NN Weights Research Articles

Adaptive Set-Membership State Estimation for Nonlinear Systems Under Bit Rate Allocation Mechanism: A Neural-Network-Based Approach.

In this article, the adaptive neural-network-based (NN-based) set-membership state estimation problem is studied for a class of nonlinear systems subject to bit rate constraints and unknown-but-bounded noises. The measurement output signals are transmitted from sensors to a remote estimator via a bit rate constrained communication channel. To relieve the communication burden and ameliorate the state estimation accuracy, a bit rate allocation mechanism is put forward for the sensor nodes by solving a constrained optimization problem. Subsequently, through the NN learning method, an NN-based set-membership estimator is designed to determine an ellipsoidal set that contains the system state, where the proposed estimator relies upon a prediction-correction structure. With the help of the mathematical induction technique and the set theory, sufficient conditions are obtained to ensure the existence of both the adaptive tuning parameters and the set-membership estimators, and then, the corresponding parameters and estimator gains are calculated by solving a set of optimization problems. In addition, the monotonicity of the upper bound on the squared estimation error with respect to the bit rate and the convergence of the NN weight are analyzed, respectively. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed state estimation algorithm.

Neural Learning Control for Discrete-Time Strict-Feedback Systems: An Error Estimate Method

This paper addresses the issue of neural learning control for a kind of discrete-time strict-feedback system. Firstly, by using an error dynamics estimator, a new delay-free NN update law is proposed. Subsequently, after making the system output tracks a given recurrent tracking signal, the estimated NN weights can be demonstrated to converge to a small area of their ideal values, exponentially, which can be stored as constant NN weights. Then, a neural learning controller is proposed by using the constant NN weights and disturbance observer. Compared with the previous neural learning controller, the proposed scheme can not only avoid the chattering problem that may be caused by controller switching but also enhance the system robustness by implanting the disturbance observer.

Research on Lateral Maneuverability of a Supercavitating Vehicle Based on RBFNN Adaptive Sliding Mode Control with Rolling Restriction and Planing Force Avoidance

This paper addresses the lateral motion control of a supercavitating vehicle and studies its ability to maneuver. According to the unique hydrodynamic characteristics of the supercavitating vehicle, highly coupled nonlinear 6-degree-of-freedom (DOF) dynamic and kinematic models are constructed considering time-delay effects. A control scheme utilizing radial basis function (RBF) neural-network-(NN)-based adaptive sliding with planing force avoidance is proposed to simultaneously control the longitudinal stability and lateral motion of the supercavitating vehicle in the presence of external ocean-induced disturbances. The online estimation of nonlinear disturbances is conducted in real time by the designed NN and compensated for the dynamic control laws. The adaptive laws of the NN weights and control parameters are introduced to improve the performance of the NN. The least squares method is utilized to solve the actuator control efforts with rolling restriction in real-time online. Rigorous theoretical proofs based on the Lyapunov theory prove the globally asymptotic stability of the proposed controller. Finally, numerical simulations were performed to obtain maximum maneuverability and verify the effectiveness and robustness of the proposed control scheme.

Deterministic Learning-Based Adaptive Neural Control for Nonlinear Full-State Constrained Systems.

In this article, an adaptive neural learning method is introduced for a category of nonlinear strict-feedback systems with time-varying full-state constraints. The two challenging problems of state constraints and learning capability are investigated and solved in a unified framework. To obtain the learning of unknown functions and satisfy full-state constraints, three main steps are considered. First, an adaptive dynamic surface controller (DSC) based on barrier Lyapunov functions (BLFs) is structured to implement that the closed-loop systems signals are bounded and full-state variables remain within the prescribed time-varying intervals. Moreover, the radial basis function neural networks (RBF NNs) are used to identify unknown functions. The output of the first-order filter, instead of virtual control derivatives, is used to simplify the complexity of the RBF NN input variables. Second, the state transformation is used to obtain a class of linear time-varying subsystems with small perturbations such that the recurrence of the RBF NN input variables and the partial persistent excitation condition are actualized. Therefore, the unknown functions can be accurately approximated, and the learned knowledge is kept as constant NN weights. Third, the obtained constant weights are borrowed into an adaptive learning scheme to achieve the batter control performance. Finally, simulation studies illustrate the advantage of the reported adaptive learning method on higher tracking accuracy, faster convergence rate, and lower computational expense by reusing learned knowledge.

