Nonlinear Predictive Control Research Articles

A new approach for security of wireless sensor networks based on anti-synchronization of the fractional-order hyper-chaotic system

Chaotic systems have wide applications in secure communication engineering and cryptography. In this paper, improved nonlinear predictive control with whale algorithm for anti-synchronization of a fractional-order economic hyper-chaotic system is used for increasing the security of wireless sensor networks and preventing intrusion. By chaotic masking method and the T-S fuzzy model, the message signal is encoded at the wireless sensor side and it is placed along the transmitter route. In the central station, the message signal is decoded using the T-S fuzzy model and the predictive control by anti-synchronizing the fractional-order hyper-chaotic slave system. To reduce the effect of disturbances, a sign function of error is added to the predictive control. Finally, simulation results indicate the proper performance of the proposed nonlinear predictive control for anti-synchronizing the fractional-order hyper-chaotic systems in secure communications.

Robust non-linear control of a hybrid water pumping system based on induction motor

This contribution presents a non-linear control of a hybrid pumping system supplied with a photovoltaic generator and a battery. This system is employed for delivering a continuous volume of water whatever the climatic conditions. In the DC side, a boost converter is controlled with the indirect double integral sliding mode controller (DISMC) for maximum power point tracking (MPPT). The DISMC is suitable for MPPT because it gives a fast response and reduces the amplitude of power oscillations. Then, a bidirectional buck-boost converter is adopted to ensure the energy management between the battery and the DC-bus, and this converter is controlled with integral sliding mode control (ISMC) theory. The non-linear predictive control (NPC) is chosen to drive an induction motor (IM), the NPC is known by its fast dynamic and high capacity to reject disturbances. The hybrid system is modelled in MATLAB/Simulink software. During simulations, the DISMC-MPPT is compared with other techniques such as sliding mode controller (SMC) MPPT and integral SMC MPPT, the DISMC provides the best tracking performances under different irradiances. Moreover, the designed controller for the bidirectional converter regulates the DC-link voltage with better performances than the classical PI controller. Lastly, the NPC regulates the speed of the IM with high robustness.

Constrained Nonlinear Discrete-Time Sliding Mode Control Based on a Receding Horizon Approach

In this article, a discrete-time sliding mode control law is proposed for nonlinear (possibly multiinput) systems, in the presence of mixed input-state constraints and additive bounded disturbances. The control law is defined by formulating a nonlinear predictive control problem aimed at generating a control input that imitates an unconstrained discrete-time sliding mode law. In addition to satisfying input and state constraints, the resulting control law has all the properties of discrete-time sliding mode, and in particular, finite time convergence of the state onto the sliding manifold in the nominal case, or into an a-priori defined boundary layer of the sliding manifold in case bounded disturbances are present.

Design and Experimental Verification of Real-Time Nonlinear Predictive Controller for Improving the Stability of Production Vehicles

Vehicle stability control under extreme conditions is influenced by the coupled nonlinear characteristics of vehicle dynamics, corresponding safety constraints, and rapid response requirements. To address these problems, this brief proposes a real-time nonlinear predictive controller for a distributed drive electric vehicle. First, nonlinear lateral dynamics of the vehicle are applied to develop the stability controller on low friction coefficient surfaces. Second, the requirement for suppressing the sideslip angle is integrated into the objective function to prevent the vehicle from destabilizing due to excessive sideslip angles. Finally, a fast solution algorithm is proposed by solving the transformed two-point boundary value problem, making it possible to apply nonlinear predictive controller to experimental road tests. The experiments with a production vehicle are conducted on the snow-covered dynamic roads of the DongFeng's winter test center. The test results on low friction coefficient roads show that the overall passing speed can be improved from 50-55 to 60-70 km/h with the proposed controller.

Research and Analysis of Nonlinear Predictive Model Identification Control Based on Pumped Storage Unit in Construction Site

In this paper, a generalized predictive control method for the speed control system of pumped storage units is proposed, which is suitable for different working conditions of the power generation direction of pumped storage units. Through a combination of mechanism modeling and data-driven model order and parameter reduction strategy to determine the time delay and order of the instantaneous linear prediction model of the speed control system of pumped storage unit. According to the operation state and control target of the unit, the design scheme of the generalized predictive control frequency regulation mode and the opening regulation mode are given respectively, and the dynamic analysis of the control process under different operation conditions is carried out according to the actual parameters of the speed regulation system of a single 300MW pumped storage unit of a pumped storage power station in Central China, which verifies the effectiveness of the control method.

