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NASA NTRS1992

A reliable algorithm for optimal control synthesis

In recent years, powerful design tools for linear time-invariant multivariable control systems have been developed based on direct parameter optimization. In this report, an algorithm for reliable optimal control synthesis using parameter optimization is presented. Specifically, a robust numerical algorithm is developed for the evaluation of the H(sup 2)-like cost functional and its gradients with respect to the controller design parameters. The method is specifically designed to handle defective degenerate systems and is based on the well-known Pade series approximation of the matrix exponential. Numerical test problems in control synthesis for simple mechanical systems and for a flexible structure with densely packed modes illustrate positively the reliability of this method when compared to a method based on diagonalization. Several types of cost functions have been considered: a cost function for robust control consisting of a linear combination of quadratic objectives for deterministic and random disturbances, and one representing an upper bound on the quadratic objective for worst case initial conditions. Finally, a framework for multivariable control synthesis has been developed combining the concept of closed-loop transfer recovery with numerical parameter optimization. The procedure enables designers to synthesize not only observer-based controllers but also controllers of arbitrary order and structure. Numerical design solutions rely heavily on the robust algorithm due to the high order of the synthesis model and the presence of near-overlapping modes. The design approach is successfully applied to the design of a high-bandwidth control system for a rotorcraft.

Vansteenwyk, Brett↗

NASA NTRS2002

A Nonlinear, Human-Centered Approach to Motion Cueing with a Neurocomputing Solver

This paper discusses the continuation of research into the development of new motion cueing algorithms first reported in 1999. In this earlier work, two viable approaches to motion cueing were identified: the coordinated adaptive washout algorithm or 'adaptive algorithm', and the 'optimal algorithm'. In this study, a novel approach to motion cueing is discussed that would combine features of both algorithms. The new algorithm is formulated as a linear optimal control problem, incorporating improved vestibular models and an integrated visual-vestibular motion perception model previously reported. A control law is generated from the motion platform states, resulting in a set of nonlinear cueing filters. The time-varying control law requires the matrix Riccati equation to be solved in real time. Therefore, in order to meet the real time requirement, a neurocomputing approach is used to solve this computationally challenging problem. Single degree-of-freedom responses for the nonlinear algorithm were generated and compared to the adaptive and optimal algorithms. Results for the heave mode show the nonlinear algorithm producing a motion cue with a time-varying washout, sustaining small cues for a longer duration and washing out larger cues more quickly. The addition of the optokinetic influence from the integrated perception model was shown to improve the response to a surge input, producing a specific force response with no steady-state washout. Improved cues are also observed for responses to a sway input. Yaw mode responses reveal that the nonlinear algorithm improves the motion cues by reducing the magnitude of negative cues. The effectiveness of the nonlinear algorithm as compared to the adaptive and linear optimal algorithms will be evaluated on a motion platform, the NASA Langley Research Center Visual Motion Simulator (VMS), and ultimately the Cockpit Motion Facility (CMF) with a series of pilot controlled maneuvers. A proposed experimental procedure is discussed. The results of this evaluation will be used to assess motion cueing performance.

