Neural Approximation Research Articles

Adaptive Control Using Radial Basis Function Neural Networks for Pneumatic Artificial Muscle Systems

This study introduces a novel adaptive controller employing neural networks, particularly radial basis function (RBF) algorithms, to enhance the control performance of pneumatic artificial muscle (PAM)-based systems. The proposed controller seeks to address the nonlinearities and hysteresis inherent in PAM-based systems by integrating neural approximation. Experimental testing and comparisons with conventional controllers are conducted using an antagonistic configuration of PAMs. The results illustrate the precision and reliability of the proposed controller, suggesting potential for future advancements in trajectory tracking control of PAM-based systems.

ZeroGrads: Learning Local Surrogates for Non-Differentiable Graphics

Gradient-based optimization is now ubiquitous across graphics, but unfortunately can not be applied to problems with undefined or zero gradients. To circumvent this issue, the loss function can be manually replaced by a "surrogate" that has similar minima but is differentiable. Our proposed framework, ZeroGrads , automates this process by learning a neural approximation of the objective function, which in turn can be used to differentiate through arbitrary black-box graphics pipelines. We train the surrogate on an actively smoothed version of the objective and encourage locality, focusing the surrogate's capacity on what matters at the current training episode. The fitting is performed online, alongside the parameter optimization, and self-supervised, without pre-computed data or pre-trained models. As sampling the objective is expensive (it requires a full rendering or simulator run), we devise an efficient sampling scheme that allows for tractable run-times and competitive performance at little overhead. We demonstrate optimizing diverse non-convex, non-differentiable black-box problems in graphics, such as visibility in rendering, discrete parameter spaces in procedural modelling or optimal control in physics-driven animation. In contrast to other derivative-free algorithms, our approach scales well to higher dimensions, which we demonstrate on problems with up to 35k interlinked variables.

Deep Learning of Transition Probability Densities for Stochastic Asset Models with Applications in Option Pricing

Transition probability density functions (TPDFs) are fundamental to computational finance, including option pricing and hedging. Advancing recent work in deep learning, we develop novel neural TPDF generators through solving backward Kolmogorov equations in parametric space for cumulative probability functions. The generators are ultra-fast, very accurate and can be trained for any asset model described by stochastic differential equations. These are “single solve,” so they do not require retraining when parameters of the stochastic model are changed (e.g., recalibration of volatility). Once trained, the neural TDPF generators can be transferred to less powerful computers where they can be used for e.g. option pricing at speeds as fast as if the TPDF were known in a closed form. We illustrate the computational efficiency of the proposed neural approximations of TPDFs by inserting them into numerical option pricing methods. We demonstrate a wide range of applications including the Black-Scholes-Merton model, the standard Heston model, the SABR model, and jump-diffusion models. These numerical experiments confirm the ultra-fast speed and high accuracy of the developed neural TPDF generators. This paper was accepted by Kay Giesecke, finance. Funding: H. Su received research funding support from Nottingham Business School at Nottingham Trent University. M. V. Tretyakov was supported by the Engineering and Physical Sciences Research Council [Grant EP/X022617/1]. D. P. Newton received research funding support from the School of Management at Bath University. Supplemental Material: The online appendices and data files are available at https://doi.org/10.1287/mnsc.2022.01448 .

Spectral neural approximations for models of transcriptional dynamics

The advent of high-throughput transcriptomics provides an opportunity to advance mechanistic understanding of transcriptional processes and their connections to cellular function at an unprecedented, genome-wide scale. These transcriptional systems, which involve discrete stochastic events, are naturally modeled using chemical master equations (CMEs), which can be solved for probability distributions to fit biophysical rates that govern system dynamics. While CME models have been used as standards in fluorescence transcriptomics for decades to analyze single-species RNA distributions, there are often no closed-form solutions to CMEs that model multiple species, such as nascent and mature RNA transcript counts. This has prevented the application of standard likelihood-based statistical methods for analyzing high-throughput, multi-species transcriptomic datasets using biophysical models. Inspired by recent work in machine learning to learn solutions to complex dynamical systems, we leverage neural networks and statistical understanding of system distributions to produce accurate approximations to a steady-state bivariate distribution for a model of the RNA life cycle that includes nascent and mature molecules. The steady-state distribution to this simple model has no closed-form solution and requires intensive numerical solving techniques: our approach reduces likelihood evaluation time by several orders of magnitude. We demonstrate two approaches, whereby solutions are approximated by 1) learning the weights of kernel distributions with constrained parameters or 2) learning both weights and scaling factors for parameters of kernel distributions. We show that our strategies, denoted by kernel weight regression and parameter-scaled kernel weight regression, respectively, enable broad exploration of parameter space and can be used in existing likelihood frameworks to infer transcriptional burst sizes, RNA splicing rates, and mRNA degradation rates from experimental transcriptomic data.

