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This paper proposes a parallelizable algorithm for linear-quadratic model predictive control (MPC) problems with state and input constraints. The algorithm itself is based on a parallel MPC scheme that has originally been designed for…
The computation of the tropical prevariety is the first step in the application of polyhedral methods to compute positive dimensional solution sets of polynomial systems. In particular, pretropisms are candidate leading exponents for the…
Aspects of compatibility of topologies of parallel computing systems and tasks are investigated. The introduction of appropriate indexes based on the original topological model of parallel computations and on the nontraditional description…
In the last fifteen years, the high performance computing (HPC) community has claimed for parallel programming environments that reconciles generality, higher level of abstraction, portability, and efficiency for distributed-memory parallel…
Numerical continuation methods track a solution path defined by a homotopy. The systems we consider are defined by polynomials in several variables with complex coefficients. For larger dimensions and degrees, the numerical conditioning…
Homotopy methods are attractive due to their capability of solving difficult optimisation and optimal control problems. The underlying idea is to construct a homotopy, which may be considered as a continuous (zero) curve between the…
The objective of this research is to construct parallel implementations of the Jacobi algorithm used for the solution of linear algebraic systems, to measure their speedup with respect to the serial case and to compare each other, regarding…
We describe a new implementation of a parallel Tree-SPH code with the aim to simulate Galaxy Formation and Evolution. The code has been parallelized using SHMEM, a Cray proprietary library to handle communications between the 256 processors…
While automatically generated polynomial elimination templates have sparked great progress in the field of 3D computer vision, there remain many problems for which the degree of the constraints or the number of unknowns leads to…
Miller and Reif's FOCS'85 classic and fundamental tree contraction algorithm is a broadly applicable technique for the parallel solution of a large number of tree problems. Additionally it is also used as an algorithmic design technique for…
Dynamic programming is a powerful technique that is, unfortunately, often inherently sequential. That is, there exists no unified method to parallelize algorithms that use dynamic programming. In this paper, we attempt to address this issue…
Processing massive application graphs on distributed memory systems requires to map the graphs onto the system's processing elements (PEs). This task becomes all the more important when PEs have non-uniform communication costs or the input…
Using (a,b)-trees as an example, we show how to perform a parallel split with logarithmic latency and parallel join, bulk updates, intersection, union (or merge), and (symmetric) set difference with logarithmic latency and with information…
In the article the problem of output setpoint tracking for affine non-linear system is considered. Presented approach combines state feedback linearization and homotopy numerical continuation in subspaces of phase space where feedback…
This article presents the parallel implementation of the coupled harmonic oscillator. From the analytical solution of the coupled harmonic oscillator, the design parameters are obtained. After that, a numerical integration of the system…
Model predictive control (MPC) samples a generally unknown and complicated feedback law point by point. The solution for the current state $x$ contains, however, more information than only the optimal signal $u$ for this particular state.…
Counting non-isomorphic tree-like multigraphs that include self-loops and multiple edges is an important problem in combinatorial enumeration, with applications in chemical graph theory, polymer science, and network modeling. Traditional…
This paper presents a systematic approach for computing local solutions to motion planning problems in non-convex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal…
The Massive Parallel Computation (MPC) model is a theoretical framework for popular parallel and distributed platforms such as MapReduce, Hadoop, or Spark. We consider the task of computing a large matching or small vertex cover in this…
Meshless methods are used to solve partial differential equations by approximating differential operators at a node as a weighted sum of values at its neighbours. One of the algorithms for generating nodes suitable for meshless numerical…