Robust model predictive control of nonlinear systems with unmodeled dynamics and bounded uncertainties based on neural networks

On the Guaranteed Almost Equivalence Between Imitation Learning From Observation and Demonstration

Imitation learning from observation (LfO) is more preferable than imitation learning from demonstration (LfD) because of the nonnecessity of expert actions when reconstructing the expert policy from the expert data. However, previous studies imply that the performance of LfO is inferior to LfD by a tremendous gap, which makes it challenging to employ LfO in practice. By contrast, this article proves that LfO is almost equivalent to LfD in the deterministic robot environment, and more generally even in the robot environment with bounded randomness. In the deterministic robot environment, from the perspective of the control theory, we show that the inverse dynamics disagreement between LfO and LfD approaches zero, meaning that LfO is almost equivalent to LfD. To further relax the deterministic constraint and better adapt to the practical environment, we consider bounded randomness in the robot environment and prove that the optimizing targets for both LfD and LfO remain almost the same in the more generalized setting. Extensive experiments for multiple robot tasks are conducted to demonstrate that LfO achieves comparable performance to LfD empirically. In fact, the most common robot systems in reality are the robot environment with bounded randomness (i.e., the environment this article considered). Hence, our findings greatly extend the potential of LfO and suggest that we can safely apply LfO in practice without sacrificing the performance compared to LfD.

Two-Timescale Multilayer Recurrent Neural Networks for Nonlinear Programming

This article presents a neurodynamic approach to nonlinear programming. Motivated by the idea of sequential quadratic programming, a class of two-timescale multilayer recurrent neural networks is presented with neuronal dynamics in their output layer operating at a bigger timescale than in their hidden layers. In the two-timescale multilayer recurrent neural networks, the transient states in the hidden layer(s) undergo faster dynamics than those in the output layer. Sufficient conditions are derived on the convergence of the two-timescale multilayer recurrent neural networks to local optima of nonlinear programming problems. Simulation results of collaborative neurodynamic optimization based on the two-timescale neurodynamic approach on global optimization problems with nonconvex objective functions or constraints are discussed to substantiate the efficacy of the two-timescale neurodynamic approach.

Neural network-based model predictive tracking control of an uncertain robotic manipulator with input constraints

This paper proposes a neural network-based model predictive control (MPC) method for robotic manipulators with model uncertainty and input constraints. In the presented NN-based MPC structure, two groups of radial basis function neural networks (RBFNNs) are considered for online model estimation and effective optimization. The first group of RBFNNs is introduced as a predictive model for the robotic system with online learning strategies for handling the system uncertainty and improving the model estimation accuracy. The second one is developed for solving the optimization problem. By taking into account an actor-critic scheme with different weights and the same activation function, adaptive learning strategies are established for balancing between optimal tracking performance and predictive system stability. In addition, aiming at guaranteeing the input constraints, a nonquadratic cost function is adopted for the NN-based MPC. The ultimately uniformly boundedness (UUB) of all variables is verified through the Lyapunov approach. Simulation studies are conducted to explain the effectiveness of the proposed method.

A New Projected Active Set Conjugate Gradient Approach for Taylor-Type Model Predictive Control: Application to Lower Limb Rehabilitation Robots With Passive and Active Rehabilitation

In this paper, a three-order Taylor-type numerical differentiation formula is firstly utilized to linearize and discretize constrained conditions of model predictive control (MPC), which can be generalized from lower limb rehabilitation robots. Meanwhile, a new numerical approach that projected an active set conjugate gradient approach is proposed, analyzed, and investigated to solve MPC. This numerical approach not only incorporates both the active set and conjugate gradient approach but also utilizes a projective operator, which can guarantee that the equality constraints are always satisfied. Furthermore, rigorous proof of feasibility and global convergence also shows that the proposed approach can effectively solve MPC with equality and bound constraints. Finally, an echo state network (ESN) is established in simulations to realize intention recognition for human–machine interactive control and active rehabilitation training of lower-limb rehabilitation robots; simulation results are also reported and analyzed to substantiate that ESN can accurately identify motion intention, and the projected active set conjugate gradient approach is feasible and effective for lower-limb rehabilitation robot of MPC with passive and active rehabilitation training. This approach also ensures computational when disturbed by uncertainties in system.

