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Deterministic optimal control, discussing Bellman dynamic programming method, Pontryagin maximum principle, orbital transfer, interplanetary guidance, etc
In this work, we introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical deformation and flow processes. The proposed framework utilizes a hypothesized coarse-graining methodology with manifold learning and surrogate-based optimization techniques. Coarse-grained high-dimensional data describing quantities of interest of the multiscale models are projected onto a nonlinear manifold whose geometric and topological structure is exploited for measuring behavioral discrepancies in the form of manifold distances. A surrogate model is constructed using Gaussian process regression to identify a mapping between stochastic parameters and distances. Derivative-free optimization is employed to adaptively identify a unique set of parameters of the upper-scale model capable of rapidly reproducing the system's behavior while maintaining consistency with coarse-grained atomic-level simulations. The proposed method is applied to learn the parameters of the shear transformation zone (STZ) theory of plasticity that describes plastic deformation in amorphous solids as well as coarse-graining parameters needed to translate between atomistic and continuum representations. We show that the methodology is able to successfully link coarse-grained microscale simulations to macroscale observables and achieve a high-level of parity between the models across scales.
We propose a dynamic sampling allocation and selection paradigm for finding the alternative with the optimal quantile in a Bayesian framework. Myopic allocation policies (MAPs), analogous to existing methods in classic ranking and selection for selecting the alternative with the optimal mean, and computationally efficient selection policies are derived for selecting the alternative with the optimal quantile. Under certain conditions, we prove that the proposed MAPs and selection procedures are consistent, which means that the best quantile would be eventually correctly selected as the sample size goes to infinity. Numerical experiments demonstrate that the proposed schemes can significantly improve the performance.
Optimal discrete control strategy for terminal guidance using computation procedure based on theory of dynamic programming
Computer program constructs a sequence of optimal solutions to dynamically-approximate linear equations. Specification of the number and type of subarcs in the optimal solution allows simultaneous satisfaction of all switching criteria.
A reduced-dynamic technique for precise orbit determination of low earth satellites is described. This technique optimally combines the conventional dynamic technique with the nondynamic technique which uses differential GPS continuous carrier phase to define the state transition. A Kalman filter formulation for this reduced-dynamic technique is given. A covariance analysis shows that when neither the dynamic nor the nondynamic technique is clearly superior, the reduced-dynamic technique appreciably improves the orbit accuracy. Guidelines for selecting a near-optimum weighting for the combination are given. Sensitivity to suboptimal weighting is assessed.
The third Air Force/NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization was held on 24-26 Sept. 1990. Sessions were on the following topics: dynamics and controls; multilevel optimization; sensitivity analysis; aerodynamic design software systems; optimization theory; analysis and design; shape optimization; vehicle components; structural optimization; aeroelasticity; artificial intelligence; multidisciplinary optimization; and composites.
The Kalman filter is the optimal filter in the presence of known gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions. Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz model as well as more realistic models of the means and atmosphere. A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter situations to allow for correct update of the ensemble members. The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to be quite puzzling in that results state estimates are worse than for their filter analogue. In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use the Lorenz model to test and compare the behavior of a variety of implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.
The Kalman filter is the optimal filter in the presence of known Gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions (e.g., Miller 1994). Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz (1963) model as well as more realistic models of the oceans (Evensen and van Leeuwen 1996) and atmosphere (Houtekamer and Mitchell 1998). A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter equations to allow for correct update of the ensemble members (Burgers 1998). The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to quite puzzling in that results of state estimate are worse than for their filter analogue (Evensen 1997). In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use Lorenz (1963) model to test and compare the behavior of a variety implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.
Computational Fluid Dynamics - Discrete Element Method is used to model gas-solid systems in several applications in energy, pharmaceutical and petrochemical industries. Computational performance bottlenecks often limit the problem sizes that can be simulated at industrial scale. The data structures used to store several millions of particles in such large-scale simulations have a large memory footprint that does not fit into the processor cache hierarchies on current high-performance-computing platforms, leading to reduced computational performance. This paper specifically addresses this aspect of memory access bottlenecks in industrial scale simulations. The use of space-filling curves to improve memory access patterns is described and their impact on computational performance is quantified in both shared and distributed memory parallelization paradigms. The Morton space filling curve applied to uniform grids and k-dimensional tree partitions are used to reorder the particle data-structure thus improving spatial and temporal locality in memory. The performance impact of these techniques when applied to two benchmark problems, namely the homogeneous-cooling-system and a fluidized-bed, are presented. We report these optimization techniques lead to approximately two-fold performance improvement in particle focused operations such as neighbor-list creation and data-exchange, with ~ 1.5 times overall improvement in a fluidization simulation with 1.27 million particles.
This paper presents a secure reinforcement learning (RL) based control method for unknown linear time-invariant cyber-physical systems (CPSs) that are subjected to compositional attacks such as eavesdropping and covert attack. We consider the attack scenario where the attacker learns about the dynamic model during the exploration phase of the learning conducted by the designer to learn a linear quadratic regulator (LQR), and thereafter, use such information to conduct a covert attack on the dynamic system, which we refer to as doubly learning-based control and attack (DLCA) framework. We propose a dynamic camouflaging based attack-resilient reinforcement learning (ARRL) algorithm which can learn the desired optimal controller for the dynamic system, and at the same time, can inject sufficient misinformation in the estimation of system dynamics by the attacker. The algorithm is accompanied by theoretical guarantees and extensive numerical experiments on a consensus multi-agent system and on a benchmark power grid model.