Event-Triggered Adaptive Saturated Fault-Tolerant Control for Unknown Nonlinear Systems With Full State Constraints

This paper investigates the issue of event-triggered adaptive saturated fault-tolerant control (ESFC) for uncertain nonlinear systems with time-varying full state constraints (TFSCs), actuator saturation and faults as well as unknown control direction. A bounded function with an auxiliary variable is constructed by utilizing a novel dynamics of the auxiliary system, which contributes to reducing the adverse impact of actuator saturation. Different from the previous backstepping-based event-triggered control methods such specifications by either using fuzzy approximation or by employing neural approximation techniques, this paper skillfully addresses the unknown nonlinearities, actuator saturation and faults without involving any approximation structures, and thus, we proposes the ESFC on the basis of low-complexity design framework as contributing to communication and computational resource reduction. A rigorous theoretical analysis shows that the proposed control method is an effective way to handle with the problems of actuator saturation and faults, full state constraints, and unknown system uncertainties, while simultaneously simplifying the backstepping design and avoiding the issue of explosion of complexity. The asymptotic stability of the closed-loop system is guaranteed and the Zeno behavior can be effectively removed. We present an application example of a linear motor scenario to illustrate the effectiveness of the method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Since state constraints, actuator saturation and faults, unknown mechanism model, and limited bandwidths exist extensively in practical engineering systems, which constantly degrade the operation performance of the plant. To handle these disadvantages, this paper is focus on providing simple but effective ESFC methods to ensure the asymptotic stability and enhance reliability. Compared to existing results, the presented method only uses the state signals of system without using system dynamic functions under mild conditions, which provides a theoretical basis, and has the advantages of low-complexity design, and easy implementation in practical engineering. Preliminary physical experimental comparisons demonstrate that this method is applicable to practical liner-motor platform, and achieves satisfactory control performance.

Tensor-Based Traffic Recovery of Industrial Network by BCD-Inspired Neural Approximation to Latent Nonlinearity and Sparsity

Tensor-Based Traffic Recovery of Industrial Network by BCD-Inspired Neural Approximation to Latent Nonlinearity and Sparsity

Attitude Control With Discrete-Time Prescribed Performance for Seeker Stabilized Platform via Event-Triggered Neural Approximation

Attitude Control With Discrete-Time Prescribed Performance for Seeker Stabilized Platform via Event-Triggered Neural Approximation

Koopman-operator-based learning control of air-breathing hypersonic vehicles with nonminimum phase properties

In this article, a prescribed learning controller is developed for nonminimum phase air-breathing hypersonic vehicles (AHVs) in the presence of parametric uncertainties and external disturbances. In comparison with the current state of the art, the most significant feature of our control design lies in introducing the Koopman operator to construct an intelligent output redefinition to overcome the nonminimum phase behavior. To evaluate the current control behavior and enhance the learning ability, an improved continuous-time performance index is developed under the actor–critic learning structure. Furthermore, combined with a nonlinear disturbance observer, prescribed learning control is proposed to design control commands, while compensating for lumped disturbances, including neural approximation errors and external disturbances. Numerical simulations have been performed to highlight the superiority of the proposed learning control.

Guaranteeing Global Stability for Neuro-Adaptive Control of Unknown Pure-Feedback Nonaffine Systems via Barrier Functions.

Most existing approximation-based adaptive control (AAC) approaches for unknown pure-feedback nonaffine systems retain a dilemma that all closed-loop signals are semiglobally uniformly bounded (SGUB) rather than globally uniformly bounded (GUB). To achieve the GUB stability result, this article presents a neuro-adaptive backstepping control approach by blending the mean value theorem (MVT), the barrier Lyapunov functions (BLFs), and the technique of neural approximation. Specifically, we first resort the MVT to acquire the intermediate and actual control inputs from the nonaffine structures directly. Then, neural networks (NNs) are adopted to approximate the unknown nonlinear functions, in which the compact sets for maintaining the approximation capabilities of NNs are predetermined actively through the BLFs. It is shown that, with the developed neuro-adaptive control scheme, global stability of the resulting closed-loop system is ensured. Simulations are conducted to verify and clarify the developed approach.

Autonomous driving controllers with neuromorphic spiking neural networks.

Autonomous driving is one of the hallmarks of artificial intelligence. Neuromorphic (brain-inspired) control is posed to significantly contribute to autonomous behavior by leveraging spiking neural networks-based energy-efficient computational frameworks. In this work, we have explored neuromorphic implementations of four prominent controllers for autonomous driving: pure-pursuit, Stanley, PID, and MPC, using a physics-aware simulation framework. We extensively evaluated these models with various intrinsic parameters and compared their performance with conventional CPU-based implementations. While being neural approximations, we show that neuromorphic models can perform competitively with their conventional counterparts. We provide guidelines for building neuromorphic architectures for control and describe the importance of their underlying tuning parameters and neuronal resources. Our results show that most models would converge to their optimal performances with merely 100-1,000 neurons. They also highlight the importance of hybrid conventional and neuromorphic designs, as was suggested here with the MPC controller. This study also highlights the limitations of neuromorphic implementations, particularly at higher (> 15 m/s) speeds where they tend to degrade faster than in conventional designs.