Coal Classification Method Based on Improved Local Receptive Field-Based Extreme Learning Machine Algorithm and Visible-Infrared Spectroscopy

In the process of using coal, if the type of coal cannot be accurately determined, it will have a significant impact on production efficiency, environmental pollution, and economic loss. At present, the traditional classification method of coal mainly relies on technician's experience. This requires a lot of manpower and time, and it is difficult to automate. This paper mainly studies the application of visible-infrared spectroscopy and machine learning methods in coal mine identification and analysis to provide guidance for coal mining and production. This paper explores a fast and high-precision method for coal identification. In this paper, for the characteristics of high dimensionality, strong correlation, and large redundancy of spectral data, the local receptive field (LRF) is used to extract the advanced features of spectral data, which is combined with the extreme learning machine (ELM). We improved the coyote optimization algorithm (COA). The improved coyote optimization algorithm (I-COA) and local receptive field-based extreme learning machine (ELM-LRF) are used to optimize the structure and training parameters of the extreme learning machine network. The experimental results show that the coal classification model based on the network and visible-infrared spectroscopy can effectively identify the coal types through the spectral data. Compared with convolutional neural networks (CNN algorithm) and principal component analysis (PCA algorithm), LRF can extract the spectral characteristics of coal more effectively.

Deep neural networks as add-on modules for enhancing robot performance in impromptu trajectory tracking

High-accuracy trajectory tracking is critical to many robotic applications, including search and rescue, advanced manufacturing, and industrial inspection, to name a few. Yet the unmodeled dynamics and parametric uncertainties of operating in such complex environments make it difficult to design controllers that are capable of accurately tracking arbitrary, feasible trajectories from the first attempt (i.e., impromptu trajectory tracking). This article proposes a platform-independent, learning-based “add-on” module to enhance the tracking performance of black-box control systems in impromptu tracking tasks. Our approach is to pre-cascade a deep neural network (DNN) to a stabilized baseline control system, in order to establish an identity mapping from the desired output to the actual output. Previous research involving quadrotors showed that, for 30 arbitrary hand-drawn trajectories, the DNN-enhancement control architecture reduces tracking errors by 43% on average, as compared with the baseline controller. In this article, we provide a platform-independent formulation and practical design guidelines for the DNN-enhancement approach. In particular, we: (1) characterize the underlying function of the DNN module; (2) identify necessary conditions for the approach to be effective; (3) provide theoretical insights into the stability of the overall DNN-enhancement control architecture; (4) derive a condition that supports data-efficient training of the DNN module; and (5) compare the novel theory-driven DNN design with the prior trial-and-error design using detailed quadrotor experiments. We show that, as compared with the prior trial-and-error design, the novel theory-driven design allows us to reduce the input dimension of the DNN by two thirds while achieving similar tracking performance.

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

Different 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.

Supervisory predictive control for wheel slip prevention and tracking of desired speed profile in electric trains

This article presents a supervisory model predictive control system to track the desired speed profile and simultaneously prevent the wheels from slipping in acceleration mode of electrical trains. The proposed control strategy employs field-oriented control (FOC) to control the angular speed of the wheel. Model predictive control (MPC) is used to control the longitudinal velocity of the train to track the desired speed profile and prevent the wheels from slipping by generating the desired angular velocity for the FOC. Since, it is not possible to control the longitudinal velocity and slip ratio independently, a fuzzy supervisor system is proposed to control the train dynamics at the appropriate operating point. A method is presented to estimate train longitudinal velocity and the adhesion coefficient between the wheels and rail surface. These components are vital to implement the proposed method in a real train control system. The closed loop stability of the control system has been studied. Simulations were run under different friction coefficients corresponding to real train parameters to verify the effectiveness of the proposed re-adhesion control system. The simulation results have been compared with the results of other researches to show the feasibility and validity of the presented approach.

