A comparison of general-purpose optimization algorithms forfinding optimal approximate experimental designs

Several common general purpose optimization algorithms are compared for findingA- and D-optimal designs for different types of statistical models of varying complexity,including high dimensional models with five and more factors. The algorithms of interestinclude exact methods, such as the interior point method, the Nelder–Mead method, theactive set method, the sequential quadratic programming, and metaheuristic algorithms,such as particle swarm optimization, simulated annealing and genetic algorithms.Several simulations are performed, which provide general recommendations on theutility and performance of each method, including hybridized versions of metaheuristicalgorithms for finding optimal experimental designs. A key result is that general-purposeoptimization algorithms, both exact methods and metaheuristic algorithms, perform wellfor finding optimal approximate experimental designs

Multi-Agent Orbit Design For Perception Enhancement Purpose

This paper develops a robust optimization based method to design orbits on which the sensory perception of the desired physical quantities are maximized. It also demonstrates how to incorporate various constraints imposed by many spacecraft missions such as collision avoidance, co-orbital configuration, altitude and frozen orbit constraints along with Sun-Synchronous orbit. The paper specifically investigates designing orbits for constrained visual sensor planning applications as the case study. For this purpose, the key elements to form an image in such vision systems are considered and effective factors are taken into account to define a metric for perception quality. The simulation results confirm the effectiveness of the proposed method for several scenarios on low and medium Earth orbits as well as a challenging Space-Based Space Surveillance program application.Comment: 12 pages, 18 figure

High performance implementation of MPC schemes for fast systems

In recent years, the number of applications of model predictive control (MPC) is rapidly increasing due to the better control performance that it provides in comparison to traditional control methods. However, the main limitation of MPC is the computational e ort required for the online solution of an optimization problem. This shortcoming restricts the use of MPC for real-time control of dynamic systems with high sampling rates. This thesis aims to overcome this limitation by implementing high-performance MPC solvers for real-time control of fast systems. Hence, one of the objectives of this work is to take the advantage of the particular mathematical structures that MPC schemes exhibit and use parallel computing to improve the computational e ciency. Firstly, this thesis focuses on implementing e cient parallel solvers for linear MPC (LMPC) problems, which are described by block-structured quadratic programming (QP) problems. Speci cally, three parallel solvers are implemented: a primal-dual interior-point method with Schur-complement decomposition, a quasi-Newton method for solving the dual problem, and the operator splitting method based on the alternating direction method of multipliers (ADMM). The implementation of all these solvers is based on C++. The software package Eigen is used to implement the linear algebra operations. The Open Message Passing Interface (Open MPI) library is used for the communication between processors. Four case-studies are presented to demonstrate the potential of the implementation. Hence, the implemented solvers have shown high performance for tackling large-scale LMPC problems by providing the solutions in computation times below milliseconds. Secondly, the thesis addresses the solution of nonlinear MPC (NMPC) problems, which are described by general optimal control problems (OCPs). More precisely, implementations are done for the combined multiple-shooting and collocation (CMSC) method using a parallelization scheme. The CMSC method transforms the OCP into a nonlinear optimization problem (NLP) and de nes a set of underlying sub-problems for computing the sensitivities and discretized state values within the NLP solver. These underlying sub-problems are decoupled on the variables and thus, are solved in parallel. For the implementation, the software package IPOPT is used to solve the resulting NLP problems. The parallel solution of the sub-problems is performed based on MPI and Eigen. The computational performance of the parallel CMSC solver is tested using case studies for both OCPs and NMPC showing very promising results. Finally, applications to autonomous navigation for the SUMMIT robot are presented. Specially, reference tracking and obstacle avoidance problems are addressed using an NMPC approach. Both simulation and experimental results are presented and compared to a previous work on the SUMMIT, showing a much better computational e ciency and control performance.Tesi

Optimization techniques for tree-structured nonlinear problems

Robust model predictive control approaches and other applications lead to nonlinear optimization problems defined on (scenario) trees. We present structure-preserving Quasi-Newton update formulas as well as structured inertia correction techniques that allow to solve these problems by interior-point methods with specialized KKT solvers for tree-structured optimization problems. The same type of KKT solvers could be used in active-set based SQP methods. The viability of our approach is demonstrated by two robust control problems

An elastic primal active-set method for structured QPs

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Improved gradient-based algorithm for solving aeroassisted vehicle trajectory optimization problems

Space maneuver vehicles (SMVs) [1,2] will play an increasingly important role in the future exploration of space because their on-orbit maneuverability can greatly increase the operational flexibility, and they are more difficult as a target to be tracked and intercepted. Therefore, a well-designed trajectory, particularly in the skip entry phase, is a key for stable flight and for improved guidance control of the vehicle [3,4]. Trajectory design for space vehicles can be treated as an optimal control problem. Because of the highly nonlinear characteristics and strict path constraints of the problem, direct methods are usually applied to calculate the optimal trajectories, such as the direct multiple shooting method [5], direct collocation method [5,6], or hp hp -adaptive pseudospectral method [7,8]

Distributed algorithms for nonlinear tree-sparse problems

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