Discrete-Time Adaptive Backstepping Nonlinear Control via High-Order Neural Networks

Treatment for T1DM patients by a neuro-fuzzy inverse optimal controller including multi-step prediction

Diabetes Mellitus is a serious metabolic condition for global health associations. Recently, the number of adults, adolescents and children who have developed Type 1 Diabetes Mellitus (T1DM) has increased as well as the mortality statistics related to this disease. For this reason, the scientific community has directed research in developing technologies to reduce T1DM complications. This contribution is related to a feedback control strategy for blood glucose management in population samples of ten virtual adult subjects, adolescents and children. This scheme focuses on the development of an inverse optimal control (IOC) proposal which is integrated by neural identification, a multi-step prediction (MSP) strategy, and Takagi-Sugeno (T-S) fuzzy inference to shape the convenient insulin infusion in the treatment of T1DM patients. The MSP makes it possible to estimate the glucose dynamics 15 min in advance; therefore, this estimation allows the Neuro-Fuzzy-IOC (NF-IOC) controller to react in advance to prevent hypoglycemic and hyperglycemic events. The T-S fuzzy membership functions are defined in such a way that the respective inferences change basal infusion rates for each patient's condition. The results achieved for scenarios simulated in Uva/Padova virtual software illustrate that this proposal is suitable to maintain blood glucose levels within normoglycemic values (70-115 mg/dL); furthermore, this level remains less than 250 mg/dL during the postprandial event. A comparison between a simple neural IOC (NIOC) and the proposed NF-IOC is carried out using the analysis for control variability named CVGA chart included in the Uva/Padova software. This analysis highlights the improvement of the NF-IOC treatment, proposed in this article, on the NIOC approach because each subject is located inside safe zones for the entire duration of the simulation.

An Autonomous Path Controller in a System on Chip for Shrimp Robot

This paper presents a path planning and trajectory tracking system for a BlueBotics Shrimp III®, which is an articulate mobile robot for rough terrain navigation. The system includes a decentralized neural inverse optimal controller, an inverse kinematic model, and a path-planning algorithm. The motor control is obtained based on a discrete-time recurrent high order neural network trained with an extended Kalman filter, and an inverse optimal controller designed without solving the Hamilton Jacobi Bellman equation. To operate the whole system in a real-time application, a Xilinx Zynq® System on Chip (SoC) is used. This implementation allows for a good performance and fast calculations in real-time, in a way that the robot can explore and navigate autonomously in unstructured environments. Therefore, this paper presents the design and implementation of a real-time system for robot navigation that integrates, in a Xilinx Zynq® System on Chip, algorithms of neural control, image processing, path planning, and inverse kinematics and trajectory tracking.

Trajectory Tracking on Uncertain Complex Networks via NN-Based Inverse Optimal Pinning Control

A new approach for trajectory tracking on uncertain complex networks is proposed. To achieve this goal, a neural controller is applied to a small fraction of nodes (pinned ones). Such controller is composed of an on-line identifier based on a recurrent high-order neural network, and an inverse optimal controller to track the desired trajectory; a complete stability analysis is also included. In order to verify the applicability and good performance of the proposed control scheme, a representative example is simulated, which consists of a complex network with each node described by a chaotic Lorenz oscillator.

Adaptive Neural Control for MIMO Pure-Feedback Nonlinear Systems With Periodic Disturbances

In this paper, an adaptive neural control design method is presented for a class of multiple-input-multiple-output (MIMO) pure-feedback nonlinear systems with periodically time-varying disturbances appearing nonlinearly in unknown nonaffine functions. The nonaffine functions do not need to be differentiable, and the bounded condition of unknown nonaffine functions is relaxed such that only a more general semibounded assumption is required as the controllability condition of the considered MIMO pure-feedback system. To facilitate the control design, the gain functions are designed to be continuous and positive with the bounds being unknown functions. Furthermore, for handling with the difficulty caused by these unknown bounds, several appropriate compact sets are defined to obtain the bounds of gain functions. By utilizing Lyapunov analysis, all the variables of the resulting closed-loop system are proven to be semiglobally uniformly ultimately bounded, and the tracking error can converge to an arbitrarily small neighborhood around zero by choosing design parameters appropriately. The effectiveness of the proposed control algorithm is demonstrated by two simulations.

Observer-Based Adaptive Fault-Tolerant Tracking Control of Nonlinear Nonstrict-Feedback Systems

This paper studies an output-based adaptive fault-tolerant control problem for nonlinear systems with nonstrict-feedback form. Neural networks are utilized to identify the unknown nonlinear characteristics in the system. An observer and a general fault model are constructed to estimate the unavailable states and describe the fault, respectively. Adaptive parameters are constructed to overcome the difficulties in the design process for nonstrict-feedback systems. Meanwhile, dynamic surface control technique is introduced to avoid the problem of "explosion of complexity". Furthermore, based on adaptive backstepping control method, an output-based adaptive neural tracking control strategy is developed for the considered system against actuator fault, which can ensure that all the signals in the resulting closed-loop system are bounded, and the system output signal can be regulated to follow the response of the given reference signal with a small error. Finally, the simulation results are provided to validate the effectiveness of the control strategy proposed in this paper.

