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Parameter estimation of photovoltaic modules is an essential step to observe, analyze, and optimize the performance of solar power systems. An efficient optimization approach is needed to obtain the finest value of unknown parameters. Herewith, this article proposes a novel opposition-based tunicate swarm algorithm for parameter estimation. The proposed algorithm is developed based on the exploration and exploitation components of the tunicate swarm algorithm. The opposition-based learning mechanism is employed to improve the diversification of the search space to provide a precise solution. The parameters of three types of photovoltaic modules (two polycrystalline and one monocrystalline) are estimated using the proposed algorithm. The estimated parameters show good agreement with the measured data for three modules at different irradiance levels. Performance of the developed opposition-based tunicate swarm algorithm is compared with other predefined algorithms in terms of robustness, statistical, and convergence analysis. The root mean square error values are minimum ( 6.83×10−4 , 2.06×10−4 , and 4.48×10−6 ) compared to the tunicate swarm algorithm and other predefined algorithms. Proposed algorithm decreases the function cost by 30.11%, 97.65%, and 99.80% for the SS2018 module, SolarexMSX-60 module, and Leibold solar module, respectively, as compared to the basic tunicate swarm algorithm. The statistical results and convergence speed depicts the outstanding performance of the anticipated approach. Furthermore, the Friedman ranking tests confirm the competence and reliability of the developed approach., This work was supported in part by the European Commission H2020 TWINNING Joint Universal activities for Mediterranean PV integration Excellence (JUMP2Excel) Project under Grant 810809., peer-reviewed

This paper investigates the opinion dynamics on the adaptive networks with the community structure. A coevolution model of opinions and networks is proposed, in which the influence weights among agents can not be precisely obtained, and there exist the confidence heterogeneities and the frequency difference of exchanging opinion between the inner-community and the inter-community. A two-dimensional fuzzy inference system is designed to obtain the influence weights among agents’ opinions, which deals with the difficulties that the influence weights can not be precisely obtained. The simulation results show that the imbalance levels between the inner-community confidence and the inter-community confidence not only affect strongly the average relative frequency of survival opinions, but also dominate the distribution of survival opinions. The polarization state of opinions easily appears in the population with the higher inner-community confidence, whereas when the inter-community confidence is higher, the system tends to exhibit a large number of small-size clusters and a plural state is achieved. Moreover, the simulation results also show that the convergence time to the stable state varies non-monotonically with the increase of the inner-community confidence or the inter-community confidence.

In this paper, we propose an inertial derivative-free projection method for solving convex constrained nonlinear monotone operator equations (CNME). The method incorporates the inertial step with an existing method called derivative-free projection (DFPI) method for solving CNME. The reason is to improve the convergence speed of DFPI as it has been shown and reported in several works that indeed the inertial step can speed up convergence. The global convergence of the proposed method is proved under some mild assumptions. Finally, numerical results reported clearly show that the proposed method is more efficient than the DFPI.

The generalized vector sampled pattern matching (GVSPM) algorithm is widely utilized in the EIT (electrical impedance tomography) reconstruction to solve the ill-posed inverse problem. An improved algorithm, which is called the generalized vector sampled pattern matching-fast (GVSPM-F), is proposed to improve the spatial resolution and reduce the iteration time based on the conventional GVSPM. The GVSPM merely applied the orthogonal projections to approximate the weights in the coordinate directions. The iteration of the proposed GVSPM-F algorithm is calculated in the projection direction of the space constructed by nonlinear correlated column vectors in the column space of the original sensitive matrix. Hence, the proposed GVSPM-F algorithm could achieve stable convergence without an empirical value to preserve the shape information and reduce the time consumption of GVSPM. In the experimental results, GVSPM-F is compared with the traditional GVSPM method in terms of voltage error, iteration time, and image error. The voltage error decreases by approximately 35%, and the number of iteration decreases from thousands to fewer than 100. The image error of GVSPM-F is 6% less than that of GVSPM. The proposed GVSPM-F algorithm is confirmed to be effective for the reconstruction of EIT images.

