Robust stabilization of MIMO uncertain nonlinear systems without strict feedback conditions

An optimal adaptive actuator failure compensation control scheme is proposed for a class of multi-input multi-output (MIMO) uncertain nonlinear continuous-time systems with redundant actuators subject to uncertain failures. Only single neural network is used in the proposed adaptive dynamic programming (ADP) scheme to simultaneously learn the infinite horizon cost function and the approximate optimal control input that minimizes the Hamilton-Jacobi-Bellman (HJB) equation. Besides, an uncertainty estimator is designed to estimate the uncertain dynamics and an adaptive parameter adjustment law is designed to estimate the actuator failure coefficients. Stability analysis and simulation results can demonstrate the effectiveness of the proposed method.

In this paper, an adaptive neural network (NN) tracking controller is developed for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with input saturation. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions in the MIMO system. A novel auxiliary system is developed to compensate the effects induced by input saturation (in both magnitude and rate) during tracking control. Endowed with a switching structure that integrates two existing representative auxiliary system designs, this novel auxiliary system improves control performance by preserving their advantages. It provides a comprehensive design structure in which parameters can be adjusted to meet the required control performance. The auxiliary system signal is utilized in both the control law and the neural network weight-update laws. The performance of the resultant closed-loop system is analyzed, and the bound of the transient error is established. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive neural network control.

Disturbance-observer-based fuzzy terminal sliding mode control for MIMO uncertain nonlinear systems

The paper proposes an approach to second order sliding mode control for multi-input multi-output (MIMO) nonlinear uncertain systems. Second order sliding mode techniques for single-input single-output (SISO) systems show, with respect to standard sliding mode control, the same properties of robustness and precision, feature a higher order accuracy and can be exploited to eliminate the chattering effect. The application of second order sliding mode control to MIMO nonlinear systems is a challenging matter. The presented MIMO control method applies to a quite large class of nonlinear processes affected by uncertainties of general nature; the control design is simple; the conditions of existence on the controllers are weak. The proposed procedure represents a general approach to the second order sliding mode control of MIMO systems

This article focuses on adaptive finite time control of multi-input multi-output (MIMO) nonlinear systems under time-varying actuator failures.A finite time adaptive control policy is proposed, guaranteeing the practical finite-time stability of the MIMO nonlinear systems with actuator failures. Simulation study illustrates the usefulness of the proposed policy.

This chapter presents two fuzzy adaptive variable structure controllers for a class of uncertain multi-input multi-output nonlinear systems with actuator nonlinearities (i.e. with sector nonlinearities and dead-zones). The design of the first controller concerns systems with symmetric and positive definite control-gain matrix, while the design of the second one is extended to the case of non-symmetric control-gain matrix thanks to an appropriate matrix decomposition, namely the product of a symmetric positive-definite matrix, a diagonal matrix with diagonal entries +1 or -1, and a unity upper triangular matrix. An appropriate adaptive fuzzy-logic system is used to reasonably approximate the uncertain functions. A Lyapunov approach is adopted to derive the parameter adaptation laws and prove the stability of the closed-loop control system. Finally, some simulation results are carried out to show the effectiveness of the proposed controllers.

A robust adaptive NN output feedback control is proposed to control a class of uncertain discrete-time nonlinear multi-input–multi-output (MIMO) systems. The high-order neural networks are utilized to approximate the unknown nonlinear functions in the systems. Compared with the previous research for discrete-time MIMO systems, robustness of the proposed adaptive algorithm is obvious improved. Using Lyapunov stability theorem, the results show all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood of zero by choosing the design parameters appropriately.

This article addresses the robust stability for a class of nonlinear uncertain discrete-time systems with convex polytopic of uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic-type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of nonlinear uncertain discrete-time control systems is given. Numerical examples are included to illustrate the effectiveness of our results. MSC:15A09, 52A10, 74M05, 93D05.

