650 research outputs found
Robust Mission Design Through Evidence Theory and Multi-Agent Collaborative Search
In this paper, the preliminary design of a space mission is approached
introducing uncertainties on the design parameters and formulating the
resulting reliable design problem as a multiobjective optimization problem.
Uncertainties are modelled through evidence theory and the belief, or
credibility, in the successful achievement of mission goals is maximised along
with the reliability of constraint satisfaction. The multiobjective
optimisation problem is solved through a novel algorithm based on the
collaboration of a population of agents in search for the set of highly
reliable solutions. Two typical problems in mission analysis are used to
illustrate the proposed methodology
Recommended from our members
Numerical Techniques for Optimization Problems with PDE Constraints
The development, analysis and implementation of eļ¬cient and robust numerical techniques for optimization problems associated with partial diļ¬erential equations (PDEs) is of utmost importance for the optimal control of processes and the optimal design of structures and systems in modern technology. The successful realization of such techniques invokes a wide variety of challenging mathematical tasks and thus requires the application of adequate methodologies from various mathematical disciplines. During recent years, signiļ¬cant progress has been made in PDE constrained optimization both concerning optimization in function space according to the paradigm āOptimize ļ¬rst, then discretizeā and with regard to the fast and reliable solution of the large-scale problems that typically arise from discretizations of the optimality conditions. The contributions at this Oberwolfach workshop impressively reļ¬ected the progress made in the ļ¬eld. In particular, new insights have been gained in the analysis of optimal control problems for PDEs that have led to vastly improved numerical solution methods. Likewise, breakthroughs have been made in the optimal design of structures and systems, for instance, by the socalled āall-at-onceā approach featuring simultaneous optimization and solution of the underlying PDEs. Finally, new methodologies have been developed for the design of innovative materials and the identiļ¬cation of parameters in multi-scale physical and physiological processes
Multiobjective Optimization of Non-Smooth PDE-Constrained Problems
Multiobjective optimization plays an increasingly important role in modern
applications, where several criteria are often of equal importance. The task in
multiobjective optimization and multiobjective optimal control is therefore to
compute the set of optimal compromises (the Pareto set) between the conflicting
objectives. The advances in algorithms and the increasing interest in
Pareto-optimal solutions have led to a wide range of new applications related
to optimal and feedback control - potentially with non-smoothness both on the
level of the objectives or in the system dynamics. This results in new
challenges such as dealing with expensive models (e.g., governed by partial
differential equations (PDEs)) and developing dedicated algorithms handling the
non-smoothness. Since in contrast to single-objective optimization, the Pareto
set generally consists of an infinite number of solutions, the computational
effort can quickly become challenging, which is particularly problematic when
the objectives are costly to evaluate or when a solution has to be presented
very quickly. This article gives an overview of recent developments in the
field of multiobjective optimization of non-smooth PDE-constrained problems. In
particular we report on the advances achieved within Project 2 "Multiobjective
Optimization of Non-Smooth PDE-Constrained Problems - Switches, State
Constraints and Model Order Reduction" of the DFG Priority Programm 1962
"Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation
and Hierarchical Optimization"
Recommended from our members
Numerical Methods for PDE Constrained Optimization with Uncertain Data
Optimization problems governed by partial differential equations (PDEs) arise in many applications in the form of optimal control, optimal design, or parameter identification problems. In most applications, parameters in the governing PDEs are not deterministic, but rather have to be modeled as random variables or, more generally, as random fields. It is crucial to capture and quantify the uncertainty in such problems rather than to simply replace the uncertain coefficients with their mean values. However, treating the uncertainty adequately and in a computationally tractable manner poses many mathematical challenges. The numerical solution of optimization problems governed by stochastic PDEs builds on mathematical subareas, which so far have been largely investigated in separate communities: Stochastic Programming, Numerical Solution of Stochastic PDEs, and PDE Constrained Optimization.