Nonlinear magnetic network is an effective model to solve the magnetic field of the motor. For the strong nonlinearity of magnetic network parameters, it is difficult to solve the nonlinear magnetic network equations. To overcome the divergent issue for solving the nonlinear magnetic network equations, a new method, the homotopy continuation method, is proposed. Based on the benchmark model of Testing Electromagnetic Analysis Methods Problem 20 (TEAM P20), the two-dimensional nonlinear magnetic network model is established. Next, homotopy equations of nonlinear magnetic network equations are derived, and they are solved by the homotopy continuation method. So that solving the nonlinear magnetic network equations is transformed into solving a set of homotopy equations. Then, the magnetic flux density of iron core with different saturation levels is calculated using the simple iteration method, the relaxation iteration method, Newton-Raphson method, and the homotopy continuation method, respectively. The results and convergence performance of the four methods are compared. It is proved that the proposed method can effectively expand the convergence domain and simplify the calculation process. The magnetic flux density calculated by the homotopy continuation method is compared with the finite element method in the supersaturated state, and the results are in good agreement. The relative error of the magnetic flux density of the core is less than 5%, which verifies the correctness of the proposed algorithm.

In order to improve the algorithm efficiency in point matching and reduce the error of displacement field in deformation calculation, an Improved Digital Volume Correlation (IDVC) method is proposed. Aimed at the problem that the accuracy of initial displacement estimation of DVC has a great influence on the convergence calculation accuracy by the sub-voxel measurement algorithm, the coordinates of the estimated points in deformation are quickly matched by the Explosion Search Algorithm (ESA), with the displacement vectors obtained. Then, the non-physical fluctuation of displacement field and the wrong strain concentration are suppressed in regularization. Finally, the deformation information obtained by correlation search is substituted into the iterative least squares algorithm to attain the sub-voxel precision displacement. The results of the simulation experiment and concrete uni-axial compression experiment show that the computational efficiency by the proposed method is 20.44% higher than that by the traditional DVC method, and that the accuracy level of displacement field measurement reaches 0.001 voxels.

The aim of this paper is to investigate implicit viscosity iterative algorithm for nonexpansive mappings in the framework of CAT(0) spaces. We prove strong convergence theorems of such algorithm under some suitable assumptions on the sequences of parameters involved therein. We also proved that the presented algorithm is faster than a number of existing iteration processes in literature. Our results extend and improve some recent results of Ahmad et al.[J. Appl. Math. Informatics 35 (5-6)(2017), 423-438] and others.

To accelerate the scanning speed of magnetic resonance imaging (MRI) and improve the quality of magnetic resonance (MR) image reconstruction, a fast MRI technology based on compressed sensing is proposed. Nesterov's accelerated gradient descent (NAG) algorithm uses Nesterov acceleration to optimize the gradient descent (GD) method. However, this form of acceleration factor uses a fixed iteration curve update and can not adapt to different iteration processes. A generalized Nesterov acceleration concept is proposed. Combining the total variation model, a generalized Nesterov accelerated conjugate gradient based on total variation (GNACG_TV) algorithm is proposed. It extends the acceleration factor in a generalized manner, introducing the Frobenius norm of the objective function as a parameter, so that the acceleration factor is related not only to the number of iterations but also to the iteration process and guarantees the convergence of the iterative process. Experiments on three MR images (abdomen, head, and ankles) at different sampling ratios show that the proposed GNACG_TV algorithm compares favorably with conjugate gradient (CG), conjugate gradient based on total variation (CG_TV), Nesterov accelerated conjugate gradient based on total variation (NACG_TV), and conjugate gradient based on adaptive moment estimation (ADAMCG) algorithms in the MSE, PSNR and SSIM exhibit better performance and robustness in denoising performance for the proposed algorithm. Comparing with the result of qualitative and quantitative analysis, it was concluded that the proposed method can better reconstruct under-sampled MR images than other 4 methods. GNACG_TV can further improve the convergence speed based on Nesterov acceleration and get better reconstruction performance.

Wood moisture content (WMC) is an important technical index used in the wood drying process, and assessing its change accurately and reliably is the key to improving wood drying quality. In order to improve the accuracy and reliability of WMC forecasting, a modeling method is proposed that uses a modified ant colony algorithm (MACA) to optimize the least square support vector machine (LSSVM). The MACA combines the large-step size global search with the small-step size local fine search to obtain the optimal parameter combination automatically and are tested by five standard functions. Then the MACA-LSSVM model is proposed to predict the WMC and compared with back propagation neural network (BP-NN), LSSVM model, and ant colony optimization LSSVM (ACO-LSSVM). The drying data from a small-sized wood drying kiln independently developed by Northeast Forestry University are taken as the samples for analyzing. The results indicate that the root mean square relative error (RMSRE) obtained by the proposed method (MACA-LSSVM) is only 1.82%, which is 0.77%, 0.50%, and 0.20% less than those of the BP-NN, LSSVM, and ACO-LSSVM models. The forecasting time are 0.0070 s, 0.0030 s, and 0.0010 s shorter, respectively. The relative error (RE) and the mean absolute error (MAE) are also lower than those of the latter three models. The MACA-LSSVM shows the characteristics of low computational complexity, fast convergence speed, high prediction accuracy and strong generalization ability, and the prediction effect is ideal. This model can provide the theoretical support for intelligent control of the wood drying process.

