Smooth Nonlinear Function Research Articles

Improved modeling and active disturbance rejection control of tank gun control system

In order to improve the stability control performance of the tank barrel at high speed, a new 2-degree-of-freedom nonlinear dynamics model of yaw and pitch bodies is established, taking into account the 6-degree-of-freedom motion of the tank chassis. By analyzing the direction of the tank barrel in space, the barrel stability control scheme for the tank gun control system with the arbitrary motion of the tank chassis in space is realized. The new dynamics equations of the tank gun control system are established by analytical mechanics. It effectively solves the problem of modeling methods for the tank gun control system in azimuth and elevation when considering the 6-degree-of-freedom motion of tank chassis. Then, an improved active disturbance rejection control strategy for tank gun control system is proposed. A smooth nonlinear function faln(·) is constructed to avoid the switching problem of the function fal(·) at the piecewise points. Next, an improved extended state observer is designed based on the deviation principle by means of the deviation between each state variable and its observation. Afterwards, the stability of the system is analyzed by constructing a Lyapunov function. Simulations were carried out with different input signals to verify the reliability of the dynamics model and control algorithm. The improved active disturbance rejection control has a faster response speed and smaller steady state error. The results show that the stability and tracking performance of the tank gun control system has been improved using the proposed method.

Suboptimal Local Minima Exist for Wide Neural Networks with Smooth Activations

Does a large width eliminate all suboptimal local minima for neural nets? An affirmative answer was given by a classic result published in 1995 for one-hidden-layer wide neural nets with a sigmoid activation function, but this result has not been extended to the multilayer case. Recently, it was shown that, with piecewise linear activations, suboptimal local minima exist even for wide nets. Given the classic positive result on smooth activation and the negative result on nonsmooth activations, an interesting open question is: Does a large width eliminate all suboptimal local minima for deep neural nets with smooth activation? In this paper, we give a largely negative answer to this question. Specifically, we prove that, for neural networks with generic input data and smooth nonlinear activation functions, suboptimal local minima can exist no matter how wide the network is (as long as the last hidden layer has at least two neurons). Therefore, the classic result of no suboptimal local minimum for a one-hidden-layer network does not hold. Whereas this classic result assumes sigmoid activation, our counterexample covers a large set of activation functions (dense in the set of continuous functions), indicating that the limitation is not a result of the specific activation. Together with recent progress on piecewise linear activations, our result indicates that suboptimal local minima are common for wide neural nets.

Study on the influence of automatic voltage control system with dead zone on the stability of hydropower unit

The existing research on automatic voltage control of hydropower station is mostly simplified as linear control model, ignoring the dead time and delay effect. Based on the existing automatic voltage control model, this paper considers the dead zone of automatic voltage control, establishes the corresponding theoretical equivalent model of dead zone, and analyzes the influence of dead zone on the stability of hydropower grid connection. In this method, the dead zone is simplified as a smooth nonlinear function, which makes the small signal analysis method suitable for the nonlinear system with dead zone. This method has good guidance for the actual operation. The effectiveness of the method is verified by the analysis of an actual hydropower plant.

Cooperative Fault-Tolerant Control for Networks of Stochastic Nonlinear Systems With Nondifferential Saturation Nonlinearity

This article addresses the cooperative fault-tolerant control problem for networks of stochastic nonlinear systems with actuator faults and input saturation. The fuzzy neural networks (FNNs) are employed to estimate the unknown functions and stochastic disturbance terms. To analyze the nondifferential saturation nonlinearity, a smooth nonlinear function of the control input signal is constructed to estimate the saturation function. A novel adaptive fault-tolerant control protocol is proposed by using backstepping design technique. By using the stochastic Lyapunov functional strategy, it is proved that all the followers’ outputs eventually converge to a small neighborhood of the leader’s output, and all the signals in the closed-loop systems are bounded in probability. Finally, the performance of the proposed control strategy is illustrated through simulation.

Observer-based event-triggered adaptive containment control for multiagent systems with prescribed performance

This paper focuses on the problem of the event-triggered adaptive containment control for a class of nonlinear multiagent systems (MASs) with prescribed performance and immeasurable states. First, the radial basis function neural networks (RBFNNs) are adopted to approximate the uncertain smooth nonlinear function, and the neural network-based state observer is designed to estimate the unmeasurable state. Besides, to reduce the control resource consumption and get a better balance between the system performance and network constraints, the switching threshold-based event-triggered control strategy is introduced. Based on this, the novel distributed containment controller is designed by utilizing the adaptive backstepping technique and the dynamic surface control (DSC) technique to guarantee that the output of each follower converges to the convex hull formed by multileader. Moreover, the containment errors can be converged to the prescribed boundary and all signals in closed-loop system are semi-global uniformly ultimately bounded (SGUUB) as well. Finally, the simulation examples are carried out to illustrate the efficiency of the proposed controller.