A Unified Approach to Adaptive Neural Control for Nonlinear Discrete-Time Systems With Nonlinear Dead-Zone Input

In this paper, an effective adaptive control approach is constructed to stabilize a class of nonlinear discrete-time systems, which contain unknown functions, unknown dead-zone input, and unknown control direction. Different from linear dead zone, the dead zone, in this paper, is a kind of nonlinear dead zone. To overcome the noncausal problem, which leads to the control scheme infeasible, the systems can be transformed into a m -step-ahead predictor. Due to nonlinear dead-zone appearance, the transformed predictor still contains the nonaffine function. In addition, it is assumed that the gain function of dead-zone input and the control direction are unknown. These conditions bring about the difficulties and the complicacy in the controller design. Thus, the implicit function theorem is applied to deal with nonaffine dead-zone appearance, the problem caused by the unknown control direction can be resolved through applying the discrete Nussbaum gain, and the neural networks are used to approximate the unknown function. Based on the Lyapunov theory, all the signals of the resulting closed-loop system are proved to be semiglobal uniformly ultimately bounded. Moreover, the tracking error is proved to be regulated to a small neighborhood around zero. The feasibility of the proposed approach is demonstrated by a simulation example.

Adaptive NN controller design for a class of nonlinear MIMO discrete-time systems

An adaptive neural network tracking control is studied for a class of multiple-input multiple-output (MIMO) nonlinear systems. The studied systems are in discrete-time form and the discretized dead-zone inputs are considered. In addition, the studied MIMO systems are composed of N subsystems, and each subsystem contains unknown functions and external disturbance. Due to the complicated framework of the discrete-time systems, the existence of the dead zone and the noncausal problem in discrete-time, it brings about difficulties for controlling such a class of systems. To overcome the noncausal problem, by defining the coordinate transformations, the studied systems are transformed into a special form, which is suitable for the backstepping design. The radial basis functions NNs are utilized to approximate the unknown functions of the systems. The adaptation laws and the controllers are designed based on the transformed systems. By using the Lyapunov method, it is proved that the closed-loop system is stable in the sense that the semiglobally uniformly ultimately bounded of all the signals and the tracking errors converge to a bounded compact set. The simulation examples and the comparisons with previous approaches are provided to illustrate the effectiveness of the proposed control algorithm.

Decentralized Neural Backstepping Control Applied to a Robot Manipulator

This paper presents a discrete-time decentralized control scheme for trajectory tracking of a two degrees of freedom (DOF) robot manipulator. A high order neural network (HONN) is used to approximate a decentralized control law designed by the backstepping technique as applied to a block strict feedback form (BSFF). The weights for each neural network are adapted online by an extended Kalman filter training algorithm. The motion for each joint is controlled independently using only local angular position and velocity measurements. The stability analysis for the closed-loop system via the Lyapunov approach is included. Finally, the real-time results show the feasibility of the proposed control scheme using a robot manipulator.

DISCRETE-TIME REDUCED ORDER NEURAL OBSERVERS FOR UNCERTAIN NONLINEAR SYSTEMS

This paper focusses on a novel discrete-time reduced order neural observer for nonlinear systems, which model is assumed to be unknown. This neural observer is robust in presence of external and internal uncertainties. The proposed scheme is based on a discrete-time recurrent high order neural network (RHONN) trained with an extended Kalman filter (EKF)-based algorithm, using a parallel configuration. This work includes the stability proof of the estimation error on the basis of the Lyapunov approach; to illustrate the applicability, simulation results for a nonlinear oscillator are included.

BLOOD GLUCOSE LEVEL NEURAL MODEL FOR TYPE 1 DIABETES MELLITUS PATIENTS

This paper deals with the blood glucose level modeling for Type 1 Diabetes Mellitus (T1DM) patients. The model is developed using a recurrent neural network trained with an extended Kalman filter based algorithm in order to develop an affine model, which captures the nonlinear behavior of the blood glucose metabolism. The goal is to derive a dynamical mathematical model for the T1DM as the response of a patient to meal and subcutaneous insulin infusion. Experimental data given by continuous glucose monitoring system is utilized for identification and for testing the applicability of the proposed scheme to T1DM subjects.

Adaptive bridge control strategy for opinion evolution on social networks

In this paper, we present an efficient opinion control strategy for complex networks, in particular, for social networks. The proposed adaptive bridge control (ABC) strategy calls for controlling a special kind of nodes named bridge and requires no knowledge of the node degrees or any other global or local knowledge, which are necessary for some other immunization strategies including targeted immunization and acquaintance immunization. We study the efficiency of the proposed ABC strategy on random networks, small-world networks, scale-free networks, and the random networks adjusted by the edge exchanging method. Our results show that the proposed ABC strategy is efficient for all of these four kinds of networks. Through an adjusting clustering coefficient by the edge exchanging method, it is found out that the efficiency of our ABC strategy is closely related with the clustering coefficient. The main contributions of this paper can be listed as follows: (1) A new high-order social network is proposed to describe opinion dynamic. (2) An algorithm, which does not require the knowledge of the nodes' degree and other global∕local network structure information, is proposed to control the "bridges" more accurately and further control the opinion dynamics of the social networks. The efficiency of our ABC strategy is illustrated by numerical examples. (3) The numerical results indicate that our ABC strategy is more efficient for networks with higher clustering coefficient.

Adaptive NN control for discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constraints

This paper focuses on the problem of adaptive neural network tracking control for a class of discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constraints. Two novel state-feedback and output-feedback dynamic control laws are established where the function tanh(.) is employed to solve the saturation constraint problem. Implicit function theorem and mean value theorem are exploited to deal with non-affine variables that are used as actual control. Radial basis function neural networks are used to approximate the desired input function. Discrete Nussbaum gain is used to estimate the unknown sign of control gain. The uniform boundedness of all closed-loop signals is guaranteed. The tracking error is proved to converge to a small residual set around the origin. A simulation example is provided to illustrate the effectiveness of control schemes proposed in this paper.