Many conventional adaptive channel estimation methods are based on minimum mean square error (MMSE) criterion, maximum correntropy criterion (MCC) or least p-norm criterion. However, these criteria are not always desirable in the presence of the various kinds of noises in different wireless channels. To further enhance the adaptability of the channel estimation to different noises, this paper introduces a new criterion named generalized maximum correntropy criterion (GMCC), and calculates the estimated channel parameters using the fixed-point iteration. The convergence analysis of the fixed-point iteration based on GMCC is discussed theoretically and is verified by experiments. More experiments are implemented to show the steady-state performance of the algorithm under different noise environments and the guide of parameter selection is provided.

In this paper, we extend the original Normalized Least Mean Fourth (NLMF) and Normalized Least Mean Square (NLMS) adaptive filtering algorithms into Geometric Algebra (GA) space to enable them to process multidimensional signals. We redefine the cost functions and propose the GA based NLMF and NLMS algorithms (GA-NLMF & GA-NLMS). We take full advantage of the ability of GA to represent multidimensional signals in GA space. GA-NLMS minimizes the cost function of the normalized mean square of the error signal, and remain stable as the input signal of the filter increases. GA-NLMS has fast convergence rate but higher steady-state error. The GA-NLMF algorithm minimizes the cost function of the normalized mean fourth of the error signal. Simulation results show that our proposed GA-NLMS adaptive filtering algorithm outperforms original NLMS algorithm in terms of convergence rate and steady-state error, and GA-NLMF outperforms both NLMF and GA-NLMS algorithms. GA-NLMF has faster convergence rate and lower steady state error, which is proved in the experiments.

This paper deals with the problem of proportional-difference observer design for singular systems in the discrete-time domain. Several necessary and sufficient conditions for the existence and convergence of the proposed observer are given and proved. Without using any additional transformations, a necessary and sufficient condition for the solvability of this problem is obtained in terms of linear matrix inequalities. The explicit expression of desired observer is also given. Furthermore, an extension to a class of nonlinear singular systems with Lipschitz constraints is investigated. Finally, a practical example and a numerical one are simulated to illustrate the effectiveness of the proposed approaches.

The article finds conditions for convergence of the functional from the sum sequence of series of independent, equally distributed in each series of random variables with values from N - dimensional Euclidean space, to the functional from the Wiener process. The results obtained are further applied to investigate the maximum of partial Erdos-Renyi sums of independent, identically distributed random variables. Sufficient conditions are obtained for the convergence of the distribution function to the limit law.

This paper presents the solution of 2 engineering problems, namely, AC systems and large electrical circuits, through representing them as linear systems of equations (LSEs) and solving them numerically, in an iterative manner. The proposed technique aims at finding the optimum weighting factors, A, that would accelerate the convergence of the successive over relaxation (SOR).

The acquisition of a discrete-time signal is an important part in compressive sensing problem. Instead of using $\ell_{0}$ -norm optimization, much attention is paid to $\ell_{p}$ -norm formulation for $p\in(0,1)$ due to its fast convergence and comparable accuracy. Iteratively reweighted least squares (IRLS) minimization is known as an improved algorithm of the typical basis pursuit with $\ell_{1}$ -norm criterion. In this work, an alternative enhancement of the IRLS criterion is presented. The proposed method invokes a descending sort of the absolute values of all elements in the solution and updates the nonzero indices in each iteration. Numerical examples illustrate that the proposed nonzero index update can help the IRLS minimization to recover the sparse signal with lower normalized root mean square error.

A novel strategy to the speed estimation including classical polynomial regression and parameter identification using Dynamic Regression Extension and Mixing (DREM) is presented in the paper. The reactive power $(Q=V_{sq}.i_{sd}-V_{sd}.i_{sq})$ is formed using instantaneous voltage and current values to get a regressor quantity and speed is taken as a response variable which enables an estimator fit. Since no additional gain calculation is required, the proposed regression-based speed estimation approach is simple to implement. The DREM is applied to estimate the Induction Motor (IM) parameters since it enhances transient response and global convergence of signals which are not square integrable. Linear Regression method requires to satisfy the persistency of excitation (PE) condition for parameter convergence and also struggles with signals that are not square integrable. Simulation results demonstrate the effectiveness of proposed speed estimator and DREM algorithm for parameter identification.

