Abstract: This paper concerns high-accuracy tracking control for hydraulic actuators with nonlinear friction compensation Typically, LuGre model-based friction compensation has been widely employed in sundry industrial servomechanisms However, due to the piecewise continuous property, it is difficult to be integrated with backstepping design, which needs the time derivation of the employed friction model Hence, nonlinear model-based hydraulic control rarely sets foot in friction compensation with nondifferentiable friction models, such as LuGre model, Stribeck effects, although they can give excellent friction description and prediction In this paper, a novel continuously differentiable nonlinear friction model is first derived by modifying the traditional piecewise continuous LuGre model, then an adaptive backstepping controller is proposed for precise tracking control of hydraulic systems to handle parametric uncertainties along with nonlinear friction compensation In the formulated nonlinear hydraulic system model, friction parameters, servovalve null shift, and orifice-type internal leakage are all uniformly considered in the proposed controller The controller theoretically guarantees asymptotic tracking performance in the presence of parametric uncertainties, and the robustness against unconsidered dynamics, as well as external disturbances, is also ensured via Lyapunov analysis The effectiveness of the proposed controller is demonstrated via comparative experimental results

Abstract: 3D scene flow estimation aims to jointly recover dense geometry and 3D motion from stereoscopic image sequences, thus generalizes classical disparity and 2D optical flow estimation. To realize its conceptual benefits and overcome limitations of many existing methods, we propose to represent the dynamic scene as a collection of rigidly moving planes, into which the input images are segmented. Geometry and 3D motion are then jointly recovered alongside an over-segmentation of the scene. This piecewise rigid scene model is significantly more parsimonious than conventional pixel-based representations, yet retains the ability to represent real-world scenes with independent object motion. It, furthermore, enables us to define suitable scene priors, perform occlusion reasoning, and leverage discrete optimization schemes toward stable and accurate results. Assuming the rigid motion to persist approximately over time additionally enables us to incorporate multiple frames into the inference. To that end, each view holds its own representation, which is encouraged to be consistent across all other viewpoints and frames in a temporal window. We show that such a view-consistent multi-frame scheme significantly improves accuracy, especially in the presence of occlusions, and increases robustness against adverse imaging conditions. Our method currently achieves leading performance on the KITTI benchmark, for both flow and stereo.

Abstract: The solution of the inverse kinematics problem of soft manipulators is essential to generate paths in the task space. The inverse kinematics problem of constant curvature or piecewise constant curvature manipulators has already been solved by using different methods, which include closed-form analytical approaches and iterative methods based on the Jacobian method. On the other hand, the inverse kinematics problem of nonconstant curvature manipulators remains unsolved. This study represents one of the first attempts in this direction. It presents both a model-based method and a supervised learning method to solve the inverse statics of nonconstant curvature soft manipulators. In particular, a Jacobian-based method and a feedforward neural network are chosen and tested experimentally. A comparative analysis has been conducted in terms of accuracy and computational time.

Abstract: We study a class of Piecewise Deterministic Markov Processes with state space Rd x E where E is a finite set. The continuous component evolves according to a smooth vector field that is switched at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Working under the general assumption that the process stays in a compact set, we detail a possible construction of the process and characterize its support, in terms of the solutions set of a differential inclusion. We establish results on the long time behaviour of the process, in relation to a certain set of accessible points, which is shown to be strongly linked to the support of invariant measures. Under Hormander-type bracket conditions, we prove that there exists a unique invariant measure and that the processes converges to equilibrium in total variation. Finally we give examples where the bracket condition does not hold, and where there may be one or many invariant measures, depending on the jump rates between the flows.

Abstract: A new behavioral model for digital predistortion of radio frequency (RF) power amplifiers (PAs) is proposed in this paper. It is derived from a modified form of the canonical piecewise-linear (CPWL) functions using a decomposed vector rotation (DVR) technique. In this model, the nonlinear basis function is constructed from piecewise vector decomposition, which is completely different from that used in the conventional Volterra series. Theoretical analysis has shown that this model is much more flexible in modeling RF PAs with non-Volterra-like behavior, and experimental results confirmed that the new model can produce excellent performance with a relatively small number of coefficients when compared to conventional models.

Abstract: The orbital boundary value problem, also known as Lambert problem, is revisited. Building upon Lancaster and Blanchard approach, new relations are revealed and a new variable representing all problem classes, under L-similarity, is used to express the time of flight equation. In the new variable, the time of flight curves have two oblique asymptotes and they mostly appear to be conveniently approximated by piecewise continuous lines. We use and invert such a simple approximation to provide an efficient initial guess to an Householder iterative method that is then able to converge, for the single revolution case, in only two iterations. The resulting algorithm is compared, for single and multiple revolutions, to Gooding’s procedure revealing to be numerically as accurate, while having a significantly smaller computational complexity.