Here, we consider numerical approaches for deterministic, finite-dimensional optimal control problems whose dynamics depend on unknown or uncertain parameters. We seek to amortize the solution over a set of relevant parameters in an offline stage to enable rapid decision-making and be able to react to changes in the parameter in the online stage. To tackle the curse of dimensionality arising when the state and/or parameter are high-dimensional, we represent the policy using neural networks. We compare two training paradigms: First, our model-based approach leverages the dynamics and definition of the objective function to learn the value function of the parameterized optimal control problem and obtain the policy using a feedback form. Second, we use actor-critic reinforcement learning to approximate the policy in a data-driven way. Using an example involving a two-dimensional convection-diffusion equation, which features high-dimensional state and parameter spaces, we investigate the accuracy and efficiency of both training paradigms. While both paradigms lead to a reasonable approximation of the policy, the model-based approach is more accurate and considerably reduces the number of PDE solves.
This study focuses on optimizing solid oxide electrolysis cell (SOEC) systems for efficient and durable long-term hydrogen (H2) production. While the elevated operating temperatures of SOECs offer advantages in terms of efficiency, they also lead to chemical degradation, which shortens cell lifespan. To address this challenge, dynamic degradation models are coupled with a steady-state, two-dimensional, non-isothermal SOEC model and steady-state auxiliary balance of plant equipment models, within the IDAES modeling and optimization framework. A quasi-steady state approach is presented to reduce model size and computational complexity. Long-term dynamic simulations at constant H2 production rate illustrate the thermal effects of chemical degradation. Dynamic optimization is used to minimize the lifetime cost of H2 production, accounting for SOEC replacement, operating, and energy expenses. Several optimized operating profiles are compared by calculating the Levelized Cost of Hydrogen (LCOH).
This study focuses on optimizing solid oxide electrolysis cell (SOEC) systems for efficient and durable long-term hydrogen (H2) production. While the elevated operating temperatures of SOECs offer advantages in terms of efficiency, they also lead to chemical degradation, which shortens cell lifespan. To address this challenge, dynamic degradation models are coupled with a steady-state, two-dimensional, non-isothermal SOEC model and steady-state auxiliary balance of plant equipment models, within the IDAES modeling and optimization framework. A quasi-steady state approach is presented to reduce model size and computational complexity. Long-term dynamic simulations at constant H2 production rate illustrate the thermal effects of chemical degradation. Dynamic optimization is used to minimize the lifetime cost of H2 production, accounting for SOEC replacement, operating, and energy expenses. Several optimized operating profiles are compared by calculating the Levelized Cost of Hydrogen (LCOH).
The optimal design was investigated of simple structures subjected to dynamic loads, with constraints on the structures' responses. Optimal designs were examined for one dimensional structures excited by harmonically oscillating loads, similar structures excited by white noise, and a wing in the presence of continuous atmospheric turbulence. The first has constraints on the maximum allowable stress while the last two place bounds on the probability of failure of the structure. Approximations were made to replace the time parameter with a frequency parameter. For the first problem, this involved the steady state response, and in the remaining cases, power spectral techniques were employed to find the root mean square values of the responses. Optimal solutions were found by using computer algorithms which combined finite elements methods with optimization techniques based on mathematical programming. It was found that the inertial loads for these dynamic problems result in optimal structures that are radically different from those obtained for structures loaded statically by forces of comparable magnitude.
Scandium (Sc)-doped aluminum nitride (AlN) exhibits improved piezoelectric properties, which is favorable for sensor applications. Although many experimental studies exist to fine tune the material properties for design purposes, an atomistic level understanding of the structure-property (S-P) relationships is needed, which is the aim of this work. Molecular dynamics can be used to understand the S-P relationships. However, the limited availability of suitable force fields has been a major challenge for accurate property predictions. In this article, a robust force field calibration method using a scalable multi-objective Bayesian optimization approach is presented. Optimizations with three, six, and eight objectives are applied to calibrate aluminum scandium nitride force fields based on the piezoelectric characteristics, modulus of elasticity, and lattice parameters at different Sc-doped levels. Furthermore, the performances of the different force fields are compared, and the performance of the higher dimensional objective problems is discussed. The highly scalable molecular dynamics force field development method is successfully implemented, resulting in the creation of several aluminum scandium nitride molecular dynamics force fields for piezoelectric applications at varying Sc dope levels.
Developing the analytical model of a multibody system is often the initial step in control and optimization. The analytical model (equations of motion) describes a system’s time evolution under specified forcing conditions. Although developing these equations is easy for simple systems, this process becomes more complex for systems composed of multiple bodies. Deriving equations of motion for complex multibody systems requires specialized expertise in multibody dynamics, is time-consuming, and is susceptible to error. To address this issue, this paper presents an open-source, easy-to-use, systematic framework to derive symbolic equations of motion in both Python and MATLAB using the joint coordinate formulation. This formulation results in a set of ordinary differential equations that use the minimum set of coordinates needed to model a system. The symbolic representation provides better insight into the influence of design parameters on system performance, facilitates sensitivity analysis and parameter studies, and supports direct implementation of control and optimization routines. The tool enables numerical simulation for specified parameter sets, is modular for straightforward integration with other tools and libraries, and allows incorporation of hydrodynamics, mooring, and other external forces. The result is a reproducible, extensible pipeline for modeling, simulation, and design of complex multibody systems. The proposed tool is versatile and can be applied to domains such as robotics, control, and design. In addition, we integrated external libraries that provide capabilities for modeling offshore systems such as underwater robots and marine energy converters.