The majority of strongly nonlinear oscillators of higher fractional order do not have accurate analytical solution. As a result, this work provides an approximate approach, known as the optimal homotopy Asymptotic Method (OHAM) to provide approximate analytic solution of strongly oscillators having fractional derivatives. We give an exemple to show that the OHAM is a reliable approach to control the convergence of approximate solution.

We study the convergence of the Proximal-Gradient algorithm for convex composite problems when both the gradient and the proximal mapping are computed approximately. This scenario occurs when the gradient is computationally expensive and the proximal operator is not available in closed form and may be computed only up to a certain fixed precision. We establish tight deterministic bounds and propose new probabilistic upper bounds on the suboptimality of the function values along the iterations under some statistical assumptions on the perturbed iterates. We use the Proximal-Gradient algorithm to solve randomly generated LASSO problems while varying the fixed-point machine representation and the proximal computation precision.

This paper focuses on developing an exponentially weighted sine cosine algorithm that helps achieve faster convergence and better global optimal solutions. The proposed algorithm has been achieved by incorporating exponential weight functions in the position updation equations that change during each algorithm iteration. Further, a comparison of the proposed algorithm with the traditional technique is made on various benchmark functions-selecting these functions of multiple categories such as unimodal, multimodal, and composite. The optimization results indicated that the proposed exponentially weighted algorithm performed superior to the traditional and other adaptive weighted algorithms. The best performance is proper for most functions concerning mean, best, and standard deviation values. Moreover, the conventional technique has reached the worst global minima values for most of the test functions than the proposed algorithm.

The present paper deals with the issue of measurement delays which constitute a very prominent problem faced by most control systems. The system considered is that of a bioreactor used for the biological treatment of wastewater. The recording of the output substrate concentration of such systems usually involves a delay which results from the dependency of the flow of the liquid on its consistency. A PI observer-based control is applied and its performance is analysed in terms of the maximum delay for which the system is stable and converges as well as in terms of the convergence times. Based on these parameters, the results are compared to those obtained by a feedback linearising observer-based system. This comparative analysis showed that the PI controller performed better than the feedback controller, hence confirming its efficiency in biomass regulation in the presence of delayed measurements.

This paper proposes the application of a Proportional-Integral (PI) controller for the observer-based regulation of biomass concentration for a continuous-discrete system. An observer is essential to estimate the values of biomass concentration since the controller depends on these measurements. The analysis focuses on the continuous-discrete nature of the system which is represented by a continuous bioreactor system with discrete output measurements. The maximum allowable sampling partition diameter is determined along with the corresponding convergence time. These results are then compared to another work that used a feedback linearising control to achieve biomass regulation. The results obtained with the PI controller proved to be far more superior both in terms of maximum possible sampling time and convergence time. These findings confirmed the satisfactory and improved performance of the proposed observer-based controller.

The propagation mode based on the convergence zone in the deep sea is an important method for long-distance detection. In order to effectively identify the deep-sea convergence area, this paper proposes a method for identifying the deep-sea convergence area and shadow area based on the correlation matrix eigenvalue decline index of the horizontal array. The eigenvalue decline index of the correlation matrix refers to the ratio of the maximum eigenvalue to the second largest eigenvalue of the receiving signal correlation matrix, which is calculated to characterize the oscillation properties of the correlation coefficient matrix. The index can effectively characterize the oscillation characteristics of the correlation matrix in convergence area and shadow area which can be used to convergence zone and shadow zone discrimination. Simulation experiments show that setting a reasonable threshold of the eigenvalue decline index can effectively distinguish the convergence area from the shadow area.

In this paper, we proposed a saturated self-propelled particle system, where the weight between two particles could be saturated if the Euclidean distance between particles is smaller than a certain value or bigger than a certain value. In order to represent the weight of each particle, we introduced the saturated piecewise function into original Vicsek model, the bounds of the function are fixed value. Furthermore, due to different upper limit value could result in different convergence speed, we introduce a exponent into upper limit of saturation and investigate the convergence of the system when the upper limit increases exponentially. The simulation results demonstrate that the saturated model has faster convergence speed than original Vicsek model under different particle number and different system parameters and the convergence speed can be further improved as the exponent increases, the system is much easier to obtain consensus even for the noise disturbance.

This paper addresses performance limits analysis of MPC by comparing performance of MPC with that of finite or infinite horizon optimal control through value-iteration-based dynamic programming method. For receding horizon optimization problems with arbitrary positive definite terminal cost, three different cases are discussed in detail. Novel convergence properties of value iteration are exploited for each case based on principle of optimality. These properties are then utilized to analyze the stability and further quantify performance limits of the closed-loop MPC systems. Upper and lower bounds of the ratio between the cost of MPC and finite or infinite optimal cost are obtained.