Zero-sum differential game guidance law for missile interception engagement via neuro-dynamic programming

In this paper, for solving the nonlinear control problem of the missile intercepting the maneuvering target, a novel nonlinear zero-sum differential game guidance law is proposed via the neuro-dynamic programming approach. First, the continuous-time nonlinear differential game problem is transformed into solving the nonlinear Hamilton–Jacobi–Isaacs (HJI) equation. Then, a critic neural network is designed to solve the corresponding nonlinear HJI equation. An adaptive weight tuning law for the critic weights is proposed, where an additional term is added to ensure the stability of the closed-loop nonlinear system. Furthermore, the uniform ultimate boundedness of the closed-loop system and the critic NN weights estimation error are proved with the Lyapunov approach. Finally, some simulation results are presented to demonstrate the effectiveness of the proposed differential game guidance law for nonlinear interception.

Neural Network Compression for Noisy Storage Devices

Compression and efficient storage of neural network (NN) parameters is critical for applications that run on resource-constrained devices. Despite the significant progress in NN model compression, there has been considerably less investigation in the actual physical storage of NN parameters. Conventionally, model compression and physical storage are decoupled, as digital storage media with error-correcting codes (ECCs) provide robust error-free storage. However, this decoupled approach is inefficient as it ignores the overparameterization present in most NNs and forces the memory device to allocate the same amount of resources to every bit of information regardless of its importance. In this work, we investigate analog memory devices as an alternative to digital media – one that naturally provides a way to add more protection for significant bits unlike its counterpart, but is noisy and may compromise the stored model’s performance if used naively. We develop a variety of robust coding strategies for NN weight storage on analog devices, and propose an approach to jointly optimize model compression and memory resource allocation. We then demonstrate the efficacy of our approach on models trained on MNIST, CIFAR-10, and ImageNet datasets for existing compression techniques. Compared to conventional error-free digital storage, our method reduces the memory footprint by up to one order of magnitude, without significantly compromising the stored model’s accuracy.

Event‐triggered neural experience replay learning for nonzero‐sum tracking games of unknown continuous‐time nonlinear systems

AbstractIn this paper, an online event‐triggered integral reinforcement learning is proposed to solve the nonzero‐sum tracking games of the two‐player nonlinear system with unknown dynamics and constrained input. Firstly, an augmented system of the nonzero‐sum game is constructed to describe the tracking problem. Thus, the optimal tracking problem is treated as solving the coupled Hamilton‐Jacobi (HJ) equations of the augmented system. To restrict the number of sampling states, a novel triggering threshold containing the augmented states is designed, and it avoids the existence of Zeno behavior. Secondly, a single‐critic network is utilized to approximate the solution of the coupled HJ equations. The critic network turning law with experience replay technology relaxes the dependence on the persistence of excitation (PE) conditions in traditional integral reinforcement learning (IRL) by using historical data in the stack. Moreover, the augmented system states and the critic NN weight errors are uniformly ultimate boundedness (UUB) by Lyapunov theory. Simulation examples are provided to demonstrate the availability of the proposed algorithm.

Reinforcement learning‐based optimal trajectory tracking control of surface vessels under input saturations

AbstractThis paper develops a reinforcement learning (RL)‐based optimal trajectory tracking control scheme of surface vessels with unknown dynamics, unknown disturbances, and input saturations of surface vessels. The control scheme is designed by combining the optimal control theory, adaptive neural networks, and the RL method in a unified actor‐critic NN framework. A hyperbolic‐type penalty function of the control input is designed so as to deal with the input saturations of surface vessels. An actor‐critic NN‐based RL mechanism is established to learn the optimal trajectory tracking control law without the knowledge of the surface vessel dynamics and disturbances, where NN weights are tuned online on the basis of devised tuning laws. Theoretical analysis and simulation results prove that the proposed RL‐based optimal trajectory tracking control scheme can ensure surface vessels track the desired trajectory, while guaranteeing the boundedness of all signals in the surface vessel optimal trajectory tracking closed‐loop control system.

A Memory-Efficient Learning Framework for Symbol Level Precoding With Quantized NN Weights

This paper proposes a memory-efficient deep neural network (DNN) framework-based symbol level precoding (SLP). We focus on a DNN with realistic finite precision weights and adopt an unsupervised deep learning (DL) based SLP model (SLP-DNet). We apply a stochastic quantization (SQ) technique to obtain its corresponding quantized version called SLP-SQDNet. The proposed scheme offers a scalable performance vs memory trade-off, by quantizing a scalable percentage of the DNN weights, and we explore binary and ternary quantizations. Our results show that while SLP-DNet provides near-optimal performance, its quantized versions through SQ yield ~3.46× and ~2.64× model compression for binary-based and ternary-based SLP-SQDNets, respectively. We also find that our proposals offer ~20× and ~10× computational complexity reductions compared to SLP optimization-based and SLP-DNet, respectively.

