNN Weight Update Laws to Counteract Catastrophic Forgetting. to Adeptly Address Constraints for Safety Assurances, Taking into Account the Effects Caused by Disturbances, We Utilize a Time-Varying Barrier Lyapunov Function (TBLF) that Ensures a Uniformly Ultimately Bounded Closed-Loop System. the Effectiveness of the Proposed Safe LL MNN Approach is Demonstrated through a Leader-Follower Formation Scenario Involving Unknown Kinematics and Dynamics. Supporting Simulation Results of Mobile Robot Formation Control Are Provided, Confirming the Theoretical Findings