In recent years, the well-known Vicsek model (VM) has attracted the interest of many researchers. In this paper, we investigate a revised Vicsek model based on diffusion concept, named as diffusion Vicsek model. The proposed diffusion Vicsek model can use weights to make the agents in the cluster more dispersed without introducing additional repulsive forces. In diffusion Vicsek model, the λ is introduced to adjust the degree of dispersion. When the value of λ is larger, it is more conducive to increase the dispersion of the cluster. Especially when λ = 0, the diffusion model will become the original Vicsek model. In the simulation experiments, the original Vicsek model and the diffusion Vicsek model are compared. The results show that there is an optimal λ under different number of agents N, communication radius R and absolute velocity v 0 , which effectively improves the convergence speed of the cluster.

In order to improve the ability of BBPSO to jump out of the local optimal solution and avoid it falling into the local optimal solution, this paper proposes the BBPSO with linear variable weights. First, a linearly changing adjustment factor β is introduced into the iterative formula to balance the exploration and exploitation. Secondly, the scale factor D is introduced for the fast convergence of BBPSO, so that the adjustment factor will decrease to its minimum in the first half of the iterative process. The experimental results show that BBPSO with linear variable weight has better global optimality and can effectively balance the exploration and exploitation.

This paper is concerned with the least squares estimator for a basic class of nonlinear autoregressive models, whose outputs are not necessarily to be ergodic. Several asymptotic properties of the least squares estimator have been established under mild conditions. These properties suggest the strong consistency of the least squares estimates in nonlinear autoregressive models which are not divergent.

Fourier series of Linear Complementarity is introduced into the field of bathymetric data fitting. Firstly, in data preprocessing, the principles of grid processing in bathymetry is given in the paper. And then, different methods of complementarity (none complementarity, direct complementarity and linear complementarity) are compared and analyzed, which shows that the Fourier Series of linear complementarity method can effectively improve the convergence speed of modeling. And the result futher illustrated that the Fourier series of linear complementarity has a wide application in the bathymetric data processing.

The Information bottleneck (IB) method enables optimizing over the trade-off between compression of data and prediction accuracy of learned representations, and has successfully and robustly been applied to both supervised and unsupervised representation learning problems. However, IB has several limitations. First, the IB problem is hard to optimize. The IB Lagrangian $\mathcal{L}_{IB}:=I(X;Z)-\beta I(Y;Z)$ is non-convex and existing solutions guarantee only local convergence. As a result, the obtained solutions depend on initialization. Second, the evaluation of a solution is also a challenging task. Conventionally, it resorts to characterizing the information plane, that is, plotting $I(Y;Z)$ versus $I(X;Z)$ for all solutions obtained from different initial points. Furthermore, the IB Lagrangian has phase transitions while varying the multiplier $\beta$. At phase transitions, both $I(X;Z)$ and $I(Y;Z)$ increase abruptly and the rate of convergence becomes significantly slow for existing solutions. Recent works with IB adopt variational surrogate bounds to the IB Lagrangian. Although allowing efficient optimization, how close are these surrogates to the IB Lagrangian is not clear. In this work, we solve the IB Lagrangian using augmented Lagrangian methods. With augmented variables, we show that the IB objective can be solved with the alternating direction method of multipliers (ADMM). Different from prior works, we prove that the proposed algorithm is consistently convergent, regardless of the value of $\beta$. Empirically, our gradient-descent-based method results in information plane points that are comparable to those obtained through the conventional Blahut-Arimoto-based solvers and is convergent for a wider range of the penalty coefficient than previous ADMM solvers., Comment: 8 pages, 1 figure

We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to circumvent the curse of dimensionality in Wasserstein distance: when the dimension is high, it has diminishing testing power, which is inherently due to the slow concentration property of Wasserstein metrics in the high dimension space. A key contribution is to couple optimal projection to find the low dimensional linear mapping to maximize the Wasserstein distance between projected probability distributions. We characterize theoretical properties of the two-sample convergence rate on IPMs and this new distance. Numerical examples validate our theoretical results.