In wireless communication, multiple signals are utilized to receive and send information in the form of signals simultaneously. These signals consume little power and are usually inexpensive, with a high data rate during data transmission. An Multi Input Multi Output (MIMO) system uses numerous antennas to enhance the functionality of the system. Moreover, system intricacy and power utilization are difficult and highly complicated tasks to achieve in an Analog to Digital Converter (ADC) at the receiver side. An infinite number of MIMO channels are used in wireless networks to improve efficiency with Cross Entropy Optimization (CEO). ADC is a serious issue because the data of the accepted signal are completely lost. ADC is used in the MIMO channels to overcome the above issues, but it is very hard to implement and design. So, an efficient way to enhance the estimation of channels in the MIMO system is proposed in this paper with the utilization of the heuristic-based optimization technique. The main task of the implemented channel prediction framework is to predict the channel coefficient of the MIMO system at the transmitter side based on the receiver side error ratio, which is obtained from feedback information using a Hybrid Serial Cascaded Network (HSCN). Then, this multi-scaled cascaded autoencoder is combined with Long Short Term Memory (LSTM) with an attention mechanism. The parameters in the developed Hybrid Serial Cascaded Multi-scale Autoencoder and Attention LSTM are optimized using the developed Hybrid Revised Position-based Wild Horse and Energy Valley Optimizer (RP-WHEVO) algorithm for minimizing the "Root Mean Square Error (RMSE), Bit Error Rate (BER) and Mean Square Error (MSE)" of the estimated channel. Various experiments were carried out to analyze the accomplishment of the developed MIMO model. It was visible from the tests that the developed model enhanced the convergence rate and prediction performance along with a reduction in the computational costs.

This paper studies an adaptive tracking control for a class of multi-input multi-output (MIMO) non-affine nonlinear systems, with input dead-zone nonlinearity and external disturbances. By using the mean-value theorem, the system model is transformed into an affine form so as the difficulty in controlling non-affine systems is overcome. In the proposed control design, neural networks (NNs) are used to approximate the unknown nonlinearities based on their universal approximation properties. To compensate for approximation errors and external disturbances, an adaptive robust control term is introduced. In comparison with existing approaches, the structure of the designed controller is considerably simpler, and can handle a wider range of nonlinear systems. The stability of the closed-loop system is investigated by using Lyapunov theory. The simulation results illustrate the proposed method.

This paper presents a method of continuous-time simple-adaptive control (SAC) for multi-input multi-output (MIMO) nonlinear systems using multifraction neural networks. The control input is given by the sum of the output of the simple adaptive controller and the output of the multifraction neural network is used to compensate the nonlinearity of plant dynamics that is not taken into consideration in the usual SAC. The role of the multifraction neural network is to construct a linearized model by minimizing the output error caused by nonlinearities in the control systems.

In this paper, the adaptive maneuvering control based on output feedback is studied for uncertain nonlinear multi-input multi-output (MIMO) systems. The high frequency gain matrix of the systems only needs to be Hurwitz, which relaxes the positive definite limitation in the existing results. Based on the backstepping approach with vector form, an output feedback adaptive maneuvering control scheme is proposed. The geometric and the dynamic tasks are solved meanwhile the global stability of the closed-loop systems is guaranteed through the proposed control scheme.

Memoryless Adaptive Robust Controllers Guaranteeing Asymptotic Stability for Uncertain Nonlinear Time–-Delay Systems

In this paper, an adaptive neural networks control approach is proposed for a class of multi-input multi-output (MIMO) non-affine nonlinear dynamic systems in the presence of input saturation. The difficulty in controlling the saturated non-affine system is overcome by introducing a system transformation, so as the system can be reformulated as an affine of a canonical system. In the control design, neural networks are used in the online learning of the unknown dynamics and the input saturation is approximated to reduce the influence caused by the nonlinearities, and a robustifying control term is used to compensate for the approximation errors. Compared to the literature, in the proposed approach, the structure of the designed controller is much simpler since the causes for the problem of complexity growing in existing methods are eliminated. The stability analysis of the closed-loop system is investigated by using Lyapunov theory. Numerical simulation illustrated the proposed control scheme with satisfactory results.

This paper provides an inverse-model-based iterative learning control (ILC) for the unknown multi-input multi-output (MIMO) nonlinear system with neural network (NN), where a novel gradient adaptive law is used to update the NN weights both hidden and output layers such a faster convergence can be achieved. First, a three-layer NN structure is introduced to observe the MIMO nonlinear system with input–output data, and a new gradient algorithm is proposed to update the unknown parameters of both hidden and output layers. Then, the input dynamic can be obtained with the NN observer, and the inversion-model-based control is designed. Moreover, the ideal inversion control can be obtained based on the reference signal, and the inverse ILC is designed. The stability of the NN observer and the convergence of the inverse-model-based control are analyzed. Finally, a SCARA manipulator MIMO model is simulated to illustrate the correctness of the proposed methods.