Abstract: This article aims to fill in the gap of the second-order accurate schemes for the time-fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are first proposed for the time-fractional subdiffusion equation with space discretized by finite element method and time discretized by the fractional linear multistep methods. These two methods are unconditionally stable with maximum global convergence order of O ( τ + h r +1 )in the L 2 norm, where τ and h are the step sizes in time and space, respectively, and r is the degree of the piecewise polynomial space. The average convergence rates for the two methods in time are also investigated, which shows that the average convergence rates of the two methods are O ( τ 1 . 5 + h r +1 ). Furthermore, two improved algorithms are constructed, and they are also unconditionally stable and convergent of order O ( τ 2 + h r +1 ). Numerical examples are provided to verify the theoretical analysis. Comparisons between the present algorithms and the existing ones are included, showing that our numerical algorithms exhibit better performances than the known ones.

Abstract: In recent years, decision rules have been established as the preferred solution method for addressing computationally demanding, multistage adaptive optimization problems. Despite their success, existing decision rules (a) are typically constrained by their a priori design and (b) do not incorporate in their modeling adaptive binary decisions. To address these problems, we first derive the structure for optimal decision rules involving continuous and binary variables as piecewise linear and piecewise constant functions, respectively. We then propose a methodology for the optimal design of such decision rules that have a finite number of pieces and solve the problem robustly using mixed-integer optimization. We demonstrate the effectiveness of the proposed methods in the context of two multistage inventory control problems. We provide global lower bounds and show that our approach is (i) practically tractable and (ii) provides high quality solutions that outperform alternative methods.

Abstract: A posteriori error estimation and adaptivity are very useful in the context of the virtual element and mimetic discretization methods due to the flexibility of the meshes to which these numerical schemes can be applied. Nevertheless, developing error estimators for virtual and mimetic methods is not a straightforward task due to the lack of knowledge of the basis functions. In the new virtual element setting, we develop a residual based a posteriori error estimator for the Poisson problem with (piecewise) constant coefficients, that is proven to be reliable and efficient. We moreover show the numerical performance of the proposed estimator when it is combined with an adaptive strategy for the mesh refinement.

Abstract: Mesh surface denoising is a fundamental problem in geometry processing The main challenge is to remove noise while preserving sharp features (such as edges and corners) and preventing generating false edges We propose in this paper to combine total variation (TV) and piecewise constant function space for variational mesh denoising We first give definitions of piecewise constant function spaces and associated operators A variational mesh denoising method will then be presented by combining TV and piecewise constant function space It is proved that, the solution of the variational problem (the key part of the method) is in some sense continuously dependent on its parameter, indicating that the solution is robust to small perturbations of this parameter To solve the variational problem, we propose an efficient iterative algorithm (with an additional algorithmic parameter) based on variable splitting and augmented Lagrangian method, each step of which has closed form solution Our denoising method is discussed and compared to several typical existing methods in various aspects Experimental results show that our method outperforms all the compared methods for both CAD and non-CAD meshes at reasonable costs It can preserve different levels of features well, and prevent generating false edges in most cases, even with the parameters evaluated by our estimation formulae

Abstract: We propose a new nonparametric procedure (referred to as MuBreD) for the detection and estimation of multiple structural breaks in the autocovariance function of a multivariate (second-order) piecewise stationary process, which also identifies the components of the series where the breaks occur. MuBreD is based on a comparison of the estimated spectral distribution on different segments of the observed time series and consists of three steps: it starts with a consistent test, which allows us to prove the existence of structural breaks at a controlled Type I error. Second, it estimates sets containing possible break points and finally these sets are reduced to identify the relevant structural breaks and corresponding components which are responsible for the changes in the autocovariance structure. In contrast to all other methods proposed in the literature, our approach does not make any parametric assumptions, is not especially designed for detecting one single change point, and addresses the problem of m...

Abstract: The asymptotical synchronization problem is investigated for two identical chaotic Lur’e systems with time delays. The sampled-data control method is employed for the system design. A new synchronization condition is proposed in the form of linear matrix inequalities. The error system is shown to be asymptotically stable with the constructed new piecewise differentiable Lyapunov–Krasovskii functional (LKF). Different from the existing work, the new LKF makes full use of the information in the nonlinear part of the system. The obtained stability condition is less conservative than some of the existing ones. A longer sampling period is achieved with the new method. The numerical examples are given and the simulations are performed on Chua’s circuit. The results show the superiorities and effectiveness of the proposed control method.

