Adaptive Neural Control Design of MIMO Nonaffine Nonlinear Systems with Input Saturation

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.

In this paper, a robust control approach is applied for both MIMO/SISO affine/non-affine nonlinear systems based on a modeling error-based adaptive fuzzy observer controller, in the presence of input saturation. In the proposed scheme, non-affine nonlinear systems can be transformed to affine systems and unknown higher-order term of expansion (HOTE) that appears due to the use of this method can be estimated by an adaptive fuzzy technique. Using the modeling error between the system states observer and a serial–parallel estimator model, a modeling error-based adaptive fuzzy observer estimator is proposed that uses the modeling error as the input of fuzzy system to approximate and adaptively compensate the unknown HOTE and also the external disturbance. The proposed scheme is able to hold control performance in the presence of input saturation. An analysis of the controlled system is presented to verify the stability of the system under control. The stability of the closed-loop system is provided based on the strictly positive real condition and Lyapunov theory. The proposed approach is effectual and robust. The simulation results demonstrate the usefulness of the proposed method for both MIMO and SISO systems.

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.

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 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.

A multilayer recurrent neural network-based approach for the identification and self-tuning adaptive control of multi-input multi-output nonlinear dynamical systems is developed. An efficient online implementation of the control strategy, by a fast updating of the control actions to track the dynamical variations in the system, is facilitated by the recurrent neural network, which is trained by a supervised training scheme that uses a simple updating rule. An application of this approach for the adaptive control of synchronous power generators under fault conditions is described, and a quantitative performance evaluation is given to bring out certain important characteristic features of the neural network used for control. >

To achieve more precise positioning of the electronic throttle plate, a nonlinear backstepping tracking control strategy is presented in this paper. In contrast to the existing control schemes for electronic throttles, the input saturation and unknown external disturbances are explicitly considered in the tracking control design. The difficulties in controlling an electronic throttle include the strong nonlinearity of the spring and friction as well as the unknown external disturbance. In particular, the valve plate angle is adjusted by the control input voltage of the driving motor, and the input voltage is limited to a certain range. Therefore, input saturation problems exist in the control system for an electronic throttle. To overcome the abovementioned difficulties, an auxiliary design system is presented to handle the input saturation, and its state is applied in the proposed control design. A sliding-mode control term is also utilized in the tracking controller to counteract the unknown external disturbance. The proof and analysis show that the satisfactory tracking performance of the valve plate angle can be achieved by using the designed control scheme for the electronic throttle system in the presence of input saturation and unknown external disturbances. Simulation studies and results are provided to illustrate the desired performance of the proposed nonlinear tracking controller.

In this article, an improved model-free adaptive control (iMFAC) is proposed for discrete-time multi-input multioutput (MIMO) nonlinear systems with an event-triggered transmission scheme and quantization (ETQ). First, an event-triggered scheme is designed, and the structure of the uniform quantizer with an encoding-decoding mechanism is given. With the concept of partial form dynamic linearization based on event-triggered and quantization (PFDL-ETQ), a linearized data model of the MIMO nonlinear system is constructed. Then, an improved model-free adaptive controller with the ETQ process is designed. By this design, the update of the pseudo partitioned Jacobean matrix (PPJM) estimates and control inputs occurs only when the trigger conditions are met, which reduces the network transmission burden and saves the computing resources. Theoretical analysis shows that the proposed iMFAC with the ETQ process can achieve a bounded convergence of tracking error. Finally, a numerical simulation and a biaxial gantry motor contour tracking control system simulation are given to illustrate the feasibility of the proposed iMFAC method with the ETQ process.

This paper deals with a approximating method for large time-delays of multi-input multi-output (MIMO) dynamical systems. The methodology is an improved rational approximation approach. Time delay terms of the state space equations can be described by delay matrix in the complex domain and approximated by rational matrix Pade-type functions. The minimum variance estimation error is minimized to obtain rational approximation of MIMO systems to guarantee the poles located in the left half plane. Matrix Pade-type approximation can largely reduce the instability and the overshoot, so the fast-response property is improved. Simulation results of the proposed method are presented to illustrate the correctness and effectively.

This manuscript introduces a novel methodology to solve the state estimation of discrete-time multi-input multi-output (MIMO) nonlinear systems with uncertain dynamics. The mathematical model of the nonlinear systems considered in this paper satisfies the usual Lagrangian structure that characterizes many mechanical, electrical or electromechanical systems. A recurrent neural network (RNN) estimates the uncertain dynamics of the MIMO system with an updating law based on a particular variant of the discrete-time version of the super-twisting algorithm (DSTA). A Lyapunov stability analysis defines the convergence zone for the state estimation error throughout the solution of a matrix inequality. The convergence zone for the estimation is smaller when the DSTA and the RNN work together in an observer. Numerical examples demonstrate how the adaptive observer reduces the zone of convergence and the oscillations in the steady state compared with a discrete version of the STA with additional linear correcting terms. An experimental implementation shows how the observer estimates the unknown states of a Van Der Pol Oscillator. A comparison against some variations of the DSTA justifies the advantages of the mixed DSTA-RNN observer.

The article proposes a robust control approach based on self-organizing Hermite-polynomial-based neural network disturbance observer for a class of non-affine nonlinear systems with input saturation, state constraint, and unknown compound disturbance. Using Taylor series expansion, a hyperbolic tangent function, the non-affine nonlinear system with input saturation is transformed into time-varying affine system without input saturation, which can reduce step n + 1 of the backstepping technique compared with conventional method. Next, a self-organizing Hermite-polynomial-based neural network disturbance observer is proposed to estimate the compound disturbance online. Then, the auxiliary systems are designed to solve state constraint for subsystems, and hyperbolic tangent function is used to approximate the saturated control input. Simulation results proved the effectiveness of the proposed control scheme.

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.

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.

In this paper, a fuzzy adaptive control system is investigated for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with both unknown dead-zone and unknown sign of the control gain matrix (i.e. unknown control direction). To deal with the unknown sign of the control gain matrix, the Nussbaum-type function is used. In the designing of the fuzzy adaptive control scheme, we will fully exploit a decomposition property of the control gain matrix. To compensate the effects of the dead-zone, we require neither the knowledge of dead-zone parameters nor the construction of its inverse. Simulation results demonstrate the effectiveness of the approach.

In this paper, an algorithm using an artificial neural network (ANN)-based direct adaptive control algorithm is presented for multi-input multi-output (MIMO) nonlinear systems with unknown output delays. This algorithm contains two parameter estimations, one for estimating unknown plant delays and the other for unknown control parameters. If the number of center frequency is enough, the predicted output signal can approximate the true delayed output, especially for large output delays. It is shown that the proposed algorithm not only can guarantee control parameter estimation convergence but can achieve the tracking purposes. Simulation studies are presented to validate the theoretical findings.