Telban, Robert J.↗

NASA NTRS2004

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

Ortiz, Francisco↗

NASA NTRS2010

Robust Optimization Design Algorithm for High-Frequency TWTs

Traveling-wave tubes (TWTs), such as the Ka-band (26-GHz) model recently developed for the Lunar Reconnaissance Orbiter, are essential as communication amplifiers in spacecraft for virtually all near- and deep-space missions. This innovation is a computational design algorithm that, for the first time, optimizes the efficiency and output power of a TWT while taking into account the effects of dimensional tolerance variations. Because they are primary power consumers and power generation is very expensive in space, much effort has been exerted over the last 30 years to increase the power efficiency of TWTs. However, at frequencies higher than about 60 GHz, efficiencies of TWTs are still quite low. A major reason is that at higher frequencies, dimensional tolerance variations from conventional micromachining techniques become relatively large with respect to the circuit dimensions. When this is the case, conventional design- optimization procedures, which ignore dimensional variations, provide inaccurate designs for which the actual amplifier performance substantially under-performs that of the design. Thus, this new, robust TWT optimization design algorithm was created to take account of and ameliorate the deleterious effects of dimensional variations and to increase efficiency, power, and yield of high-frequency TWTs. This design algorithm can help extend the use of TWTs into the terahertz frequency regime of 300-3000 GHz. Currently, these frequencies are under-utilized because of the lack of efficient amplifiers, thus this regime is known as the "terahertz gap." The development of an efficient terahertz TWT amplifier could enable breakthrough applications in space science molecular spectroscopy, remote sensing, nondestructive testing, high-resolution "through-the-wall" imaging, biomedical imaging, and detection of explosives and toxic biochemical agents.

Wilson, Jeffrey D.↗

NASA NTRS1967

Study of a global search algorithm for optimal control.

Adaptive random search algorithm utilizing boundary cost-function hypersurfaces measurement to implement Pontryagin maximum principle, discussing hybrid computer use, iterative solution and convergence properties

Brocker, D. H.↗

NASA NTRS1970

Global search algorithm for optimal control

Random-search algorithm employs local and global properties to solve two-point boundary value problem in Pontryagin maximum principle for either fixed or variable end-time problems. Mixed boundary value problem is transformed to an initial value problem. Mapping between initial and terminal values utilizes hybrid computer.

Brocker, D. H.↗

NASA NTRS1970

Study of optimal guidance algorithms

Indirect, linear and nonlinear optimal guidance schemes from precomputed reference trajectory, using iterative techniques for boundary equations

Andrus, J. F.↗

NASA NTRS1988

A near optimal guidance algorithm for aero-assisted orbit transfer

The paper presents a near optimal guidance algorithm for aero-assited orbit plane change, based on minimizing the energy loss during the atmospheric portion of the maneuver. The guidance algorithm makes use of recent results obtained from energy state approximations and singular perturbation analysis of optimal heading change for a hypersonic gliding vehicle. This earlier work ignored the terminal constraint on altitude needed to insure that the vehicle exits that atmosphere. Thus, the resulting guidance algorithm was only appropriate for maneuvering reentry vehicle guidance. In the context of singular perturbation theory, a constraint on final altitude gives rise to a difficult terminal boundary layer problem, which cannot be solved in closed form. This paper will demonstrate the near optimality of a predictive/corrective guidance algorithm for the terminal maneuver. Comparisons are made to numerically optimized trajectories for a range or orbit plane angles.

Calise, Anthony J.↗

NASA NTRS2002

Application of the SDC optimal control algorithm to low-thrust escape and capture trajectory optimization

An application of the new optimization alorithm called Static/Dynamic Control (SDC) to design low-thrust escape and capture trajectories is presented.

low-thrust↗

NASA NTRS2020

Communication-Aware Orbit Design for Small Spacecraft Swarms around Small Bodies

Exploration of small Solar System bodies has traditionally been performed by single monolithic spacecraft carrying a number of science instruments. However, science instruments typically cannot be operated simultaneously due to the instrument requirements including optimal viewing angle, surface illumination, altitude and ground resolution, power, and data constraints. This observation has motivated interest in multi-spacecraft architectures where a swarm of small spacecraft, each carrying a single science instrument, studies a small body after being deployed by a carrier spacecraft, which then collects data from the vehicles and relays it to Earth. Such architectures hold promise to yield significant improvements in mission efficiency, increases in data quality, and shorter mission duration. A key difficulty in the design of such missions is the selection of orbits for the small spacecraft, which must satisfy not only instrument requirements, but also strict inter-spacecraft communication and on-board storage constraints. To address this, in this paper, we present a novel computationally-efficient optimization algorithm for \emph{communication-aware design} of the orbits of a small spacecraft swarm orbiting a small body. The proposed approach captures constraints including instrument requirements, inter-spacecraft communication bandwidths, and on-board memory usage, and it can accommodate highly irregular gravity field models and surface geometries. We propose an efficient algorithm for optimization of instrument observations and inter-spacecraft communications; we then leverage the differentiable nature of the proposed algorithm to accelerate a gradient-based global search algorithm. Numerical simulations of a six-spacecraft swarm studying 433 Eros show that the proposed approach successfully identifies high-quality orbits, and significantly outperform communication-agnostic optimization techniques, resulting in a 10% increase in scientific returns and a 30% increase in the quality of the collected data.