The workshop achieved an impulse towards cross-fertilization of those disciplines which also was the subject of several scientific discussions. It is to be expected that future exchange of ideas between these areas will give rise to new insights and powerful new numerical methods
An efficient method for multiobjective optimal control and optimal control subject to integral constraints
We introduce a new and efficient numerical method for multicriterion optimal
control and single criterion optimal control under integral constraints. The
approach is based on extending the state space to include information on a
"budget" remaining to satisfy each constraint; the augmented
Hamilton-Jacobi-Bellman PDE is then solved numerically. The efficiency of our
approach hinges on the causality in that PDE, i.e., the monotonicity of
characteristic curves in one of the newly added dimensions. A semi-Lagrangian
"marching" method is used to approximate the discontinuous viscosity solution
efficiently. We compare this to a recently introduced "weighted sum" based
algorithm for the same problem. We illustrate our method using examples from
flight path planning and robotic navigation in the presence of friendly and
adversarial observers.Comment: The final version accepted by J. Comp. Math. : 41 pages, 14 figures.
Since the previous version: typos fixed, formatting improved, one mistake in
bibliography correcte
International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book
The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions.
This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more
Optimization based control design techniques for distributed parameter systems
The study presents optimization based control design techniques for the systems that are governed by partial differential equations. A control technique is developed for systems that are actuated at the boundary. The principles of dynamic inversion and constrained optimization theory are used to formulate a feedback controller. This control technique is demonstrated for heat equations and thermal convection loops. This technique is extended to address a practical issue of parameter uncertainty in a class of systems. An estimator is defined for unknown parameters in the system. The Lyapunov stability theory is used to derive an update law of these parameters. The estimator is used to design an adaptive controller for the system. A second control technique is presented for a class of second order systems that are actuated in-domain. The technique of proper orthogonal decomposition is used first to develop an approximate model. This model is then used to design optimal feedback controller. Approximate dynamic programming based neural network architecture is used to synthesize a sub-optimal controller. This control technique is demonstrated to stabilize the heave dynamics of a flexible aircraft wings. The third technique is focused on the optimal control of stationary thermally convected fluid flows from the numerical point of view. To overcome the computational requirement, optimization is carried out using reduced order model. The technique of proper orthogonal decomposition is used to develop reduced order model. An example of chemical vapor deposition reactor is considered to examine this control technique --Abstract, page iii
Optimality conditions for differential system of Petrowsky type with infinite number of variables and boundary control
AbstractIn this paper, we study the optimal control problem for an nĆn coupled Petrowsky type system involving a 2ā-th order self-adjoint elliptic operator with an infinite number of variables and constrained boundary control acting through Neumann conditions. Also, we derived the necessary and sufficient conditions of optimality for two types of performance index (quadratic one, general integral form).By using standard Lionsās arguments [J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, vol. 170, Springer-Verlag, 1971] we proved the existence of a solution to the nĆn coupled Petrowsky system and we derived optimality conditions for the optimal control problem with a quadratic performance index. In the case of the general integral form of the performance index we applied DubovitskiiāMilyutinās formalism earlier used in Kotarski [W. Kotarski, Some problems of optimal and pareto optimal control for distributed parameter systems, Reports of Silesian University Katowice, Poland, 1997, no.Ā 1668]. Finally, we provided some special cases
Fiscal Policy Coordination within a Monetary Union in the Presence of Risk Premia
This paper extends the differential game analysis of Engwerda et al (2002)on the interaction between fiscal stabilisation policies in a two-country monetary union. It considers the effect on the behaviour of authorities when there are country and/or union risk premia that depend on the fiscal position of both countries in the monetary union. These effects are discussed in the context of a monetary authority adopting a fixed rate and a Taylor rule, respectively, for its monetary policy. Noncooperative open-loop Nash equilibria and Pareto equilibria are computed numerically for these cases and their adjustment dynamics compared
- ā¦