Dynamics of Time-Delayed Optoelectronic Oscillators With Nonlinear Amplifiers and Its Potential Application to Random Numbers Generation

Time-delayed dynamical systems generally feature smooth nonlinear transfer functions in the feedback loop, such as polynomial or sinusoidal functions. As a consequence, the complexity of their dynamical behavior mainly originates from the time-delay. In this paper, we explore the opposite case where the nonlinear transfer function is complex ( cos <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (sinh)), and therefore, non-smooth. We perform a bifurcation analysis of the system, and evidence that this novel type of time-delayed system can display a chaotic behavior characterized by positive maximum Lyapunov exponent and quasi-maximal entropy. The high entropy behavior of the system combined with post-processing are used to generate random numbers for small values of the feedback gain with an overall bit rate up to 1.478 Gb/s. Our theoretical results are in excellent agreement with experimental measurements, performed with an optoelectronic oscillator involving a complex transfer function designed ad hoc.

Gradient temporal-difference learning for off-policy evaluation using emphatic weightings

The problem of off-policy evaluation (OPE) has long been advocated as one of the foremost challenges in reinforcement learning. Gradient-based and emphasis-based temporal-difference (TD) learning algorithms comprise the major part of off-policy TD learning methods. In this work, we investigate the derivation of efficient OPE algorithms from a novel perspective based on the advantages of these two categories. The gradient-based framework is adopted, and the emphatic approach is used to improve convergence performance. We begin by proposing a new analogue of the on-policy objective, called the distribution-correction-based mean square projected Bellman error (DC-MSPBE). The key to the construction of DC-MSPBE is the use of emphatic weightings on the representable subspace of the original MSPBE. Based on this objective function, the emphatic TD with lower-variance gradient correction (ETD-LVC) algorithm is proposed. Under standard off-policy and stochastic approximation conditions, we provide the convergence analysis of the ETD-LVC algorithm in the case of linear function approximation. Further, we generalize the algorithm to nonlinear smooth function approximation. Finally, we empirically demonstrate the improved performance of our ETD-LVC algorithm on off-policy benchmarks. Taken together, we hope that our work can guide the future discovery of a better alternative in the off-policy TD learning algorithm family.

Global well-posedness of solutions for the epitaxy thin film growth model

In this paper, we consider the global well-posedness of solutions for the initial-boundary value problems of the epitaxy growth model. We first construct the local smooth solution, then by combining some a priori estimates, continuity argument, the local smooth solutions are extended step by step to all t &gt; 0, provided that the initial datums sufficiently small and the smooth nonlinear functions satisfy certain local growth conditions.

Event-Driven Connectivity-Preserving Coordinated Control for Multiple Spacecraft Systems With a Distance-Dependent Dynamic Graph.

This article considers the connectivity preservation coordinated control problem for multiple spacecraft systems subject to limited communication resources and sensing capability. By constructing a novel bump function, a distance-dependent dynamic communication network model is first presented, which characterizes the interaction strength as a nonlinear smooth function varying with the relative distance of spacecraft continuously. Subsequently, based on an edge-tension potential function, a distributed event-driven coordinated control scheme is proposed to achieve formation consensus, while ensuring that adjacent spacecraft is always within the allowable connectivity range. Meanwhile, to avoid redundant data transmissions, a hybrid dynamic event-triggered mechanism with maximum triggering interval is developed to schedule the communication frequency among spacecraft. It is proven that the onboard communication resources occupation can be reduced significantly and the Zeno phenomenon is strictly excluded. Finally, the efficiency of the proposed method for, as an example, four-spacecraft formation system is substantiated.

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.

Neural-networks and event-based fault-tolerant control for spacecraft attitude stabilization

This paper proposes a neural network and event-based fault-tolerant control scheme for spacecraft attitude stabilization in the presence of lumped disturbances, which consists of space disturbances, inertia uncertainties, and actuator faults. A neuro-adaptive estimator is employed to approximate the lumped disturbances, with the help of its powerful adaptive estimation capability of approximating any unknown smooth nonlinear function with arbitrary accuracy. The estimation is then utilized to formulate an integrated event-based dual-channel control scheme that can both guarantee the system's convergence and ensure the event triggering sequence possessing no-Zeno behavior simultaneously. The proposed control scheme provides a new and straightforward way for spacecraft attitude control to deal with lumped disturbances while requiring a low actuator updating frequency, thus saves on-board communication resources. Numerical simulations show the effectiveness of the algorithms.