A Constrained Non-Linear Model Predictive Controller for the Rotor Flux-Oriented Control of an Induction Motor Drive

Predictive controllers have been extensively studied and applied to electrical drives, mainly because they provide fast dynamic responses and are suitable for multi-variable control and non-linear systems. Many approaches perform the prediction and optimization process on-line, which requires a high computational capacity for fast dynamics, such as, for example, the control of AC electric motors. Due to the complexity of embedding constraints in controller design, which demands a high computational capacity to solve the optimization problem, off-line approaches are one of the choices to overcome this problem. However, these strategies do not deal with the inherent constraints of the drive system, which significantly simplifies the design of the controller. This paper proposes a non-linear and multi-variable predictive controller to control the speed and rotor flux of an induction motor, where the constraints are treated after the controller design. Besides dealing with the constraints of the electric drive system, our proposal allows increasing the stability of the system when the model does not incorporate disturbances and when parameter incompatibilities occur. Several computer simulations and experimental tests were performed to evaluate the behavior of the proposed controller, showing good performance to track the controlled variables under normal operating conditions, under load disturbances, parametric incompatibility, and at a very low rotor speed.

Explicit nonlinear predictive control algorithms for Laguerre filter and sparse least square support vector machine-based Wiener model

In this paper, three computationally proficient model predictive control (MPC) algorithms for least square support vector machine (LSSVM)-based Wiener model are described. A Wiener model with Laguerre filter as dynamic linear part and LSSVM approximator as nonlinear static part is considered. Even though having excellent approximation abilities, LSSVM suffers from lack of sparseness. A pruning algorithm for LSSVM model is proposed and its comparison is made with classical pruning algorithm. The proposed pruning algorithm is able to remove 99% of support vectors with no remarkable drop in modelling accuracy. Using pruned Wiener model, three computationally efficient MPC algorithms are described. In the first algorithm, linearization of Wiener model is performed at every sampling interval and therefore control vector is determined by carrying out a quadratic optimization task. In the second algorithm, control signal is determined by an explicit control law and parameters of this control law are computed by performing lower-upper (LU) factorization of a matrix and solving linear equations without any online optimization. In the third algorithm, the parameters of explicit control law are calculated directly by another LSSVM approximator, which is trained offline. The advantages and effectiveness of proposed methods are demonstrated on the benchmark pH neutralization reactor. The control performance and computational efficiency of proposed algorithms are compared with computationally complex nonlinear MPC, which repeats a nonlinear optimization task at every sampling interval. The impact of pruning on model accuracy, computational efficiency and control accuracy is also discussed.

Nonlinear predictive control employing Carleman bilinearization and fixed search directions

AbstractThis work is concerned with the predictive control of nonlinear systems using the Carleman bilinearization technique. Given a nonlinear system model with sufficient regularity, a bilinear approximation can be obtained by means of Carleman's technique. After discretizing the continuous time model, several algorithms exist to tackle the bilinear model predictive control (BMPC) problem. More specifically, the present work exploits the combination of Carleman's approximation with a fixed search directions algorithm previously proposed within the context of BMPC. Simulations are carried out in order to compare predictive controllers designed using bilinear and linear plant models, but acting on the original nonlinear system. Moreover, the fixed search directions algorithm is compared with the use of a standard interior point optimizer. As a result, the proposed method is shown to provide improvements in terms of either stability, constraint satisfaction or reduced computational effort.

