| The objectives of this doctoral Thesis belong to a multisubject framework, in which High-Performance algorithmic solutions to the computational problems that lie behind the Simulation, Estimation and Control of Non-Linear Systems are pursued.; The behavior of several science and engineering phenomenons can be simulated by solving ordinary differential equations (ODE'S) or differential algebraic equations (DAE's). Different resolution methods exist for those types of equations. Piecewise linealization is one of them. In this Thesis, a new approach to the resolution of ODE's and DAE's has been developed. This new approach permits to solve ODE's and DAE's independently of the fact that the Jacobian matrix is singular or not.; On the other hand, it is often necessary to estimate the non-lineal behavior of robots to control them. A common way to estimate such non-linearity is the use of neural networks, which is the approach chosen in this Thesis.; Finally, the optimal linear-quadratic control problem has been tackled. In this problem, lies the solution of a differential matrix Riccati equation (DMRE). In this Thesis, the numerical integration method of such equation has been used.; The algorithmic solutions to those problems have been captured in the development of sequential and parallel algorithms, for distributed and shared memory platforms. In such implementations, the features of high-quality mathematical software have been taken into account. Some of those features are the following: (1) Power and flexibility, allowing the resolution of many variations of the original problem. As an example, the implementation made in the part devoted to control, allows to solve the optimal linear-quadratic control problem as well as to solve boundary value problems of variable coefficients with separated boundary conditions. (2) Ease of reading and modification, as the code is well documented. (3) Portability. The developed software has been run in two different platforms without additional changes in the code. This has been possible thanks to the use of standard numerical linear algebra libraries, such as BLAS, LAPACK, PBLAS and ScaLAPACK for computations, and Pthreads and MPI for communication and synchronization purposes. (4) Efficiency. All algorithms are block-oriented. This allows a more efficient use of the computer resources, specially the memory hierarchy. (5) Robustness. The methods used in the implementations guarantee their robustness. |