Neural Networks-Based Distributed Adaptive Control of Nonlinear Multiagent Systems

The cooperative control problem of nonlinear multiagent systems is studied in this paper. The followers in the communication network are subject to unmodeled dynamics. A fully distributed neural-networks-based adaptive control strategy is designed to guarantee that all the followers are asymptotically synchronized to the leader, and the synchronization errors are within a prescribed level, where some global information, such as minimum and maximum singular value of graph adjacency matrix, is not necessarily to be known. Based on the Lyapunov stability theory and algebraic graph theory, the stability analysis of the resulting closed-loop system is provided. Finally, an numerical example illustrates the effectiveness and potential of the proposed new design techniques.

Integrated vehicle dynamics management for distributed‐drive electric vehicles with active front steering using adaptive neural approaches against unknown nonlinearity

This paper proposes a new integrated vehicle dynamics management for enhancing the yaw stability and wheel slip regulation of the distributed‐drive electric vehicle with active front steering. To cope with the unknown nonlinear tire dynamics with uncertain disturbances in integrated control problem of vehicle dynamics, a neuro‐adaptive predictive control is therefore proposed for multiobjective coordination of constrained systems with unknown nonlinearity. Unknown nonlinearity with unmodeled dynamics is modeled using a random projection neural network via adaptive machine learning, where a new adaptation law is designed in premise of Lyapunov stability. Given the computational efficiency, a neurodynamic method is extended to solve the constrained programming problem with unknown nonlinearity. To test the performance of the proposed control method, simulations were conducted using a validated vehicle model. Simulation results show that the proposed neuro‐adaptive predictive controller outperforms the classical model predictive controller in tracking nominal wheel slip ratio, desired vehicle yaw rate and sideslip angle, showing its significance in vehicle yaw stability enhancement and wheels slip regulation.

An offset-free MPC formulation for nonlinear systems using adaptive integral controller

This paper investigates a novel offset-free control scheme based on a multiple model predictive controller (MMPC) and an adaptive integral action controller for nonlinear processes. Firstly, the multiple model description captures the essence of the nonlinear process, while keeping the MPC optimization linear. Multiple models also enable the controller to deal with the uncertainty associated with changing setpoint. Then, a min-max approach is utilized to counter the effect of parametric uncertainty between the linear models and the nonlinear process. Finally, to deal with other uncertainties, such as input and output disturbances, an adaptive integral action controller is run in parallel to the MMPC. Thus creating a novel offset-free approach for nonlinear systems that is more easily tuned than observer-based MPC. Simulation results for a pH-controller, which acts as an example of a nonlinear process, are presented to demonstrate the usefulness of the technique compared to using an observer-based MPC.

Model-Based Control of Soft Actuators Using Learned Non-linear Discrete-Time Models

Soft robots have the potential to significantly change the way that robots interact with the environment and with humans. However, accurately modeling soft robot and soft actuator dynamics in order to perform model-based control can be extremely difficult. Deep neural networks are a powerful tool for modeling systems with complex dynamics such as the pneumatic, continuum joint, six degree-of-freedom robot shown in this paper. Unfortunately it is also difficult to apply standard model-based control techniques using a neural net. In this work, we show that the gradients used within a neural net to relate system states and inputs to outputs can be used to formulate a linearized discrete state space representation of the system. Using the state space representation, model predictive control (MPC) was developed with a six degree of freedom pneumatic robot with compliant plastic joints and rigid links. Using this neural net model, we were able to achieve an average steady state error across all joints of approximately 1 and 2° with and without integral control respectively. We also implemented a first-principles based model for MPC and the learned model performed better in terms of steady state error, rise time, and overshoot. Overall, our results show the potential of combining empirical modeling approaches with model-based control for soft robots and soft actuators.