Design of an Adaptive Neural Predictive Nonlinear Controller for Nonholonomic Mobile Robot System Based on Posture Identifier in the Presence of Disturbance

This paper proposes an adaptive neural predictive nonlinear controller to guide a nonholonomic wheeled mobile robot during continuous and non-continuous gradients trajectory tracking. The structure of the controller consists of two models that describe the kinematics and dynamics of the mobile robot system and a feedforward neural controller. The models are modified Elman neural network and feedforward multi-layer perceptron respectively. The modified Elman neural network model is trained off-line and on-line stages to guarantee the outputs of the model accurately represent the actual outputs of the mobile robot system. The trained neural model acts as the position and orientation identifier. The feedforward neural controller is trained off-line and adaptive weights are adapted on-line to find the reference torques, which controls the steady-state outputs of the mobile robot system. The feedback neural controller is based on the posture neural identifier and quadratic performance index optimization algorithm to find the optimal torque action in the transient state for N-step-ahead prediction. General back propagation algorithm is used to learn the feedforward neural controller and the posture neural identifier. Simulation results show the effectiveness of the proposed adaptive neural predictive control algorithm; this is demonstrated by the minimised tracking error and the smoothness of the torque control signal obtained with bounded external disturbances.

A Self-triggered Position Based Visual Servoing Model Predictive Control Scheme for Underwater Robotic Vehicles

An efficient position based visual sevroing control approach for Autonomous Underwater Vehicles (AUVs) by employing Non-linear Model Predictive Control (N-MPC) is designed and presented in this work. In the proposed scheme, a mechanism is incorporated within the vision-based controller that determines when the Visual Tracking Algorithm (VTA) should be activated and new control inputs should be calculated. More specifically, the control loop does not close periodically, i.e., between two consecutive activations (triggering instants), the control inputs calculated by the N-MPC at the previous triggering time instant are applied to the underwater robot in an open-loop mode. This results in a significantly smaller number of requested measurements from the vision tracking algorithm, as well as less frequent computations of the non-linear predictive control law. This results in a reduction in processing time as well as energy consumption and, therefore, increases the accuracy and autonomy of the Autonomous Underwater Vehicle. The latter is of paramount importance for persistent underwater inspection tasks. Moreover, the Field of View constraints (FoV), control input saturation, the kinematic limitations due to the underactuated degree of freedom in sway direction, and the effect of the model uncertainties as well as external disturbances have been considered during the control design. In addition, the stability and convergence of the closed-loop system has been guaranteed analytically. Finally, the efficiency and performance of the proposed vision-based control framework is demonstrated through a comparative real-time experimental study while using a small underwater vehicle.

Model Predictive Control of Non-Linear Systems Using Tensor Flow-Based Models

The present paper proposes an approach for the development of a non-linear model-based predictive controller (NMPC) using a non-linear process model based on Artificial Neural Networks (ANNs). This work exploits recent trends on ANN literature using a TensorFlow implementation and shows how they can be efficiently used as support for closed-loop control systems. Furthermore, it evaluates how the generalization capability problems of neural networks can be efficiently overcome when the model that supports the control algorithm is used outside of its initial training conditions. The process’s transient response performance and steady-state error are parameters under focus and will be evaluated using a MATLAB’s Simulink implementation of a Coupled Tank Liquid Level controller and a Yeast Fermentation Reaction Temperature controller, two well-known benchmark systems for non-linear control problems.

Comparative Analysis of Machine Learning Models for Predictive Control of the Cyclopentadine Production Process

AbstractDifferent control strategies have been investigated to improve nonlinear system operations. One such strategy is the use of nonlinear predictive controllers (NMPCs) based on machine learning models. These models, such as artificial neural networks (NN), support vector machines (SVMs), and neuro-fuzzy networks (NF), present satisfactory adaptability to the complexity of the processes. In this aspect, a comparative study of the models in the predictive control of a complex system, such as MIMO (multiple-input-multiple-output) process of the production process of cyclopentadiene, is of interest and is the aim of this work. In this aspect, we find, through simulations, that the NMPCs presented adequate performance, especially those based on an SVM, concerning the servo and regulatory problem scenarios, keeping the process at the optimum operating point, especially for unattainable setpoint. The instability in the use of the classical proportional-integral-derivative linear control is also shown.

