We study several aspects of the dynamic programming approach to optimal control of abstract evolution equations, including a class of semilinear partial di erential equations. We introduce and prove a veri cation theorem which provides a su cient condition for optimality. Moreover we prove suband superoptimality principles of dynamic programming and present an explicit construction of -optimal ...

We describe herein the parallel implementation of the Bi-CGSTAB method with a block Red-Black Gauss-Seidel (RBGS) preconditioner applied to the systems of linear algebraic equations that arise from the Hermite collocation discretization of partial di erential equations in two spatial dimensions. The method is implemented on the Cray T3E, a parallel processing supercomputer. Speedup results are ...

For linear di erential algebraic equations of tractability index 1 the notion of the adjoint equation is analysed in full detail. Its solvability is shown at the lowest possible smoothness. The fundamental matrices of both equations are de ned and their relationships are characterized.

We present an algorithm for the solution of a nontrivial coupled system of algebraic Riccati equations appearing in risk sensitive control problems. Moreover we use comparison methods to derive non blow up conditions for the solutions of a corresponding terminal value problem for coupled systems of Riccati di erential equations.

In this paper we present some results about analytic machines regarding the power of computations over Q or R solutions of di erential equations and the stability problem of dynamical systems We rst explain the machine model which is a kind of Blum Shub Smale machine enhanced by in nite convergent computations Next we com pare the computational power of such machines over the elds Q and R showi...

In this paper we present a new symbolic approach to hybrid systems Hybrid systems are systems con taining both continuous and discrete changing quantities We model hybrid systems using hybrid automata Hybrid automata extend the classical notion of nite state machines by combining di erential equations to model the dynamic behavior of systems with a nite control In contrast to other approaches w...

This paper reviews the formulation and application of optimization techniques based on control theory for aerodynamic shape design in both inviscid and viscous compressible ow. The theory is applied to a system de ned by the partial di erential equations of the ow, with the boundary shape acting as the control. The Frechet derivative of the cost function is determined via the solution of an adj...

In this paper we review and further develop a class of strong-stability preserving (SSP) high-order time discretizations for semi-discrete method-of-lines approximations of partial di erential equations. Termed TVD (total variation diminishing) time discretizations before, this class of high-order time discretization methods preserves the strong-stability properties of rst-order Euler time step...

In this paper we consider the pair di usion process in more than two spatial dimensions. In this case we are able to prove just a local existence result, since it is not possible to deduce global a priori estimates for the equations as it can be done in the two dimensional case. The model includes a nonlinear system of reaction{ drift{di usion equations, a nonlinear ordinary di erential equatio...

On the background of a careful analysis of linear DAEs, linearizations of nonlinear index2 systems are considered. Finding appropriate function spaces and their topologies allows to apply the standard Implicit Function Theorem again. Both, solvability statements as well as the local convergence of the Newton-Kantorovich method (quasilinearization) result immediately. In particular, this applies...