Abstract: This paper presents a novel variational approach for simultaneous estimation of bias field and segmentation of images with intensity inhomogeneity. We model intensity of inhomogeneous objects to be Gaussian distributed with different means and variances, and then introduce a sliding window to map the original image intensity onto another domain, where the intensity distribution of each object is still Gaussian but can be better separated. The means of the Gaussian distributions in the transformed domain can be adaptively estimated by multiplying the bias field with a piecewise constant signal within the sliding window. A maximum likelihood energy functional is then defined on each local region, which combines the bias field, the membership function of the object region, and the constant approximating the true signal from its corresponding object. The energy functional is then extended to the whole image domain by the Bayesian learning approach. An efficient iterative algorithm is proposed for energy minimization, via which the image segmentation and bias field correction are simultaneously achieved. Furthermore, the smoothness of the obtained optimal bias field is ensured by the normalized convolutions without extra cost. Experiments on real images demonstrated the superiority of the proposed algorithm to other state-of-the-art representative methods.

Abstract: Most mesh denoising techniques utilize only either the facet normal field or the vertex normal field of a mesh surface. The two normal fields, though contain some redundant geometry information of the same model, can provide additional information that the other field lacks. Thus, considering only one normal field is likely to overlook some geometric features. In this paper, we take advantage of the piecewise consistent property of the two normal fields and propose an effective framework in which they are filtered and integrated using a novel method to guide the denoising process. Our key observation is that, decomposing the inconsistent field at challenging regions into multiple piecewise consistent fields makes the two fields complementary to each other and produces better results. Our approach consists of three steps: vertex classification , bi-normal filtering , and vertex position update . The classification step allows us to filter the two fields on a piecewise smooth surface rather than a surface that is smooth everywhere. Based on the piecewise consistence of the two normal fields, we filtered them using a piecewise smooth region clustering strategy. To benefit from the bi-normal filtering, we design a quadratic optimization algorithm for vertex position update. Experimental results on synthetic and real data show that our algorithm achieves higher quality results than current approaches on surfaces with multifarious geometric features and irregular surface sampling.

Abstract: Numerical methods for non-smooth equation-solving and optimization often require generalized derivative information in the form of elements of the Clarke Jacobian or the B-subdifferential. It is shown here that piecewise differentiable functions are lexicographically smooth in the sense of Nesterov, and that lexicographic derivatives of these functions comprise a particular subset of both the B-subdifferential and the Clarke Jacobian. Several recently developed methods for generalized derivative evaluation of composite piecewise differentiable functions are shown to produce identical results, which are also lexicographic derivatives. A vector forward mode of automatic differentiation AD is presented for evaluation of these derivatives, generalizing established methods and combining their computational benefits. This forward AD mode may be applied to any finite composition of known smooth functions, piecewise differentiable functions such as the absolute value function, , and , and certain non-smooth functions which are not piecewise differentiable, such as the Euclidean norm. This forward AD mode may be implemented using operator overloading, does not require storage of a computational graph, and is computationally tractable relative to the cost of a function evaluation. An implementation in C is discussed.

Abstract: In this study, an event-triggered control strategy is proposed to achieve consensus in a multi-agent system under a directed topology. The proposed control strategy utilises a piecewise continuous control law and an event-triggering function for each agent. The control law only updates at discrete event instants computed using an event-triggering function, which depends on the states of the agents at the current and outdated event instant. This control approach is first applied to a first-order system and is further extended to a second-order system. Simulation examples are presented to illustrate the efficiency of the proposed control strategy.

Abstract: The average consensus problem for a multi-agent system with nonlinear dynamics is studied in this paper by employing a distributed event-triggered control strategy. The strategy uses a piecewise continuous control law and an event-triggering function to control the system. The piecewise continuous control law only updates at infrequent instants and keeps steady at the previous value in the period between two instants. The event-triggering function determines these instants based on the state information of the agents at current and previous instants. This control approach is first applied to a first-order system under a connected topology in a centralized pattern. Then the switching topology case is considered. At last, both the first-order and the second-order system are considered under distributed event-triggered strategy. The distributed event-triggering function, which only employs the information of the corresponding agent and the states of its neighbors, is designed for each agent in the system. By utilizing Lyapunov method and graph theory, it is proven that the systems can reach consensus by using the event-triggered control strategy. Numerical examples are provided to show the efficacy of the proposed control strategy.

Abstract: In this paper, we propose a hybridized discontinuous Galerkin (HDG) method with reduced stabilization for the Poisson equation. The reduce stabilization proposed here enables us to use piecewise polynomials of degree $$k$$k and $$k-1$$k-1 for the approximations of element and inter-element unknowns, respectively, unlike the standard HDG methods. We provide the error estimates in the energy and $$L^2$$L2 norms under the chunkiness condition. In the case of $$k=1$$k=1, it can be shown that the proposed method is closely related to the Crouzeix---Raviart nonconforming finite element method. Numerical results are presented to verify the validity of the proposed method.