A new multimodel approach by Laguerre filters on sliding window for nonlinear system identification and control

This paper proposes an online identification procedure on sliding window with the synthesis of a nonlinear adaptive predictive control for a new nonlinear model resulting in multimodel approach. Such a model is entitled ARX-Laguerre multimodel obtained by expanding the conventional ARX multimodel on independent Laguerre orthonormal bases. It allows a significant parameter number reduction as well as a simple recursive representation compared with the ARX-multimodel. This parametric reduction is provided from an optimal iteratif identification approach of the Laguerre poles presented in Adaily et al. (2013). We propose to combine and carry out this identification approach on a sliding window to achieve an online identification procedure of the ARX-Laguerre multimodel for real time procedure depending on Fourier coefficients that are identified by a regularized square error. This property allows to synthese a new nonlinear adaptive predictive control on sliding window. We develop the general form of a new predictor and so, we propose an optimization algorithm formulated as a quadratic programming (QP) under linear constraints for an adaptive control law. The performances of the proposed online identification procedure and the developed nonlinear adaptive control algorithm are illustrated on a benchmark system as the continuous stirred tank reactor system (CSTR) with respect to the process parameter uncertainties.

Intelligent Swing-Up and Robust Stabilization via Tube-based Nonlinear Model Predictive Control for A Rotational Inverted-Pendulum System

The purpose of this paper is to introduce a new robust nonlinear model-based predictive control scheme applied to a rotational inverted-pendulum system. The rotational pendulum is composed by a mechanical arm attached to a free-motion pendulum (orthogonal to the arm), namely Furuta Pendulum. In principle, a Fuzzy controller enables the robotic arm bar to lift the rotational pendulum through oscillatory swing-up motion up to automatically achieve the upper equilibrium position in a prescribed stabilizing operation range. After the pendulum reaches the operating range, an intelligent control bypass system allows the transition between the swing-up motion controller and a robust predictive controller to maintain the angular position of the pendulum around the upward critical position. To achieve robust performance, a centralized control framework combines a triplet of control actions. The first one compensates for disturbances using the regulation trajectory ?feedforward control. The second control action corrects errors produced by modelling mismatch. The third controller assures robustness on the closed-loop system whilst compensating for deviations of the state trajectories from the nominal ones (i.e, disturbance-free). The control strategy provides robust feasibility despite constraints on the arm bar and pendulum's actuators are met. Such constraints are calculated on-line based on robust positively invariant sets characterised by polytopic sets (tubes). The proposed controller is tested in a series of simulations, and experimentally validated on a high-fidelity simulation environment including a rotational inverted-pendulum built for educational purposes. The results show that robust control performance is strengthened against disturbances of the closed-loop system benchmarked to inherently-robust linear and nonlinear predictive controllers.

GPIO-Based Nonlinear Predictive Control for Flux-Weakening Current Control of the IPMSM Servo System

This paper proposes a generalized proportional integral observer (GPIO) based nonlinear predictive control (NPC) for an interior permanent magnet synchronous motor (IPMSM) to improve the flux-weakening (FW) current control performance against the complex nonlinear cross-coupling terms and the IPMSM parameters’ variations. First, the IPMSM is remodeled to further analyze the FW control difficulties caused by such cross-coupling terms and parameters variations. Considering the parameters’ variations as a kind of disturbance, a GPIO is then designed to compensate for such disturbance. A GPIO-based NPC is finally designed to handle the nonlinear cross-coupling terms to obtain an optimized current control performance. Experiments on a digital signal processor (DSP) based IPMSM servo system validate the workability of the proposed control scheme.

Particle swarm optimisation in nonlinear model predictive control; comprehensive simulation study for two selected problems

Direct model predictive control applications for nonlinear systems can result in non-convex minimisation problems, which is additionally complicated if systems are non-minimum phase. In this paper, the Particle Swarm Optimisation (PSO) is applied for these global minimisation problems and tested on two selected nonlinear systems. Obtained results show that, in comparison to the sequential quadratic programming method, PSO is less vulnerable to local minima, and, with appropriate parameters, provides superior quality in nonlinear predictive control. The main results concerning PSO application show that the higher number of particles, comparing to the number of iterations, provides improved accuracy with limited computational burden; this way up to reduction of a proposed quality index is obtained preserving unchanged time of calculations. The performance is also boosted when after several iterations of the algorithm greater emphasis is put on the local search, which is achieved by appropriate learning factors and inertia weight.