An Inverse Neural Controller Based on the Applicability Domain of RBF Network Models

This paper presents a novel methodology of generic nature for controlling nonlinear systems, using inverse radial basis function neural network models, which may combine diverse data originating from various sources. The algorithm starts by applying the particle swarm optimization-based non-symmetric variant of the fuzzy means (PSO-NSFM) algorithm so that an approximation of the inverse system dynamics is obtained. PSO-NSFM offers models of high accuracy combined with small network structures. Next, the applicability domain concept is suitably tailored and embedded into the proposed control structure in order to ensure that extrapolation is avoided in the controller predictions. Finally, an error correction term, estimating the error produced by the unmodeled dynamics and/or unmeasured external disturbances, is included to the control scheme to increase robustness. The resulting controller guarantees bounded input-bounded state (BIBS) stability for the closed loop system when the open loop system is BIBS stable. The proposed methodology is evaluated on two different control problems, namely, the control of an experimental armature-controlled direct current (DC) motor and the stabilization of a highly nonlinear simulated inverted pendulum. For each one of these problems, appropriate case studies are tested, in which a conventional neural controller employing inverse models and a PID controller are also applied. The results reveal the ability of the proposed control scheme to handle and manipulate diverse data through a data fusion approach and illustrate the superiority of the method in terms of faster and less oscillatory responses.

Two stage neural network modelling for robust model predictive control

The paper proposes a novel robust model predictive control scheme realized by means of artificial neural networks. The neural networks are used twofold: to design the so-called fundamental model of a plant and to catch uncertainty associated with the plant model. In order to simplify the optimization process carried out within the framework of predictive control an instantaneous linearization is applied which renders it possible to define the optimization problem in the form of constrained quadratic programming. Stability of the proposed control system is also investigated by showing that a cost function is monotonically decreasing with respect to time. Derived robust model predictive control is tested and validated on the example of a pneumatic servomechanism working at different operating regimes.

LMI Conditions for Global Stability of Fractional-Order Neural Networks

Fractional-order neural networks play a vital role in modeling the information processing of neuronal interactions. It is still an open and necessary topic for fractional-order neural networks to investigate their global stability. This paper proposes some simplified linear matrix inequality (LMI) stability conditions for fractional-order linear and nonlinear systems. Then, the global stability analysis of fractional-order neural networks employs the results from the obtained LMI conditions. In the LMI form, the obtained results include the existence and uniqueness of equilibrium point and its global stability, which simplify and extend some previous work on the stability analysis of the fractional-order neural networks. Moreover, a generalized projective synchronization method between such neural systems is given, along with its corresponding LMI condition. Finally, two numerical examples are provided to illustrate the effectiveness of the established LMI conditions.

An Alternating Identification Algorithm for a Class of Nonlinear Dynamical Systems

While modeling nonlinear systems by combining a linear model with a nonlinear compensation term, namely, virtual unmodeled dynamics (VUD), the parameter estimation of the linear model and the learning-based VUD estimate influences and interacts with each other simultaneously. This paper aims to develop an alternating identification scheme for resolving such a challenging problem, where a projection algorithm is employed to identify the linear model and a feedforward neural network is used to model the VUD of a class of nonlinear dynamical systems. An open-loop estimation algorithm on the VUD is first presented under the known linear model, followed by an alternating identification algorithm for completely unknown nonlinear systems. Algorithm description is given and some simulation studies on multiple input and multiple output nonlinear systems are carried out to illustrate the effectiveness of our proposed modeling techniques.

Highly Efficient Framework for Predicting Interactions Between Proteins

Protein-protein interactions (PPIs) play a central role in many biological processes. Although a large amount of human PPI data has been generated by high-throughput experimental techniques, they are very limited compared to the estimated 130 000 protein interactions in humans. Hence, automatic methods for human PPI-detection are highly desired. This work proposes a novel framework, i.e., Low-rank approximation-kernel Extreme Learning Machine (LELM), for detecting human PPI from a protein's primary sequences automatically. It has three main steps: 1) mapping each protein sequence into a matrix built on all kinds of adjacent amino acids; 2) applying the low-rank approximation model to the obtained matrix to solve its lowest rank representation, which reflects its true subspace structures; and 3) utilizing a powerful kernel extreme learning machine to predict the probability for PPI based on this lowest rank representation. Experimental results on a large-scale human PPI dataset demonstrate that the proposed LELM has significant advantages in accuracy and efficiency over the state-of-art approaches. Hence, this work establishes a new and effective way for the automatic detection of PPI.

