33 research outputs found
Research summary, January 1989 - June 1990
The Research Institute for Advanced Computer Science (RIACS) was established at NASA ARC in June of 1983. RIACS is privately operated by the Universities Space Research Association (USRA), a consortium of 62 universities with graduate programs in the aerospace sciences, under a Cooperative Agreement with NASA. RIACS serves as the representative of the USRA universities at ARC. This document reports our activities and accomplishments for the period 1 Jan. 1989 - 30 Jun. 1990. The following topics are covered: learning systems, networked systems, and parallel systems
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period April l, 1988 through September 30, 1988
Gradient Methods for Large-Scale and Distributed Linear Quadratic Control
This thesis considers methods for synthesis of linear quadratic controllers for large-scale, interconnected systems. Conventional methods that solve the linear quadratic control problem are only applicable to systems with moderate size, due to the rapid increase in both computational time and memory requirements as the system size increases. The methods presented in this thesis show a much slower increase in these requirements when faced with system matrices with a sparse structure. Hence, they are useful for control design for systems of large order, since they usually have sparse systems matrices. An equally important feature of the methods is that the controllers are restricted to have a distributed nature, meaning that they respect a potential interconnection structure of the system. The controllers considered in the thesis have the same structure as the centralized LQG solution, that is, they are consisting of a state predictor and feedback from the estimated states. Strategies for determining the feedback matrix and predictor matrix separately, are suggested. The strategies use gradient directions of the cost function to iteratively approach a locally optimal solution in either problem. A scheme to determine bounds on the degree of suboptimality of the partial solution in every iteration, is presented. It is also shown that these bounds can be combined to give a bound on the degree of suboptimality of the full output feedback controller. Another method that treats the synthesis of the feedback matrix and predictor matrix simultaneously is also presented. The functionality of the developed methods is illustrated by an application, where the methods are used to compute controllers for a large deformable mirror, found in a telescope to compensate for atmospheric disturbances. The model of the mirror is obtained by discretizing a partial differential equation. This gives a linear, sparse representation of the mirror with a very large state space, which is suitable for the methods presented in the thesis. The performance of the controllers is evaluated using performance measures from the adaptive optics community
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
Cumulative reports and publications through December 31, 1990
This document contains a complete list of ICASE reports. Since ICASE reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available
Custom optimization algorithms for efficient hardware implementation
The focus is on real-time optimal decision making with application in advanced control
systems. These computationally intensive schemes, which involve the repeated solution of
(convex) optimization problems within a sampling interval, require more efficient computational
methods than currently available for extending their application to highly dynamical
systems and setups with resource-constrained embedded computing platforms.
A range of techniques are proposed to exploit synergies between digital hardware, numerical
analysis and algorithm design. These techniques build on top of parameterisable
hardware code generation tools that generate VHDL code describing custom computing
architectures for interior-point methods and a range of first-order constrained optimization
methods. Since memory limitations are often important in embedded implementations we
develop a custom storage scheme for KKT matrices arising in interior-point methods for
control, which reduces memory requirements significantly and prevents I/O bandwidth
limitations from affecting the performance in our implementations. To take advantage of
the trend towards parallel computing architectures and to exploit the special characteristics
of our custom architectures we propose several high-level parallel optimal control
schemes that can reduce computation time. A novel optimization formulation was devised
for reducing the computational effort in solving certain problems independent of the computing
platform used. In order to be able to solve optimization problems in fixed-point
arithmetic, which is significantly more resource-efficient than floating-point, tailored linear
algebra algorithms were developed for solving the linear systems that form the computational
bottleneck in many optimization methods. These methods come with guarantees
for reliable operation. We also provide finite-precision error analysis for fixed-point implementations
of first-order methods that can be used to minimize the use of resources while
meeting accuracy specifications. The suggested techniques are demonstrated on several
practical examples, including a hardware-in-the-loop setup for optimization-based control
of a large airliner.Open Acces
Proceedings of the 3rd Annual Conference on Aerospace Computational Control, volume 1
Conference topics included definition of tool requirements, advanced multibody component representation descriptions, model reduction, parallel computation, real time simulation, control design and analysis software, user interface issues, testing and verification, and applications to spacecraft, robotics, and aircraft
Proceedings of the Fifth NASA/NSF/DOD Workshop on Aerospace Computational Control
The Fifth Annual Workshop on Aerospace Computational Control was one in a series of workshops sponsored by NASA, NSF, and the DOD. The purpose of these workshops is to address computational issues in the analysis, design, and testing of flexible multibody control systems for aerospace applications. The intention in holding these workshops is to bring together users, researchers, and developers of computational tools in aerospace systems (spacecraft, space robotics, aerospace transportation vehicles, etc.) for the purpose of exchanging ideas on the state of the art in computational tools and techniques
Fast Numerical and Machine Learning Algorithms for Spatial Audio Reproduction
Audio reproduction technologies have underwent several revolutions from a purely mechanical, to electromagnetic, and into a digital process. These changes have resulted in steady improvements in the objective qualities of sound capture/playback on increasingly portable devices. However, most mobile playback devices remove important spatial-directional components of externalized sound which are natural to the subjective experience of human hearing. Fortunately, the missing spatial-directional parts can be integrated back into audio through a combination of computational methods and physical knowledge of how sound scatters off of the listener's anthropometry in the sound-field. The former employs signal processing techniques for rendering the sound-field. The latter employs approximations of the sound-field through the measurement of so-called Head-Related Impulse Responses/Transfer Functions (HRIRs/HRTFs).
This dissertation develops several numerical and machine learning algorithms for accelerating and personalizing spatial audio reproduction in light of available mobile computing power. First, spatial audio synthesis between a sound-source and sound-field requires fast convolution algorithms between the audio-stream and the HRIRs. We introduce a novel sparse decomposition algorithm for HRIRs based on non-negative matrix factorization that allows for faster time-domain convolution than frequency-domain fast-Fourier-transform variants. Second, the full sound-field over the spherical coordinate domain must be efficiently approximated from a finite collection of HRTFs. We develop a joint spatial-frequency covariance model for Gaussian process regression (GPR) and sparse-GPR methods that supports the fast interpolation and data fusion of HRTFs across multiple data-sets. Third, the direct measurement of HRTFs requires specialized equipment that is unsuited for widespread acquisition. We ``bootstrap'' the human ability to localize sound in listening tests with Gaussian process active-learning techniques over graphical user interfaces that allows the listener to infer his/her own HRTFs. Experiments are conducted on publicly available HRTF datasets and human listeners
Fourth NASA Workshop on Computational Control of Flexible Aerospace Systems, part 1
The proceedings of the workshop are presented. Some areas of discussion are as follows: modeling, systems identification, and control of flexible aircraft, spacecraft, and robotic systems