Event-Triggered Adaptive PID Fault-Tolerant Control of Underactuated ASVs Under Saturation Constraint

This article discusses a control problem of underactuated autonomous surface vehicles (ASVs) subject to internal/external uncertainties, input saturations, and actuator faults, and proposes a novel event-triggered adaptive PID fault-tolerant (ETAPID-FT) control solution. To resolve the design difficulty caused by the underactuated feature, a standard multivariate integral cascade form regarding the mathematical model of underactuated ASVs is established. And then, to facilitate the implementation of PID-based design framework, the nonsmooth actuator saturation nonlinearity caused by the saturation constraint is represented by a smooth saturation model. In the control design, considering full features of the actuator fault and smooth function, an indirect neural approximation with single-parameter-leaning technique is developed, which endows the function of self-tuning control gain for the control solution. To relieve the mechanical wear of actuator, an improved event-triggered protocol by implanting a decreasing function of ASV’s position error is proposed. Moreover, the theoretical results show that the proposed ETAPID-FT control solution can guarantee the boundedness of all the signals in the closed-loop control system of underactuated ASVs. Finally, the validity of the developed control solution is confirmed by the simulation and comparative results

Fuzzy Neural Pseudo Control With Prescribed Performance for Waverider Vehicles: A Fragility-Avoidance Approach.

A fuzzy-neural-approximation-based pseudo nonaffine control protocol is proposed for waverider vehicles (WVs), which is capable of guaranteeing tracking errors with desired prescribed performance and rejecting the obstacle of fragility inherent to the traditional prescribed performance control (PPC). The pseudo control is defined to approximate the nonaffine dynamics of WVs, while there is no need of model affinization. Furthermore, fuzzy neural approximators are combined with the adaptive compensation strategy to resist both system uncertainties and external disturbances. Especially, a new type of nonfragile prescribed performance, being able to self-adjust its prescribed funnel, is proposed to remedy the fragility defect associated with the existing PPC. Finally, the realizability of the spurred prescribed performance is proved via stability proof, and the superiority of the addressed design is tested by compared simulations.

Low-Complexity Fuzzy Neural Control of Constrained Waverider Vehicles via Fragility-Free Prescribed Performance Approach

In this article, we propose a concise fuzzy neural control framework for Waverider Vehicles with input constraints, while the spurred prescribed performance can be guaranteed, and the challenging fragility problem associated with the existing prescribed performance control (PPC) is avoided. Unlike the existing control protocols without considering computational costs, in this study, the low-complexity fuzzy neural approximation is combined with simple performance functions, which reduces the complexity burden and improves the practicability. Then, in order to handle the adverse effect of the actuator saturation on the control performance, bounded-input-bounded-state stable systems are developed to stabilize the closed-loop control system based on bounded compensations. Specially, flexible adjustment terms are exploited to modify the developed simple performance functions, while fragility-free prescribed performance is achieved for tracking errors, and moreover the fragility defect of the existing PPC is remedied. Finally, the efficiency and superiority of the design are verified via compared simulations.

Discovering efficient periodic behaviors in mechanical systems via neural approximators

AbstractIt is well known that conservative mechanical systems exhibit local oscillatory behaviors due to their elastic and gravitational potentials, which completely characterize these periodic motions together with the inertial properties of the system. The classification of these periodic behaviors and their geometric characterization are in an ongoing secular debate, which recently led to the so‐called eigenmanifold theory. The eigenmanifold characterizes nonlinear oscillations as a generalization of linear eigenspaces. With the motivation of performing periodic tasks efficiently, we use tools coming from this theory to construct an optimization problem aimed at inducing desired closed‐loop oscillations through a state feedback law. We solve the constructed optimization problem via gradient‐descent methods involving neural networks. Extensive simulations show the validity of the approach.

Composite learning control of strict‐feedback nonlinear system with unknown control gain function

AbstractThe composite learning control with the heterogeneous estimator is proposed to deal with the multiple uncertainties of strict‐feedback nonlinear systems. The article applies the recorded data‐based neural learning and the disturbance observer (DOB) to learn the multiple uncertainties, including the nonlinear dynamics, the unknown control gain function (CGF), and the time‐varying disturbance. The lumped prediction error is constructed and included into the update law by neural approximation and disturbance observation. Furthermore, the asymmetric saturation nonlinearity (ASN) of the control input is represented by the smooth form model to ensure the input limitation, and a projection algorithm is adopted to avoid the singularity problem. The closed‐loop system stability is rigorously analyzed and the boundedness of the system tracking error is guaranteed. Through the tests of the third‐order nonlinear system and the autonomous underwater vehicle (AUV), it is observed that the proposed approach can improve the system tracking accuracy with the expected learning performance.