The amount of net photosynthesis of leaves is a significate factor for the growth of plants. Therefore, monitoring the real-time net photosynthesis plays an essential role in improving the quality of productions in commercial greenhouses. Net photosynthesis mainly depends on three environmental parameters, that are light level, temperature and CO2 concentration. However, it is challenging to calculate accurate net photosynthesis due to the highly nonlinear relation. In this paper, Deep Learning (DL) is utilized to model this relationship in order to predict the net photosynthesis based on the three inputs. Firstly, the architecture of a Deep Neural Network (DNN) model is designed according to the features of this problem, and three activation functions are concerned for the DNN model design. Secondly, a training dataset is established, and two schedules of Learning Rate (LR), fixed LR and exponential decay LR, are elaborated. Then, to select the optimal hyperparameters for the DNN model, experiments of hyperparameters tuning related to activation functions and LR schedules are implemented, respectively. Finally, through a comprehensive evaluation of the training speed and the prediction accuracy, a DNN model that is with ReLU activation function and decay LR is determined. This DNN model can perform a dramatically high prediction accuracy in a fast training convergence speed for solving the proposed net photosynthesis prediction problem.

This paper presents approaches to the calculation of the solution of the load flow problem in ill-conditioned systems based on Newton’s Continuous philosophy. Two approaches to the Heun-King-Werner method are proposed with the objective of obtaining a better computational cost from the reduction of the number of calculations and factorizations of the Jacobian matrices. The methods performance were compared in terms of convergence with the standard Newton-Raphson and the original Heun-King-Werner method. Experiments carried out in ill-conditioned power system models demonstrated that the proposed approaches can significantly reduce the computational cost employed by the original Heun-King-Werner method.

This paper focuses on semistability and finite time semistability analysis of discrete-time dynamical systems having a continuum of equilibria. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. In this paper, we build on the theories of semistability and finite-time semistability for continuous-time dynamical systems to develop a rigorous framework for discrete semistability and discrete finite-time semistability. Specifically, Lyapunov and converse Lyapunov theorems for semistability and finite time semistability are developed, and the regularity properties of the Lyapunov function establishing finite time semistability are shown to be related to the settling time function capturing the finite settling time behavior of the dynamical system.

Relying on a conditional gradient based iteration, the Frank-Wolfe (FW) algorithm has been a popular solver of constrained convex optimization problems in signal processing and machine learning, thanks to its low complexity. The present contribution broadens its scope by replacing the gradient per FW subproblem with a weighted average of gradients. This generalization speeds up the convergence of FW by alleviating its zigzag behavior. A geometric interpretation for the averaged gradients is provided, and convergence guarantees are established for three different weight combinations. Numerical comparison shows the effectiveness of the proposed methods.

Stochastic computing has a long history as an alternative method of performing arithmetic on a computer. While it can be considered an unbiased estimator of real numbers, it has a variance and MSE on the order of $\Omega(\frac{1}{N})$. On the other hand, deterministic variants of stochastic computing remove the stochastic aspect, but cannot approximate arbitrary real numbers with arbitrary precision and are biased estimators. However, they have an asymptotically superior MSE on the order of $O(\frac{1}{N^2})$. Recent results in deep learning with stochastic rounding suggest that the bias in the rounding can degrade performance. We proposed an alternative framework, called dither computing, that combines aspects of stochastic computing and its deterministic variants and that can perform computing with similar efficiency, is unbiased, and with a variance and MSE also on the optimal order of $\Theta(\frac{1}{N^2})$. We also show that it can be beneficial in stochastic rounding applications as well. We provide implementation details and give experimental results to comparatively show the benefits of the proposed scheme., Comment: 8 pages, 16 figures, 1 table

The analysis of an optimization algorithm for solving an inverse problem for the cerebral oxygen transport model is carried out. A theorem on the solvability of the optimal control problem is presented, an optimality system is constructed, and the convergence of approximate solutions to the solution of the inverse problem is proved. The results of numerical simulation are presented.

This paper addresses the long-standing open problem of observability of mass and inertia plant parameters in the adaptive identification (AID) of second-order nonlinear models of 6 degree-of-freedom rigid-body dynamical systems subject to externally applied forces and moments. Although stable methods for AID of plant parameters for this class of systems, as well numerous approaches to stable model-based direct adaptive trajectory-tracking control of such systems, have been reported, these studies have been unable to prove analytically that the adaptive parameter estimates converge to the true plant parameter values. This paper reports necessary and sufficient conditions for the uniform complete observability (UCO) of 6-DOF plant inertial parameters for a stable adaptive identifier for this class of systems. When the UCO condition is satisfied, the adaptive parameter estimates are shown to converge to the true plant parameter values. To the best of our knowledge this is the first reported proof for this class of systems of UCO of plant parameters and for convergence of adaptive parameter estimates to true parameter values. We also report a numerical simulation study of this AID approach which shows that (a) the UCO condition can be met for fully-actuated plants as well as underactuated plants with the proper choice of control input and (b) convergence of adaptive parameter estimates to the true parameter values. We conjecture that this approach can be extended to include other parameters that appear rigid body plant models including parameters for drag, buoyancy, added mass, bias, and actuators., Comment: To appear in published proceedings of the 2021 IEEE International Conference on Robotics and Automation (ICRA), Xian, China, May 30 - June 5, 2021. 6 Pages, 2 Figures. *Replacement (v2) submitted to include author's middle initials in metadata. *Replacement (v3) submitted to include publication information