DEEP GENERATIVE STORM MODEL FOR DYNAMIC IMAGING.

We introduce a novel generative smoothness regularization on manifolds (SToRM) model for the recovery of dynamic image data from highly undersampled measurements. The proposed generative framework represents the image time series as a smooth non-linear function of low-dimensional latent vectors that capture the cardiac and respiratory phases. The non-linear function is represented using a deep convolutional neural network (CNN). Unlike the popular CNN approaches that require extensive fully-sampled training data that is not available in this setting, the parameters of the CNN generator as well as the latent vectors are jointly estimated from the undersampled measurements using stochastic gradient descent. We penalize the norm of the gradient of the generator to encourage the learning of a smooth surface/manifold, while temporal gradients of the latent vectors are penalized to encourage the time series to be smooth. The main benefits of the proposed scheme are (a) the quite significant reduction in memory demand compared to the analysis based SToRM model, and (b) the spatial regularization brought in by the CNN model. We also introduce efficient progressive approaches to minimize the computational complexity of the algorithm.

Enhanced Fractional Order Sliding Mode Approach for Maximum Power Tracking of Five-phase PMSG based WECS

Variable structure strategies have shown an efficient performance in controlling nonlinear electrical power systems by reason of its strength to handle perfectly the unmodeled system dynamics. In this study, with the exponent reaching law, a robust enhancement method of sliding mode controller (SMC) based on a nonlinear fractional order sliding surface that consists of both fractional differentiation and integration is proposed and applied to control a high-power multiphase permanent magnet synchronous generator based direct-driven Wind Energy Conversion System (WECS), in order to improve the energy efficiency and reduce the produced chattering phenomenon of conventional SMC . Moreover, a new smooth and derivable nonlinear switching control function is applied to replace the traditional non-derivable nonlinear control law, to improve dynamic performance, static performance, and robustness of the system. The proposed strategy stability is investigated under Lyapunov theory. A comparative simulation of the new proposed approach with the conventional SMC and PI controller display the excellent performance, stability and high robustness of FOSMC, by improving the system efficiency up to 98.66%, compared to conventional SMC with 91,14%, while the PI control achieves 86, 2%.

Disturbance-observer-based finite-time adaptive fuzzy control for non-triangular switched nonlinear systems with input saturation

This paper investigates finite-time adaptive fuzzy control for a class of non-triangular switched nonlinear systems with asymmetric input saturation and mismatched external disturbances. Firstly, the mismatched external disturbances and fuzzy approximation errors are regarded as total disturbances of the system, which are estimated accurately via the finite-time exact disturbance observer. Secondly, the prescribed performance function is adopted to constrain the system output to meet the prescribed dynamic properties. To cope with the obstacle arising from asymmetric input saturation, a smooth nonlinear function is applied to approximate the actuator nonlinearity by utilizing the mean-value theorem. Thirdly, on the basis of the fast practical finite-time stability criteria, a finite-time adaptive fuzzy control where the adaptive parameter laws contain fractional-order item is developed. Meanwhile, the stability analysis verifies that all the signals in closed-loop system are bounded and error signals can converge to the prescribed small compact sets in finite time. Finally, a simulation example is included to further demonstrate the effectiveness of the proposed control strategies.

Determining the theoretical trajectory of the centre of tractor’s mass when turning in a combined way

One of the ways to increase the stability of movement and improve the manoeuvrability and controllability of a wheeled universal row-crop tractor in curvilinear motion is the choice of a rational turning method. To solve the tasks, the authors proposed a combined method of turning the tractor, which consists in crabbing in the entry into the rotation, after which the rear wheels automatically return to the neutral position and then the direction of movement in the established rotation and exit from the rotation uses front steering wheels. The article developed a methodology for determining the theoretical trajectory of the centre of mass of a wheeled tractor with a combined method of rotation for the three distinct sections of the movement included in it. Based on the conditions of smoothness and continuity, we glued together three characteristic sections of the curvilinear trajectory of the centre of mass and obtained a continuous non-linear piecewise smooth function of the investigated combined rotation method. It is possible to apply the research results for theoretical calculations of the parameters for the curvilinear motion of tractors, as well as other wheeled vehicles, that allows choosing rational laws to change the speed and control modes of turning the wheels, to identify the patterns of change for ensuring the necessary stability, manoeuvrability and controllability and confirming effectiveness in comparison with known and previously investigated laws.