Abstract: Given a time series S = ((x 1 , y 1 ), (x 2 , y 2 ), …) and a prescribed error bound e, the piecewise linear approximation (PLA) problem with max-error guarantees is to construct a piecewise linear function f such that |f(x i )-y i | ≤ e for all i In addition, we would like to have an online algorithm that takes the time series as the records arrive in a streaming fashion, and outputs the pieces of f on-the-fly This problem has applications wherever time series data is being continuously collected, but the data collection device has limited local buffer space and communication bandwidth, so that the data has to be compressed and sent back during the collection process Prior work addressed two versions of the problem, where either f consists of disjoint segments, or f is required to be a continuous piecewise linear function In both cases, existing algorithms can produce a function f that has the minimum number of pieces while meeting the prescribed error bound e However, we observe that neither minimizes the true representation size of f, ie, the number of parameters required to represent f In this paper, we design an online algorithm that generates the optimal PLA in terms of representation size while meeting the prescribed max-error guarantee Our experiments on many real-world data sets show that our algorithm can reduce the representation size of f by around 15% on average compared with the current best methods, while still requiring O(1) processing time per data record and small space

Abstract: In this paper, two event-based robust sampled-data model predictive control (MPC) strategies are proposed based on the non-monotonic Lyapunov function approach for continuous-time systems with disturbances. Each event-triggering mechanism consists of the event-based MPC law and the triggering conditions. We show that although the proposed event-triggering conditions are only checked at the sampling instants and the control law is piecewise constant, the feasibility of the event-based sampled-data MPC algorithm and the stability of the closed-loop system are guaranteed in continuous time. Besides, the implementation issue is discussed, and we show that the proposed triggering conditions can be checked rapidly without obviously increasing the computational burden. Finally, an application to a nonholonomic robot system is provided to illustrate the effectiveness of the proposed results.

Abstract: We introduce a method to recover a continuous domain representation of a piecewise constant two-dimensional image from few low-pass Fourier samples. Assuming the edge set of the image is localized to the zero set of a trigonometric polynomial, we show the Fourier coefficients of the partial derivatives of the image satisfy a linear annihilation relation. We present necessary and sufficient conditions for unique recovery of the image from finite low-pass Fourier samples using the annihilation relation. We also propose a practical two-stage recovery algorithm which is robust to model-mismatch and noise. In the first stage we estimate a continuous domain representation of the edge set of the image. In the second stage we perform an extrapolation in Fourier domain by a least squares two-dimensional linear prediction, which recovers the exact Fourier coefficients of the underlying image. We demonstrate our algorithm on the super-resolution recovery of MRI phantoms and real MRI data from low-pass Fourier samples, which shows benefits over standard approaches for single-image super-resolution MRI.

Abstract: We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let $f$ be the density function of an arbitrary univariate distribution, and suppose that $f$ is $\mathrm{OPT}$-close in $L_1$-distance to an unknown piecewise polynomial function with $t$ interval pieces and degree $d$. Our algorithm draws $n = O(t(d+1)/\epsilon^2)$ samples from $f$, runs in time $\tilde{O}(n \cdot \mathrm{poly}(d))$, and with probability at least $9/10$ outputs an $O(t)$-piecewise degree-$d$ hypothesis $h$ that is $4 \cdot \mathrm{OPT} +\epsilon$ close to $f$. Our general algorithm yields (nearly) sample-optimal and nearly-linear time estimators for a wide range of structured distribution families over both continuous and discrete domains in a unified way. For most of our applications, these are the first sample-optimal and nearly-linear time estimators in the literature. As a consequence, our work resolves the sample and computational complexities of a broad class of inference tasks via a single "meta-algorithm". Moreover, we experimentally demonstrate that our algorithm performs very well in practice. Our algorithm consists of three "levels": (i) At the top level, we employ an iterative greedy algorithm for finding a good partition of the real line into the pieces of a piecewise polynomial. (ii) For each piece, we show that the sub-problem of finding a good polynomial fit on the current interval can be solved efficiently with a separation oracle method. (iii) We reduce the task of finding a separating hyperplane to a combinatorial problem and give an efficient algorithm for this problem. Combining these three procedures gives a density estimation algorithm with the claimed guarantees.

Abstract: The main objective of this work is to develop, via Brower degree theory and regularization theory, a variation of the classical averaging method for detecting limit cycles of certain piecewise continuous dynamical systems. In fact, overall results are presented to ensure the existence of limit cycles of such systems. These results may represent new insights in averaging, in particular its relation with non-smooth dynamical systems theory. An application is presented in careful detail.