Fixed-Time Incremental Neural Control for Manipulator Based on Composite Learning with Input Saturation

In this paper, an adaptive incremental neural network (INN) fixed-time tracking control scheme based on composite learning is investigated for robot systems under input saturation. Firstly, by integrating the composite learning method into the INN to cope with the inevitable dynamic uncertainty, a novel adaptive updating law of NN weights is designed, which does not need to satisfy the stringent persistent excitation (PE) conditions. In addition, for the saturated input, differing from adding the auxiliary system, this paper introduces a hyperbolic tangent function to deal with the saturation nonlinearity by converting the asymmetric input constraints into the symmetric ones. Moreover, the fixed-time control approach and Lyapunov theory are combined to ensure that all the signals of the robot closed-loop control systems converge to a small neighborhood of the origin in a fixed time. Finally, numerical simulation results verify the effectiveness of the fixed-time control and composite learning algorithm.

Online Optimal Adaptive Control of Partially Uncertain Nonlinear Discrete-Time Systems Using Multilayer Neural Networks.

This article intends to address an online optimal adaptive regulation of nonlinear discrete-time systems in affine form and with partially uncertain dynamics using a multilayer neural network (MNN). The actor-critic framework estimates both the optimal control input and value function. Instantaneous control input error and temporal difference are used to tune the weights of the critic and actor networks, respectively. The selection of the basis functions and their derivatives are not required in the proposed approach. The state vector, critic, and actor NN weights are proven to be bounded using the Lyapunov method. Our approach can be extended to neural networks with an arbitrary number of hidden layers. We have demonstrated our approach via a simulation example.

Deterministic learning from neural control for a class of sampled-data nonlinear systems

This study investigates the deterministic learning and control issues for uncertain sampled-data nonlinear systems (SDNSs). The problem of how to acquire/learn knowledge from adaptive control for SDNSs with uncertain affine terms is studied. To be specific, an appropriate neural network-based (NNB) control strategy is first presented to ensure tracking performance. To further realize learning, the exponential stability (ES) of the integrated closed-loop system coupled with the estimation error of the NN weights is considered. As the uncertain affine term prevents learning from occurring, the integrated system is converted into a discrete linear time-varying (DLTV) perturbed system by employing the state conversion technique. Tracking convergence allows the persistent excitation condition (PEC) of the NNs to be established, which guarantees the ES of the integrated DLTV system. Thus, accurate modeling of closed-loop sampled dynamics is obtained. By reutilizing the experiential knowledge obtained, a knowledge-based controller is constructed for high-performance control. Finally, simulations are performed to verify the presented strategy.

Robust Trajectory Tracking of Uncertain Systems via Adaptive Critic Learning

This study develops an adaptive dynamic programming (ADP) scheme for uncertain systems to achieve the robust trajectory tracking. In this framework, the augmented state is first established via combining the tracking error and reference trajectory, where the robust tracking control problem can be resolved using the regulation control strategy. Then, the robust control problem of uncertain system can be represented as an optimal control problem of nominal system, which provides a new pathway to address the robust control problem. To realize the optimal control, the derived Hamilton–Jacobi–Bellman equation (HJBE) is solved by training a critic neural network (CNN). Finally, two innovative critic learning techniques are suggested to calculate the unknown NN weights, where the convergence of NN weights can be guaranteed. Simulations are carried out to demonstrate the effectiveness of the proposed method.

Robust tracking control for magnetic wheeled mobile robots using adaptive dynamic programming

To handle the tracking control problem of the magnetic wheeled mobile robot (MWMR), this paper developed an online robust tracking control scheme by adaptive dynamic programming (ADP). The problem, that how to achieve optimal tracking control of continuous-time (CT) MWMR system with the time-varying unknown uncertainty, can be solved indirectly through matching the optimal tracking control of the associated nominal system . A single critic NN-based actor-critic structure is tailored for simpler controller architecture. By minimizing the Bellman error with gradient descending and least-squares updating laws, the critic NN weights can be optimized online. Thus the optimal cost function and the optimal control signal can be approximated with high precision. Using the Lyapunov stability theorem, the convergence of the critic NN weights, and the stability of the closed-loop system is provided. Simulations, in comparison with robust PD control and adaptive control, are presented to illustrate the effectiveness of the proposed tracking control method for the MWMR.

Adaptive sliding-mode control of a class of disturbed cyber–physical systems against actuator attacks

In this paper, an adaptive integral sliding-mode control scheme is presented to cope with the false data injection actuator attacks on a class of disturbed cyber–physical systems. Considering the time-varying state-dependent actuator attacks can be parameterized in the form of a neural network, a filter operator is firstly introduced to identify the unknown weight vectors. Then, an integral sliding-mode function is utilized to develop the attack tolerant controller, which can compensate for the impacts of actuator attacks and external disturbance on system performance. By using the Lyapunov stability theory, the uniformly ultimately bounded result of system states, NN weight estimation errors and sliding motion can be obtained. Finally, the effectiveness of the proposed control theory is verified via a decoupled model of an F-18 aircraft.

