The aim of this Paper is to propose a method for constructing worst-case disturbances to analyze the performance of linear time-varying systems on a finite time horizon. This is primarily motivated by the goal of anal...
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The aim of this Paper is to propose a method for constructing worst-case disturbances to analyze the performance of linear time-varying systems on a finite time horizon. This is primarily motivated by the goal of analyzing flexible aircraft, which are more realistically described as time-varying systems, but the same framework can be applied to other fields in which this feature is relevant. The performance is defined by means of a generic quadratic cost function, and the main result consists of a numerical algorithm to compute the worst-case signal verifying that a given performance objective is not achieved. The developed algorithm employs the solution to a Riccati differential equation associated with the cost function. Theoretically, the signal can also be obtained by simulating the related Hamiltonian dynamics, but this does not represent a numerically reliable strategy, as commented in the Paper. The applicability of the approach is demonstrated with a case study consisting of a flexible aircraft subject to gust during a flight-test maneuver.
A simplified axisymmetric lattice Boltzmann method (SALBM) is developed in this paper for effective simulation of incompressible swirling and rotating flows. This model explores an alternative approach of reconstructi...
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A simplified axisymmetric lattice Boltzmann method (SALBM) is developed in this paper for effective simulation of incompressible swirling and rotating flows. This model explores an alternative approach of reconstructing an axisymmetric model within the lattice Boltzmann (LB) framework. Essentially, SALBM reconstructs solutions to the macroscopic governing equations recovered from the axisymmetric LB equation through the Chapman-Enskog expansion analysis. Two variations of schemes, which bear different orders of temporal accuracy and are, respectively, suitable for the steady and the unsteady axisymmetric flow problems, can be evolved from SALBM. The proposed schemes reflect direct evolution of macroscopic variables instead of distribution functions, which could reduce the cost in virtual memory. Meanwhile, analytical interpretation of physical boundary conditions is available in SALBM which avoids tedious transformations as required in conventional LB models. numerical tests further reveal that SALBM performs better than the existing axisymmetric LB models in numerical stability. These merits endow the present SALBM with advantages over previous models and forge its prospect in engineering applications. Published under license by AIP Publishing.
The work done on probability of collision between spherical objects in orbit is extended here to the case of one spherical object and one circular or rectangular object. The former is a model for spacecraft or debris,...
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The work done on probability of collision between spherical objects in orbit is extended here to the case of one spherical object and one circular or rectangular object. The former is a model for spacecraft or debris, whereas the latter is a model for a sail or a tether. Two kinds of computations are done. The first kind is the computation of the collision rate when the flux of one object (typically debris) with respect to the other object is known. This information is important when planning a mission. The second kind is the computation of the collision probability for a particular pair of objects whose probability density functions of the positions are known. This information is necessary to decide whether an evasive maneuver will be performed or not.
Path-integral-based molecular dynamics (MD) simulations are widely used for the calculation of numerically exact quantum Boltzmann properties and approximate dynamical quantities. A nearly universal feature of MD nume...
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Path-integral-based molecular dynamics (MD) simulations are widely used for the calculation of numerically exact quantum Boltzmann properties and approximate dynamical quantities. A nearly universal feature of MD numerical integration schemes for equations of motion based on imaginary-time path integrals is the use of harmonic normal modes for the exact evolution of the free ring-polymer positions and momenta. In this work, we demonstrate that this standard practice creates numerical artifacts. In the context of conservative (i.e., microcanonical) equations of motion, it leads to numerical instability. In the context of thermostated (i.e., canonical) equations of motion, it leads to nonergodicity of the sampling. These pathologies are generally proven to arise at integration time steps that depend only on the system temperature and the number of ring-polymer beads, and they are numerically demonstrated for the cases of conventional ring-polymer MD (RPMD) and thermostated RPMD (TRPMD). Furthermore, it is demonstrated that these numerical artifacts are removed via replacement of the exact free ring-polymer evolution with a second-order approximation based on the Cayley transform. The Cayley modification introduced here can immediately be employed with almost every existing integration scheme for path-integral-based MD-including path-integral MD (PIMD), RPMD, TRPMD, and centroid MD-providing strong symplectic stability and ergodicity to the numerical integration, at no penalty in terms of computational cost, algorithmic complexity, or accuracy of the overall MD time step. Furthermore, it is shown that the improved numerical stability of the Cayley modification allows for the use of larger MD time steps. We suspect that the Cayley modification will therefore find useful application in many future path-integral-based MD simulations.
The recently established methodology to use known algorithmic expressions of the second moments of the stress field in the grains of a polycrystalline aggregate for calculating average fluctuations of lattice rotation...
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The recently established methodology to use known algorithmic expressions of the second moments of the stress field in the grains of a polycrystalline aggregate for calculating average fluctuations of lattice rotation rates and the associated average intragranular misorientation distributions using the mean-field viscoplastic self-consistent (VPSC) formulation is extended to solve the coupled problem of considering the effect of intragranular misorientations on stress and rotation rate fluctuations. In turn, these coupled expressions are used to formulate and implement a grain fragmentation (GF) model in VPSC. Case studies, including tension and plane-strain compression of face-centered cubic polycrystals are used to illustrate the capabilities of the new model. GF-VPSC predictions of intragranular misorientation distributions and texture evolution are compared with experiments and full-field numerical simulations, showing good agreement. In particular, the inclusion of misorientation spreads reduced the intensity of the deformed texture and thus improved the texture predictions. Moreover, considering that intragranular misorientations act as driving forces for recrystallization, the new GF-VPSC formulation is shown to enable modeling of microstructure evolution during deformation and recrystallization, in a computationally efficient manner.
When applying model reference control to a non-minimum phase (NMP) plant, it is important to include the NMP (transmission) zero(s) in the reference model, otherwise the controller will tend to cancel out these zeros,...
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When applying model reference control to a non-minimum phase (NMP) plant, it is important to include the NMP (transmission) zero(s) in the reference model, otherwise the controller will tend to cancel out these zeros, often causing loss of internal stability. In data-driven (DD) control it is not possible to conceive a priori a reference model with the NMP zero(s) because no model of the plant is available;accordingly, DD design methods tend to fail in NMP plants. For single-input-single-output plants, this problem has been solved by using a flexible reference model in a DD design. This letter presents an extension of that method for multi-input-multi-output plants.
Model predictive control (MPC) often requires solving an optimal control structured quadratic program (QP), possibly based on an online linearization at each sampling instant. Block-tridiagonal preconditioners have be...
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In recent years, a family of numerical algorithms to solve problems in real algebraic and semialgebraic geometry has been slowly growing. Unlike their counterparts in symbolic computation they are numerically stable. ...
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In recent years, a family of numerical algorithms to solve problems in real algebraic and semialgebraic geometry has been slowly growing. Unlike their counterparts in symbolic computation they are numerically stable. But their complexity analysis, based on the condition of the data, is radically different from the usual complexity analysis in symbolic computation as these numerical algorithms may run forever on a thin set of ill-posed inputs.
In this letter we propose an algorithm for solving constrained polynomial minimization problems. The algorithm is a variation on the random coordinate descent, in which transverse steps are sometimes taken. Differentl...
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In this letter we propose an algorithm for solving constrained polynomial minimization problems. The algorithm is a variation on the random coordinate descent, in which transverse steps are sometimes taken. Differently from other methods, the proposed technique is guaranteed to converge in probability to the global solution of the minimization problem, even when the objective polynomial is nonconvex. The technique appears to be promising for tackling nonlinear control problems in which the standard sum-of-squares methods may fail due to the problem size. The theoretical results are corroborated by numerical tests that validate the efficiency of the method.
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