The Cosserat rod equations are used to model continuum and soft robots. Solving these equations are computationally expensive, particularly due to mixed boundary values and kinematic constraints. In this paper, we present a novel nonlinear observer that can rapidly estimate the solution of the Cosserat rod equations. We present details of the observer design and analyse its convergence and stability. Furthermore, we compare the accuracy and performance of the observer with common solvers used in the literature. Our results show that the proposed observer can significantly improve the computational efficiency of continuum robots' models and estimates the solution of the Cosserat rod equations 7 times faster than common solvers.

This paper investigates linear quadratic regulator(LQR) problem of linear stochastic systems. An novel algorithm is proposed to solve the general algebraic Riccati equation(GARE) derived from linear stochastic systems based on successive over-relaxation technique. With some initial conditions satisfied, the monotone convergence can be guaranteed, and an initial value selection method is proposed. Furthermore, a numerical example is given to demonstrate the effectiveness of the algorithm.

We propose a hybrid control algorithm that guarantees fast convergence and uniform global asymptotic stability of the set of minimizers of a convex objective function. The algorithm, developed using hybrid system tools, employs a uniting control strategy, in which Nesterov's accelerated gradient descent is used “globally” and the heavy ball method is used “locally”, relative to the set of minimizers. The proposed hybrid control strategy switches between these accelerated methods to ensure convergence to the set of minimizers without oscillations, with a (hybrid) convergence rate that preserves the convergence rates of the individual optimization algorithms. We analyze key properties of the resulting closed-loop system including existence of solutions, uniform global asymptotic stability, and convergence rate. Additionally, attractivity properties of Nesterov's algorithm are analyzed. Numerical results validate the findings.

This paper is devoted to finding an explicit solution for the finite-horizon linear-quadratic regulator optimal control problem of linear time-invariant fractional-order systems based on a spectral method. The proposed technique does not pose the burden of regular Riccati fractional differential equations that demand integrating left- and right-sided fractional differential operators. The obtained solution exhibits spectral convergence with an efficient computation time. For this purpose, the closed-form of the optimal solution and the finite horizon state-feedback control are both obtained at Chebyshev-Gauss-Lobatto points by adopting operational matrices of left- and right-sided fractional-order differentiation. The validity and effectiveness of the proposed method are examined through an illustrative example.

In this paper, we consider the problem of estimating a constant (or piecewise constant) parameter of a linear regression model. Using a hybrid systems framework, a hybrid algorithm is proposed allowing the estimate to converge to the exact value of the unknown parameter in predetermined finite time. Interestingly, we show that for the case of a constant parameter, the convergence property of the hybrid algorithm holds while only requiring the regressor to be exciting on a finite interval. For the case of a piecewise constant parameter, the classical persistency of excitation condition is required to guarantee the convergence. Robustness of the proposed algorithm with respect to measurements noise is analysed. Finally, illustrative examples are provided showing the merits of the proposed approach.

We propose a non-model based strategy for locally stable convergence to Nash equilibria in quadratic noncooperative (duopoly) games with player actions subject to diffusion (heat) PDE dynamics with distinct diffusion coefficients and each player having access only to his own payoff value. The proposed approach employs extremum seeking, with sinusoidal perturbation signals employed to estimate the Gradient (first derivative) and Hessian (second derivative) of unknown quadratic functions. In our previous work, we solved Nash equilibrium seeking problems with input delays. This is the first instance of noncooperative games being tackled in a model-free fashion in the presence of heat PDE dynamics. In order to compensate distinct diffusion processes in the inputs of the two players, we employ boundary control with averaging-based estimates. We apply a small-gain analysis for the resulting Input-to-State Stable (ISS) parabolic PDE-ODE loop as well as averaging theory in infinite dimensions, due to the infinite-dimensional state of the heat PDEs, in order to obtain local convergence results to a small neighborhood of the Nash equilibrium. We quantify the size of these residual sets and illustrate the theoretical results numerically on an example of a two-player game under heat PDEs.