Fuzzy Robust Constrained Control for Nonlinear Systems With Input Saturation and External Disturbances

This article proposes a high-order disturbance observer (HODO) and dynamic surface control (DSC) technique-based adaptive fuzzy control scheme for nonlinear systems subjected to input saturation and external time-varying disturbances. First, based on a Sigmoid function, the saturation input is tackled by utilizing a well-defined nonlinear smooth function. Furthermore, HODO and fuzzy logic systems are used to estimate the external disturbances and to handle the lumped unknown functions, respectively. Then, by using the backstepping method and DSC technique, a HODO-based adaptive fuzzy tracking control scheme is proposed for nonlinear systems with saturation nonlinearity, uncertainties, and external disturbances. The Lyapunov analysis method is used to prove that all signals in the entire system are semiglobally uniformly ultimately bounded (SGUUB). In addition, the tracking error converges to a compact set with a tunable error bound determined by some design parameters. Finally, a numerical simulation of two-stage chemical reactor shows the effectiveness of the developed tracking control strategy.

Policy and Law Assessment of COVID-19 Based on Smooth Transition Autoregressive Model

As of the end of October 2020, the cumulative number of confirmed cases of COVID-19 has exceeded 45 million and the cumulative number of deaths has exceeded 1.1 million all over the world. Faced with the fatal pandemic, countries around the world have taken various prevention and control measures. One of the important issues in epidemic prevention and control is the assessment of the prevention and control effectiveness. Changes in the time series of daily new confirmed cases can reflect the impact of policies in certain regions. In this paper, a smooth transition autoregressive (STAR) model is applied to investigate the intrinsic changes during the epidemic in certain countries and regions. In order to quantitatively evaluate the influence of the epidemic control measures, the sequence is fitted to the STAR model; then, comparisons between the dates of transition points and those of releasing certain policies are applied. Our model well fits the data. Moreover, the nonlinear smooth function within the STAR model reveals that the implementation of prevention and control policies is effective in some regions with different speeds. However, the ineffectiveness is also revealed and the threat of a second wave had already emerged.

Poisson balanced spiking networks.

An important problem in computational neuroscience is to understand how networks of spiking neurons can carry out various computations underlying behavior. Balanced spiking networks (BSNs) provide a powerful framework for implementing arbitrary linear dynamical systems in networks of integrate-and-fire neurons. However, the classic BSN model requires near-instantaneous transmission of spikes between neurons, which is biologically implausible. Introducing realistic synaptic delays leads to an pathological regime known as “ping-ponging”, in which different populations spike maximally in alternating time bins, causing network output to overshoot the target solution. Here we document this phenomenon and provide a novel solution: we show that a network can have realistic synaptic delays while maintaining accuracy and stability if neurons are endowed with conditionally Poisson firing. Formally, we propose two alternate formulations of Poisson balanced spiking networks: (1) a “local” framework, which replaces the hard integrate-and-fire spiking rule within each neuron by a “soft” threshold function, such that firing probability grows as a smooth nonlinear function of membrane potential; and (2) a “population” framework, which reformulates the BSN objective function in terms of expected spike counts over the entire population. We show that both approaches offer improved robustness, allowing for accurate implementation of network dynamics with realistic synaptic delays between neurons. Both Poisson frameworks preserve the coding accuracy and robustness to neuron loss of the original model and, moreover, produce positive correlations between similarly tuned neurons, a feature of real neural populations that is not found in the deterministic BSN. This work unifies balanced spiking networks with Poisson generalized linear models and suggests several promising avenues for future research.

Adaptive Neural Network Control Scheme of Switched Systems with Input Saturation

This paper investigates a scheme of adaptive neural network control for a stochastic switched system with input saturation. The unknown smooth nonlinear functions are approximated directly by neural networks. A modified approach is proposed to deal with unknown functions with nonstrict feedback form in the design process. Furthermore, by combining the auxiliary design signal and the adaptive backstepping design, a valid adaptive neural tracking controller design algorithm is presented such that all the signals of the switched closed-loop system are in probability semiglobally, uniformly, and ultimately bounded, and the tracking error eventually converges to a small neighborhood of the origin in probability. In the end, the effectiveness of the proposed method is verified by a simulation example.

New trends in modeling and control of hybrid systems

New trends in modeling and control of hybrid systems