A Two-Time-Scale Neurodynamic Approach to Constrained Minimax Optimization

This paper presents a two-time-scale neurodynamic approach to constrained minimax optimization using two coupled neural networks. One of the recurrent neural networks is used for minimizing the objective function and another is used for maximization. It is shown that the coupled neurodynamic systems operating in two different time scales work well for minimax optimization. The effectiveness and characteristics of the proposed approach are illustrated using several examples. Furthermore, the proposed approach is applied for H_∞ model predictive control.

Low-Discrepancy Points for Deterministic Assignment of Hidden Weights in Extreme Learning Machines

The traditional extreme learning machine (ELM) approach is based on a random assignment of the hidden weight values, while the linear coefficients of the output layer are determined analytically. This brief presents an analysis based on geometric properties of the sampling points used to assign the weight values, investigating the replacement of random generation of such values with low-discrepancy sequences (LDSs). Such sequences are a family of sampling methods commonly employed for numerical integration, yielding a more efficient covering of multidimensional sets with respect to random sequences, without the need for any computationally intensive procedure. In particular, we prove that the universal approximation property of the ELM is guaranteed when LDSs are employed, and how an efficient covering affects the convergence positively. Furthermore, since LDSs are generated deterministically, the results do not have a probabilistic nature. Simulation results confirm, in practice, the good theoretical properties given by the combination of ELM with LDSs.

Recurrent-Neural-Network-Based Multivariable Adaptive Control for a Class of Nonlinear Dynamic Systems With Time-Varying Delay

At the beginning, an approximate nonlinear autoregressive moving average (NARMA) model is employed to represent a class of multivariable nonlinear dynamic systems with time-varying delay. It is known that the disadvantages of robust control for the NARMA model are as follows: 1) suitable control parameters for larger time delay are more sensitive to achieving desirable performance; 2) it only deals with bounded uncertainty; and 3) the nominal NARMA model must be learned in advance. Due to the dynamic feature of the NARMA model, a recurrent neural network (RNN) is online applied to learn it. However, the system performance becomes deteriorated due to the poor learning of the larger variation of system vector functions. In this situation, a simple network is employed to compensate the upper bound of the residue caused by the linear parameterization of the approximation error of RNN. An e -modification learning law with a projection for weight matrix is applied to guarantee its boundedness without persistent excitation. Under suitable conditions, the semiglobally ultimately bounded tracking with the boundedness of estimated weight matrix is obtained by the proposed RNN-based multivariable adaptive control. Finally, simulations are presented to verify the effectiveness and robustness of the proposed control.

Data-Driven Zero-Sum Neuro-Optimal Control for a Class of Continuous-Time Unknown Nonlinear Systems With Disturbance Using ADP

This paper is concerned with a new data-driven zero-sum neuro-optimal control problem for continuous-time unknown nonlinear systems with disturbance. According to the input-output data of the nonlinear system, an effective recurrent neural network is introduced to reconstruct the dynamics of the nonlinear system. Considering the system disturbance as a control input, a two-player zero-sum optimal control problem is established. Adaptive dynamic programming (ADP) is developed to obtain the optimal control under the worst case of the disturbance. Three single-layer neural networks, including one critic and two action networks, are employed to approximate the performance index function, the optimal control law, and the disturbance, respectively, for facilitating the implementation of the ADP method. Convergence properties of the ADP method are developed to show that the system state will converge to a finite neighborhood of the equilibrium. The weight matrices of the critic and the two action networks are also convergent to finite neighborhoods of their optimal ones. Finally, the simulation results will show the effectiveness of the developed data-driven ADP methods.

