Distributed Quadratic Programming over Arbitrary Graphs

In this paper, the locality features of infinitedimensional quadratic programming (QP) optimization problems are studied. Our approach is based on tools from operator theory and ideas from Multi Parametric Quadratic Programming (MPQP). The key idea is to use the spatially decaying operators (SD), which has been recently developed to study spatially distributed systems in [1], to capture couplings between optimization variables in the quadratic cost functional and linear constraints. As an application, it is shown that the problem of receding horizon control of spatially distributed systems with heterogeneous subsystems, input and state constraints, and arbitrary interconnection topologies can be modeled as an infinitedimensional QP problem. Furthermore, we prove that for a convex infinite-dimensional QP in which the couplings are through SD operators, optimal solution is piece-wise affine– represented as convolution sums. More importantly, we prove that the kernel of each convolution sum decays in the spatial domain at a rate proportional to the inverse of the corresponding coupling function of the optimization problem, thereby providing evidence that even centralized solutions to the infinite-dimensional QP has inherent spatial locality

GlobalFlowNet: Video Stabilization using Deep Distilled Global Motion Estimates

Videos shot by laymen using hand-held cameras contain undesirable shaky motion. Estimating the global motion between successive frames, in a manner not influenced by moving objects, is central to many video stabilization techniques, but poses significant challenges. A large body of work uses 2D affine transformations or homography for the global motion. However, in this work, we introduce a more general representation scheme, which adapts any existing optical flow network to ignore the moving objects and obtain a spatially smooth approximation of the global motion between video frames. We achieve this by a knowledge distillation approach, where we first introduce a low pass filter module into the optical flow network to constrain the predicted optical flow to be spatially smooth. This becomes our student network, named as \textsc{GlobalFlowNet}. Then, using the original optical flow network as the teacher network, we train the student network using a robust loss function. Given a trained \textsc{GlobalFlowNet}, we stabilize videos using a two stage process. In the first stage, we correct the instability in affine parameters using a quadratic programming approach constrained by a user-specified cropping limit to control loss of field of view. In the second stage, we stabilize the video further by smoothing global motion parameters, expressed using a small number of discrete cosine transform coefficients. In extensive experiments on a variety of different videos, our technique outperforms state of the art techniques in terms of subjective quality and different quantitative measures of video stability. The source code is publicly available at \href{https://github.com/GlobalFlowNet/GlobalFlowNet}{https://github.com/GlobalFlowNet/GlobalFlowNet}Comment: Accepted in WACV 202

The power dissipation method and kinematic reducibility of multiple-model robotic systems

This paper develops a formal connection between the power dissipation method (PDM) and Lagrangian mechanics, with specific application to robotic systems. Such a connection is necessary for understanding how some of the successes in motion planning and stabilization for smooth kinematic robotic systems can be extended to systems with frictional interactions and overconstrained systems. We establish this connection using the idea of a multiple-model system, and then show that multiple-model systems arise naturally in a number of instances, including those arising in cases traditionally addressed using the PDM. We then give necessary and sufficient conditions for a dynamic multiple-model system to be reducible to a kinematic multiple-model system. We use this result to show that solutions to the PDM are actually kinematic reductions of solutions to the Euler-Lagrange equations. We are particularly motivated by mechanical systems undergoing multiple intermittent frictional contacts, such as distributed manipulators, overconstrained wheeled vehicles, and objects that are manipulated by grasping or pushing. Examples illustrate how these results can provide insight into the analysis and control of physical systems

Sampled-data control of linear systems subject to input saturation : a hybrid system approach

In this work, a new method for the stability analysis and synthesis of sampled-data control systems subject to variable sampling intervals and input saturation is proposed. From a hybrid systems representation, stability conditions based on quadratic clockdependent Lyapunov functions and the generalized sector condition to handle saturation are developed. These conditions are cast in semidefinite and sum-of-squares optimization problems to provide maximized estimates of the region of attraction, to estimate the maximum intersampling interval for which a region of stability is ensured, or to produce a stabilizing controller that results in a large implicit region of attraction, through the maximization of an estimate of it.Neste trabalho é proposto um novo método para a análise da estabilidade de sistemas de controle amostrados aperiodicamente e com saturação na entrada, e também para a síntese de controladores estabilizantes. A partir de uma representação por sistemas híbridos, condições de estabilidade baseadas em funções quadráticas de Lyapunov dependentes do clock e na condição de setor generalizada para o tratamento de saturação são desenvolvidas para o sistema amostrado em questão. Essas condições são incorporadas como restrições em problemas de otimização. Os problemas de otimização são baseados em programação semidefinida e em programação sum-of-squares, e têm o objetivo de obter estimativas maximizadas da região de atração do sistema, estimativas do intervalo de amostragem máximo para o qual uma dada região de estados iniciais seja uma região de estabilidade, ou para produzir controladores (dados por ganhos estáticos estabilizantes) que resultem em uma região de atração implicitamente grande, através da maximização da estimativa dessa região de atração