We propose convex conditions to synthesize parameter-dependent state feedback control gains to regionally stabilize discrete-time linear parameter varying (LPV) systems subject to magnitude and rate saturating actuators. The regional stabilization is performed in the sense of polyquadratic stability. Through a parameter-dependent Lyapunov function candidate, the design conditions are proposed in terms of a finite set of linear matrix inequalities (LMIs). The feasibility of the proposed conditions also provides an estimate of the region of initial conditions yielding trajectories with guaranteed convergence to the origin. We provide a design parameter to increase the contractivity of the Lyapunov function. Nonlinear first-order models represent the magnitude and rate saturation of the actuators. Additionally, we propose a convex optimization procedure to enlarge the estimate of the region of attraction. Three numerical examples illustrate our proposals' efficiency and compare the achieved results with other literature approaches.

This paper considers stochastic convex optimization problems where the objective and constraint functions involve expectations with respect to the data indices or environmental variables, in addition to deterministic convex constraints on the domain of the variables. Although the setting is generic and arises in different machine learning applications, online and efficient approaches for solving such problems has not been widely studied. Since the underlying data distribution is unknown a priori, closed-form solution is generally not available, and classical deterministic optimization paradigms are not applicable. Existing approaches towards solving these problems make use of stochastic gradients of the objective and constraints that arrive sequentially over iterations. State-of-the-art approaches, such as those using the saddle point framework, are able to ensure that the optimality gap as well as the constraint violation decay as $\mathcal{O}(T^{-\frac{1}{2}})$ where $T$ is the number of stochastic gradients. In this work, we propose a novel conservative stochastic optimization algorithm (CSOA) that achieves zero average constraint violation and $\mathcal{O}(T^{-\frac{1}{2}})$ optimality gap. The efficacy of the proposed algorithm is tested on a relevant problem of fair classification.

This work provides the observation and control of biomass concentration in Waste Water Treatment Plants. To achieve this, a PI controller was designed together with an observer to form an observer-based control system. The optimal values of the proportional gain and integral gain were determined to obtain the convergence of the observer in the least amount of time without compromising on the time taken by the response to reach steady state. Encouraging results which shall provide a basis for further and more in-depth research on the system were obtained.

The relationship between the processes of forming classes of prime numbers in the generalized Artin hypothesis is investigated on the basis of the theory of randomization of algorithms of the probabilistic method and analytical number theory. It is proved that probabilistic methods are the basis for constructing computer models for the formation of classes of prime numbers in accordance with Artin's generalized hypothesis. It was found that modern methods of analytical number theory do not allow one to obtain estimates for the generalized Artin constants. Methods for calculating the Artin constants are developed and the convergence of the estimates of the constants in probability to the limiting values is established. The fundamentals of the number-theoretic analysis of Artin's constants and related classes have been created.

In electric field calculation, the accuracy of electric field strength obtained by traditional finite element method is not ideal, and the applicability of weighted average method is insufficient. In order to improve the accuracy of electric field strength solution, the improved finite element based on gradient recovery algorithm for electric field calculation is proposed. The algorithm selects superconvergence sampling points in the element slices near the nodes, and performs least square fitting on the gradient of the finite element solution of the sampling points, so as to obtain high-precision gradient approximation. The algorithm is applied to solve the two-dimensional electric field problem, the results show that the numerical algorithm is simple to implement, the cost involved in the calculation can be ignored, compared with the weighted average method, it has better solution accuracy, faster convergence speed and wider applicability.

The traditional numerical calculation methods of electrostatic field include finite element method, finite difference method and so on. Due to the time-consuming meshing, the meshless method is gradually used by scholars for physical field analysis. At present, the meshless local Petrov-Galerkin method and the meshfree weak-strong method have been reported in various fields with their better accuracy and wide applicability. This paper presents an improved meshless strong-weak coupling method based on test function. The scattered nodes are used to represent the problem domain and boundary, and the shape function is constructed by the moving least square method. For the nodes where the local integration domain does not intersect the global derivative boundary, the meshless strong form method is used to construct the basic equation. For other nodes, the meshless local weak formula method is used. The exponential function is used as a test function for weak formula expressions. By changing the coefficient of the exponential function, the shape of the test function is controlled, and the influence of the change in the size of the influence domain on the calculation accuracy is reduced. The case analysis shows that this method has higher accuracy and better convergence effect than the traditional meshless method. The proposed method has high precision and computational efficiency in processing electrical numerical calculations, and has strong astringency. This method has better application prospects than traditional methods.