Nonlinear Model Predictive Control Based on a Self-Organizing Recurrent Neural Network

A nonlinear model predictive control (NMPC) scheme is developed in this paper based on a self-organizing recurrent radial basis function (SR-RBF) neural network, whose structure and parameters are adjusted concurrently in the training process. The proposed SR-RBF neural network is represented in a general nonlinear form for predicting the future dynamic behaviors of nonlinear systems. To improve the modeling accuracy, a spiking-based growing and pruning algorithm and an adaptive learning algorithm are developed to tune the structure and parameters of the SR-RBF neural network, respectively. Meanwhile, for the control problem, an improved gradient method is utilized for the solution of the optimization problem in NMPC. The stability of the resulting control system is proved based on the Lyapunov stability theory. Finally, the proposed SR-RBF neural network-based NMPC (SR-RBF-NMPC) is used to control the dissolved oxygen (DO) concentration in a wastewater treatment process (WWTP). Comparisons with other existing methods demonstrate that the SR-RBF-NMPC can achieve a considerably better model fitting for WWTP and a better control performance for DO concentration.

A Projection Neural Network for Constrained Quadratic Minimax Optimization

This paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems. Sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network. Compared with some of the existing neural networks for quadratic minimax optimization, the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems, and the designed neural network does not include any parameter. Moreover, the neural network has lower model complexities, the number of state variables of which is equal to that of the dimension of the optimization problems. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network.

Data Partition Learning With Multiple Extreme Learning Machines

As demonstrated earlier, the learning accuracy of the single-layer-feedforward-network (SLFN) is generally far lower than expected, which has been a major bottleneck for many applications. In fact, for some large real problems, it is accepted that after tremendous learning time (within finite epochs), the network output error of SLFN will stop or reduce increasingly slowly. This report offers an extreme learning machine (ELM)-based learning method, referred to as the parent-offspring progressive learning method. The proposed method works by separating the data points into various parts, and then multiple ELMs learn and identify the clustered parts separately. The key advantages of the proposed algorithms as compared to the traditional supervised methods are twofold. First, it extends the ELM learning method from a single neural network to a multinetwork learning system, as the proposed multiELM method can approximate any target continuous function and classify disjointed regions. Second, the proposed method tends to deliver a similar or much better generalization performance than other learning methods. All the methods proposed in this paper are tested on both artificial and real datasets.

Nonlinear model predictive control based on collective neurodynamic optimization

In general, nonlinear model predictive control (NMPC) entails solving a sequential global optimization problem with a nonconvex cost function or constraints. This paper presents a novel collective neurodynamic optimization approach to NMPC without linearization. Utilizing a group of recurrent neural networks (RNNs), the proposed collective neurodynamic optimization approach searches for optimal solutions to global optimization problems by emulating brainstorming. Each RNN is guaranteed to converge to a candidate solution by performing constrained local search. By exchanging information and iteratively improving the starting and restarting points of each RNN using the information of local and global best known solutions in a framework of particle swarm optimization, the group of RNNs is able to reach global optimal solutions to global optimization problems. The essence of the proposed collective neurodynamic optimization approach lies in the integration of capabilities of global search and precise local search. The simulation results of many cases are discussed to substantiate the effectiveness and the characteristics of the proposed approach.

Trends in extreme learning machines: a review

Extreme learning machine (ELM) has gained increasing interest from various research fields recently. In this review, we aim to report the current state of the theoretical research and practical advances on this subject. We first give an overview of ELM from the theoretical perspective, including the interpolation theory, universal approximation capability, and generalization ability. Then we focus on the various improvements made to ELM which further improve its stability, sparsity and accuracy under general or specific conditions. Apart from classification and regression, ELM has recently been extended for clustering, feature selection, representational learning and many other learning tasks. These newly emerging algorithms greatly expand the applications of ELM. From implementation aspect, hardware implementation and parallel computation techniques have substantially sped up the training of ELM, making it feasible for big data processing and real-time reasoning. Due to its remarkable efficiency, simplicity, and impressive generalization performance, ELM have been applied in a variety of domains, such as biomedical engineering, computer vision, system identification, and control and robotics. In this review, we try to provide a comprehensive view of these advances in ELM together with its future perspectives.