Efficient implementation of Jacobi iterative method for large sparse linear systems on graphic processing units

In this paper, an original Jacobi implementation is considered for the solution of sparse linear systems of equations. The proposed algorithm helps to optimize the parallel implementation on GPU. The performance analysis of GPU-based (using CUDA) algorithm of the implementation of this algorithm is compared to the corresponding serial CPU-based algorithm. Numerical experiments performed on a set of matrices arising from the finite element discretization of various equations (3D Laplace equation, 3D gravitational potential equation, 3D Heat equation) with different meshes, illustrate the performance, robustness and efficiency of our algorithm, with a speed up to 23\(\times \) in double-precision arithmetics.     

Convergence of an algorithm to find maximal state constraint sets for discrete-time linear dynamical systems with bounded controls and states

In [1] an algorithm was presented to find an approximant to the maximal state constraint set for a linear discrete-time dynamical system with polyhedral state and input hounds. Here it is shown that the algorithm will yield an approximant arbitrarily close to the maximal state constraint set and the number of iterations is given as a function of the prescribed precision of the approximant.     

A design method for linear state feedback systems possessing integrity based on a solution of a Riccati-type equation

This paper is concerned with the synthesis of a state feedback control system which possesses both integrity and good responses. System integrity in multivariable control systems is defined as the property that the overall closed-loop system remains asymptotically stable in the presence of a failure in the feedback loop. A state feedback control law which retains asymptotic stability against arbitrary actuator failure is derived using a positive semidefinite solution of a type of matrix quadratic equation, and some properties of the closed-loop system are considered. Moreover, a design procedure by which the closed-loop system has the desired dynamical characteristics while maintaining integrity is proposed, and the effectiveness of the procedure is demonstrated with a numerical example.