Model-Independent Containment Control for Dynamic Multiple Euler-Lagrange Systems With Disturbances and Uncertainties

This article studies the model-independent distributed containment control problem for multiple Euler-Lagrange systems (MELSs) considering external disturbances and system uncertainties. First, we design a virtual network and propose a controller for all virtual nodes moving to the convex hull formed by all leaders. Then, we propose an adaptive tracking algorithm which combines a continuous robust integral of the sign of the error (RISE) feedback element and a neural network-based (NN-based) feedforward element to guarantee that each follower semi-globally asymptotically track the state of the corresponding virtual node. Apart from this, a smooth projection algorithm is ulitized to ensure that training values of NN weight matrices are bounded. Hence, the MELSs can achieve containment control. Furthermore, criteria for addressing the above model-independent containment control problem are given by the theoretical derivation. Finally, the correctness of the presented model-independent containment control method is checked out by a numerical simulation.

Single‐network ADP for solving optimal event‐triggered tracking control problem of completely unknown nonlinear systems

In this paper, we propose an optimal event-triggered tracking control scheme for completely unknown nonlinear systems under the adaptive dynamic programming (ADP) framework. A data-driven model based on recurrent neural networks (RNNs) is first constructed to model the system uncertainties including the drift dynamics and the input gain matrix, and the modeling error caused by NN approximation is well eliminated through adding a compensation term in the data-driven model such that the model state can asymptotically track the system state. Apart from the traditional construction of optimal tracking controllers, in this paper, an augmented system is developed and a discounted performance function is considered to achieve the optimality. By employing the Bellman optimal principle, an event-triggered tracking Hamilton–Jacobi–Bellman (HJB) equation is then formulated. The approximate solution of the HJB equation can be obtained by virtue of a critic NN, which significantly simplifies the implementation architecture of ADP. Both the historical state data and the current state data are incorporated into the updating of the weight vector in the critic NN, in this circumstance, the persistence of excitation assumption is not needed anymore. It is strictly proven via Lyapunov stability theory that the tracking error state and the critic NN weight are uniformly ultimately bounded. Simulation results examine the validity of the design scheme.

Model-Based adaptive event-Triggered control of nonlinear continuous-Time systems

This paper presents a model-based adaptive event-triggered control scheme for a class of uncertain single-input and single-output nonlinear continuous-time systems. To this aim, the explicit design of an associated controller is proposed by constructing an adaptive model, exploiting the principle of feedback linearization and using neural networks to approximate an unknown smooth nonlinear function. Then, the stability of the resulting impulsive dynamic system is strictly proved by using the Lyapunov stability theory, and the event-trigger condition is designed to realize that the NN weights and feedback signals are updated only when the condition is violated. In addition, the lower bound of inter-event times is strictly proved to be positive, which effectively avoids Zeno behavior. Compared with the conventional adaptive control based on the time-triggered scheme, feedback transmissions and NN weight updating only occur at necessary instants, such that the waste of communication resources is effectively reduced. Finally, the effectiveness of the developed control algorithm is verified by a simulation example.

Model-Free Neural Network-Based Predictive Control for Robust Operation of Power Converters

An accurate definition of a system model significantly affects the performance of model-based control strategies, for example, model predictive control (MPC). In this paper, a model-free predictive control strategy is presented to mitigate all ramifications of the model’s uncertainties and parameter mismatch between the plant and controller for the control of power electronic converters in applications such as microgrids. A specific recurrent neural network structure called state-space neural network (ssNN) is proposed as a model-free current predictive control for a three-phase power converter. In this approach, NN weights are updated through particle swarm optimization (PSO) for faster convergence. After the training process, the proposed ssNN-PSO combined with the predictive controller using a performance criterion overcomes parameter variations in the physical system. A comparison has been carried out between the conventional MPC and the proposed model-free predictive control in different scenarios. The simulation results of the proposed control scheme exhibit more robustness compared to the conventional finite-control-set MPC.

Degradation analysis and optimization of temperature effect on MEMRISTOR-based Neural Network Accelerators by electro-thermal simulation

Nowadays, memristor-based neural network accelerators have been widely studied due to their outstanding performance in massive parallel vector matrix multiplication. However, the memristor is sensitive to temperature and its on/off state operation window can be seriously degraded by the increasing temperature, which may lead to computation failures in memristor -based NN accelerators. In this work, we establish an electro-thermal simulation platform to evaluate the temperature impact on memristor -based NN accelerators. With this platform, we first investigate the impact on computation accuracy with the temperature increase in different NN layers in the accelerators. We then apply a temperature-aware NN weight mapping scheme to the most temperature-sensitive layer and achieve 28.89% improvement in computation accuracy, which only has 0.06% difference with the improvement achieved by applied the mapping scheme to the whole NN model. This finding can help to simplify the temperature-aware hardware optimization design in memristor-based neural network accelerators and reduce the power consumption.