Modeling, Analysis, and Optimization Issues for Large Space Structures

Topics concerning the modeling, analysis, and optimization of large space structures are discussed including structure-control interaction, structural and structural dynamics modeling, thermal analysis, testing, and design

Finite Elements with Switched Detection for Direct Optimal Control of Nonsmooth Systems with Set-Valued Step Functions

This paper extends the Finite Elements with Switch Detection (FESD) method [Nurkanovi\'c et al., 2022] to optimal control problems with nonsmooth systems involving set-valued step functions. Logical relations and common nonsmooth functions within a dynamical system can be expressed using linear and nonlinear expressions of the components of the step function. A prominent subclass of these systems are Filippov systems. The set-valued step function can be expressed by the solution map of a linear program, and using its KKT conditions allows one to transform the initial system into an equivalent dynamic complementarity system (DCS). Standard Runge-Kutta (RK) methods applied to DCS have only first-order accuracy. The FESD discretization makes the step sizes degrees of freedom and adds further constraints that ensure exact switch detection to recover the high-accuracy properties that RK methods have for smooth ODEs. All methods and examples in this paper are implemented in the open-source software package NOSNOC.Comment: submitted to CDC202

Steady-state initialization of object-oriented thermo-fluid models by homotopy methods

The steady-state initialization of large object-oriented thermo-hydraulic networks is a difficult problem, because of the sensitivity of the convergence to the initial guesses of the iteration variables. This paper proposes an approach to this problem based on homotopy transformation, detailing specific criteria for model simplifications in this physical domain. The approach is successfully demonstrated on large power plant test cases, having several hundreds of iteration variables

POLSYS GLP: A Parallel General Linear Product Homotopy Code for Solving Polynomial Systems of Equations

Globally convergent, probability-one homotopy methods have proven to be very effective for finding all the isolated solutions to polynomial systems of equations. After many years of development, homotopy path trackers based on probability-one homotopy methods are reliable and fast. Now, theoretical advances reducing the number of homotopy paths that must be tracked, and in the handling of singular solutions, have made probability-one homotopy methods even more practical. POLSYS GLP consists of Fortran 95 modules for nding all isolated solutions of a complex coefficient polynomial system of equations. The package is intended to be used on a distributed memory multiprocessor in conjunction with HOMPACK90 (Algorithm 777), and makes extensive use of Fortran 95 derived data types and MPI to support a general linear product (GLP) polynomial system structure. GLP structure is intermediate between the partitioned linear product structure used by POLSYS PLP (Algorithm 801) and the BKK-based structure used by PHCPACK. The code requires a GLP structure as input, and although nding the optimal GLP structure is a dicult combinatorial problem, generally physical or engineering intuition about a problem yields a very good GLP structure. POLSYS GLP employs a sophisticated power series end game for handling singular solutions, and provides support for problem denition both at a high level and via hand-crafted code. Dierent GLP structures and their corresponding Bezout numbers can be systematically explored before committing to root finding