Nonlinear predictive control applied to a biped walker with adjustable step length using a passive walking‐based reference generator

SummaryThis paper presents the use of passive dynamics to generate the sagittal plane references for a biped walker. In order to achieve an adjustable gait width, a neural network reference generator, trained with passive walking data on different slopes, was applied. The control algorithm was implemented with an Nonlinear Model Predictive Control (NMPC) strategy, in order to perform multiple‐input multiple‐output reference tracking while maintaining balance. The main contributions of the present work are using a kneed passive walker model for reference generation, which creates gait profiles that are more natural than the compass gait model, presenting a low computational cost, since only the forward kinematic model is used, and enabling adjustable gait width, due to the use of a neural network trained with data from the passive walker. Simulation results using V‐REP (Virtual Robot Experimentation Platform) are presented, using a sagittal kneed walker with a torso and arms, demonstrating the effectiveness of the proposed method.

Recurrent Interval Type-2 Fuzzy Wavelet Neural Network with Stable Learning Algorithm: Application to Model-Based Predictive Control

Fuzzy neural networks, with suitable learning strategy, have been demonstrated as an effective tool for online data modeling. However, it is a challenging task to construct a model to ensure its quality and stability for non-stationary dynamic systems with some uncertainties. To solve this problem, this paper presents a novel identification model based on recurrent interval type-2 fuzzy wavelet neural network (RIT2FWNN) with new learning algorithm. The model benefits from both advantages of recurrent and wavelet neural networks such as use of temporal data and fast convergence properties. The proposed antecedent and consequent parameters update rules are derived using sliding-mode-control-theory. To evaluate the proposed fuzzy model, it is utilized to design a nonlinear model-based predictive controller and is applied for the synchronization of fractional-order time-delay chaotic systems. Using Lyapunov stability analysis, it is shown that all update rules of the parameters are uniformly ultimately bounded. The adaptation laws obtained in this method are very simple and have closed forms. Some stability conditions are derived to prove learning dynamics and asymptotic stability of the network by using an appropriate Lyapunov function. The efficacy and performance of the proposed method is verified by simulation examples.

How does the CNS control arm reaching movements?Introducing a hierarchical nonlinear predictive control organization based on the idea of muscle synergies.

In this study, we introduce a hierarchical and modular computational model to explain how the CNS (Central Nervous System) controls arm reaching movement (ARM) in the frontal plane and under different conditions. The proposed hierarchical organization was established at three levels: 1) motor planning, 2) command production, and 3) motor execution. Since in this work we are not discussing motion learning, no learning procedure was considered in the model. Previous models mainly assume that the motor planning level produces the desired trajectories of the joints and feeds it to the next level to be tracked. In the proposed model, the motion control is described based on a regulatory control policy, that is, the output of the motor planning level is a step function defining the initial and final desired position of the hand. For the command production level, a nonlinear predictive model was developed to explain how the time-invariant muscle synergies (MSs) are recruited. We used the same computational model to explain the arm reaching motion for a combined ARM task. The combined ARM is defined as two successive ARM such that it starts from point A and reaches to point C via point B. To develop the model, kinematic and kinetic data from six subjects were recorded and analyzed during ARM task performance. The subjects used a robotic manipulator while moving their hand in the frontal plane. The EMG data of 15 muscles were also recorded. The MSs used in the model were extracted from the recorded EMG data. The proposed model explains two aspects of the motor control system by a novel computational approach: 1) the CNS reduces the dimension of the control space using the notion of MSs and thereby, avoids immense computational loads; 2) at the level of motor planning, the CNS generates the desired position of the hand at the starting, via and the final points, and this amounts to a regulatory and non-tracking structure.

A new approach in anti-synchronization of a fractional-order hyper-chaotic Duffing system based on new nonlinear predictive control

In this paper, we have carried out a new method for the anti-synchronization of a fractional-order hyperchaotic Duffing system using the nonlinear predictive control. At first, in this method master and slave systems are modeled using Takagi–Sugeno fuzzy model, Then, nonlinear predictive controller based on proposed model, is applied to the system to achieve the aim of the anti-synchronization. In this controller, the feedback coefficients of the error are set using the teaching learning based optimization, so that the cost function, which is including the error and control effort, becomes minimized. The advantage of the proposed method is the robustness of the controller against uncertainty and disturbance. Simulating results showed that, the proposed method has been able to anti-synchronize the master and slave fractional-order hyperchaotic Duffing systems with uncertainty and disturbance in highly accurately manner.