Saturated Control With Variable Prescribed Performance Applied to the Manipulator of UAV

Variable prescribed performance control (PPC) is investigated for a type of nonlinear dynamic systems subject to actuator saturation, with an application to the manipulator of unmanned aerial vehicles (UAVs). Different from the current state-of-the-art, new performance functions are proposed to construct a variable prescribed funnel which is able to be readjusted according the saturation situation. Furthermore, a new auxiliary system is developed to provide timely and bounded compensations on ideal control inputs. Thereby, the control singular problem associated with the existing PPC, caused by saturated actuator, is effectively handled, and moreover the addressed control protocol exhibits non-fragility to actuator saturation. In addition, the robustness of control is guaranteed via neural approximation. Finally, compared simulations on the manipulator of UAVs are presented to validated the design.

Prospects for control methods in engineering systems

The article discusses the prerequisites and natural consequences of the control methods development in engineering systems: (1) a simple deviation and perturbation controller, (2) a fuzzy logic controller with a fuzzifier and a rule base, (3) a neural network controller for dynamically adjusting the coefficients of the corresponding links, (4) a discrete neural network controller with a neural approximator and controller. The experience gained by researchers and engineers since the first description of the principles of regulation in 1910 and the level of information technologies design, in particular the neural network method of machine learning and the enormous computing potential of computer devices, today can be integrated into a fundamentally new method of discrete neural network regulation.&#x0D; The review carried out in the article is aimed at identifying and demonstrating the significance of experimental and operational data, which must be properly structured and marked up at the stage of their collection and archiving. It is this approach that will allow us to quickly implement neural network controllers in engineering systems, since the most important stage for their creation is the process of learning and optimizing the architecture of neural networks.&#x0D; The principle of operation, advantages and disadvantages, the optimal stages of a neural network controller improvement based on two neural networks for the formation of a control strategy, taking into account the most probable state of the system at the next point in time, are given.

Adaptive Learning Control of Switched Strict-Feedback Nonlinear Systems With Dead Zone Using NN and DOB.

This article investigates the adaptive learning control for a class of switched strict-feedback nonlinear systems with external disturbances and input dead zone. To handle unknown nonlinearity and compound disturbances, a collaborative estimation learning strategy based on neural approximation and disturbance observation is proposed, and the adaptive neural switched control scheme is studied in a dynamic surface control framework. In the adaptive learning control design, to obtain the evaluation information of uncertain learning, the prediction error is constructed based on the composite learning scheme. Then, the prediction error and the compensated tracking error are applied to construct the adaptive laws of switched neural weights and switched disturbance observers. The system stability analysis is carried out through the Lyapunov approach, where the switching signal with average dwell time is considered. Through the simulation test, the effectiveness of the proposed adaptive learning controller is verified.

Sample-Based Neural Approximation Approach for Probabilistic Constrained Programs.

This article introduces a neural approximation-based method for solving continuous optimization problems with probabilistic constraints. After reformulating the probabilistic constraints as the quantile function, a sample-based neural network model is used to approximate the quantile function. The statistical guarantees of the neural approximation are discussed by showing the convergence and feasibility analysis. Then, by introducing the neural approximation, a simulated annealing-based algorithm is revised to solve the probabilistic constrained programs. An interval predictor model (IPM) of wind power is investigated to validate the proposed method.

Learning to Solve Optimization Problems With Hard Linear Constraints

Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms that explore the feasible domain in the search for the best solution. These iterative methods are often the computational bottleneck in decision-making and adversely impact time-sensitive applications. Recently, neural approximators have shown promise as a replacement for the iterative solvers that can output the optimal solution in a single feed-forward providing rapid solutions to optimization problems. However, enforcing constraints through neural networks remains an open challenge. This paper develops a neural approximator that maps the inputs to an optimization problem with hard linear constraints to a feasible solution that is nearly optimal. Our proposed approach consists of four main steps: 1) reducing the original problem to optimization on a set of independent variables, 2) finding a gauge function that maps the infty-norm unit ball to the feasible set of the reduced problem, 3)learning a neural approximator that maps the optimization's inputs to an optimal point in the infty-norm unit ball, and 4) find the values of the dependent variables from the independent variable and recover the solution to the original problem. We can guarantee hard feasibility through this sequence of steps. Unlike the current learning-assisted solutions, our method is free of parameter-tuning and removes iterations altogether. We demonstrate the performance of our proposed method in quadratic programming in the context of the optimal power dispatch (critical to the resiliency of our electric grid) and a constrained non-convex optimization in the context of image registration problems.