The need for unified notation in atmospheric and oceanic data assimilation arises from the field's rapid theoretical expansion and the desire to translate it into practical applications. Self-consistent notation is proposed that bridges sequential and variational methods, on the one hand, and operational usage, on the other. Over various other mottoes for this risky endeavor, the authors selected: "When I use a word," Humpty Dumpty said, in rather a scornful voice tone, "it means just what I choose it to mean --- neither more nor less." Lewis Carroll, 1871. 1 J. Met. Soc. Japan, Special Issue on "Data Assimilation in Meteorology and Oceanography: Theory and Practice." Vol. 75, No. 1B, pp. 181--189, 1997. 2 Corresponding author. 3 Current affiliation: CNES, 2, place Maurice Quentin, 75039 Paris Cedex 01, France. 1 J. Met. Soc. Japan, (1997), K. Ide, P. Courtier, M. Ghil and A.C. Lorenc 2 1. Introduction and motivation Model-based assimilation of observations, or data assimilati...

We describe a novel method for controlling physics-based fluid simulations through gradient-based nonlinear optimization. Using a technique known as the adjoint method, derivatives can be computed efficiently, even for large 3D simulations with millions of control parameters. In addition, we introduce the first method for the full control of free-surface liquids. We show how to compute adjoint derivatives through each step of the simulation, including the fast marching algorithm, and describe a new set of control parameters specifically designed for liquids.

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We consider damped second order in time systems such as those arising in structures with piezoceramic actuators and sensors. These systems are naturally formulated as abstract second order systems with unbounded nonhomogeneous term. Existence, uniqueness and continuous dependence of solutions in a weak or variational setting are given. A semigroup formulation is presented and conditions under which the variational solutions and semigroup solutions are the same are discussed.

. We provide an effective and efficient implementation of a sequential quadratic programming (SQP) algorithm for the general large scale nonlinear programming problem. In this algorithm the quadratic programming subproblems are solved by an interior point method that can be prematurely halted by a trust region constraint. Numerous computational enhancements to improve the numerical performance are presented. These include a dynamic procedure for adjusting the merit function parameter and procedures for adjusting the trust region radius. Numerical results and comparisons are presented. Key words: nonlinear programming, interior point, SQP, merit function, trust region, large scale 1. Introduction. In a series of recent papers, [3], [6], and [8], the authors have developed a new algorithmic approach for solving large, nonlinear, constrained optimization problems. This proposed procedure is, in essence, a sequential quadratic programming (SQP) method that uses an interior point algorithm...

Abstract—We consider distributed parameter systems where the underlying dynamics are spatially invariant, and where the controls and measurements are spatially distributed. These systems arise in many applications such as the control of vehicular platoons, flow control, microelectromechanical systems (MEMS), smart structures, and systems described by partial differential equations with constant coefficients and distributed controls and measurements. For fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator (LQR), P and, optimal controllers can be obtained by solving a parameterized family of standard finite-dimensional problems. We show that optimal controllers have an inherent degree of decentralization, and this provides a practical distributed controller architecture. We also prove a general result that applies to partially distributed control and a variety of performance criteria, stating that optimal controllers inherit the spatial invariance structure of the plant. Connections of this work to that on systems over rings, and systems with dynamical symmetries are discussed. Index Terms—Distributed control, infinite-dimensional systems, optimal control, robust control, spatially invariant systems.

This paper presents a number of algorithm developments for adjoint methods using the `discrete' approach in which the discretisation of the nonlinear equations is linearised and the resulting matrix is then transposed

this paper addresses the validity of this design methodology for the problem of high-lift design. Traditionally, high-lift designs have been realized by careful wind tunnel testing. This approach is both expensive and challenging due to the extremely complex nature of the flow interactions that appear. CFD analyses have recently been incorporated to the high-lift design process

We consider multi-grid, or more appropriately, multi-level techniques for the numerical solution of operator Lyapunov and algebraic Riccati equations. The Riccati equation, which is quadratic, plays an essential role in the solution of linear-quadratic optimal control problems. The linear Lyapunov equation is important in the stability theory for linear systems and its solution is the primary step in the Newton-Kleinman algorithm for the solution of algebraic Riccati equations. Both equations are operator equations when the underlying linear system is infinite dimensional. In this case, finite dimensional discretization is required. However, as the level of discretization increases, the convergence rate of the standard iterative techniques for solving high order matrix Lyapunov and Riccati equations decreases. To deal with this, multi-leveling is introduced into the iterative Newton-Kleinman method for solving the algebraic Riccati equation, and Smith's method for solving matrix Lyapun...

In this paper we exploit a novel idea for the optimization of flows governed by the Euler equations. The algorithm consists of marching on the design hypersurface while improving the distance to the state and costate hypersurfaces. We consider the problem of matching the pressure distribution to adesired one, subject to the Euler equations, both for subsonic and supersonic flows. The rate of convergence to the minimum for the cases considered is 3 to 4 times slower than that of the analysis problem. Results are given for Ringleb flow and a shockless recompression case.