Rahmani, Amir↗

NASA NTRS1982

Optimal Regulator Algorithms for the Control of Linear Systems

Control-theory design package, called Optimal Regulator Algorithms for Control of Linear Systems (ORACLS), aids in design of controllers and optimal filters for systems modeled by linear, time invariant differential and difference equations. ORACLS is particularly attractive rigorous tool for dealing with multi-input and multi-output dynamic systems in both continuous and discrete forms.

Armstrong, E. S.↗

NASA NTRS1993

Attitude determination using vector observations: A fast optimal matrix algorithm

The attitude matrix minimizing Wahba's loss function is computed directly by a method that is competitive with the fastest known algorithm for finding this optimal estimate. The method also provides an estimate of the attitude error covariance matrix. Analysis of the special case of two vector observations identifies those cases for which the TRIAD or algebraic method minimizes Wahba's loss function.

Markley, F. Landis↗

NASA NTRS1993

Attitude determination using vector observations - A fast optimal matrix algorithm

Markley, F. L.↗

NASA NTRS1996

Optimized TRIAD Algorithm for Attitude Determination

TRIAD is a well known simple algorithm that generates the attitude matrix between two coordinate systems when the components of two abstract vectors are given in the two systems. TRIAD however, is sensitive to the order in which the algorithm handles the vectors, such that the resulting attitude matrix is influenced more by the vector processed first. In this work we present a new algorithm, which we call Optimized TRIAD, that blends in a specified manner the two matrices generated by TRIAD when processing one vector first, and then when processing the other vector first. On the average, Optimized TRIAD yields a matrix which is better than either one of the two matrices in that is ti the closest to the correct matrix. This result is demonstrated through simulation.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS2005

Motion Cueing Algorithm Development: New Motion Cueing Program Implementation and Tuning

A computer program has been developed for the purpose of driving the NASA Langley Research Center Visual Motion Simulator (VMS). This program includes two new motion cueing algorithms, the optimal algorithm and the nonlinear algorithm. A general description of the program is given along with a description and flowcharts for each cueing algorithm, and also descriptions and flowcharts for subroutines used with the algorithms. Common block variable listings and a program listing are also provided. The new cueing algorithms have a nonlinear gain algorithm implemented that scales each aircraft degree-of-freedom input with a third-order polynomial. A description of the nonlinear gain algorithm is given along with past tuning experience and procedures for tuning the gain coefficient sets for each degree-of-freedom to produce the desired piloted performance. This algorithm tuning will be needed when the nonlinear motion cueing algorithm is implemented on a new motion system in the Cockpit Motion Facility (CMF) at the NASA Langley Research Center.

Houck, Jacob A.↗

NASA NTRS2011

Autorotation flight control system

The present invention provides computer implemented methodology that permits the safe landing and recovery of rotorcraft following engine failure. With this invention successful autorotations may be performed from well within the unsafe operating area of the height-velocity profile of a helicopter by employing the fast and robust real-time trajectory optimization algorithm that commands control motion through an intuitive pilot display, or directly in the case of autonomous rotorcraft. The algorithm generates optimal trajectories and control commands via the direct-collocation optimization method, solved using a nonlinear programming problem solver. The control inputs computed are collective pitch and aircraft pitch, which are easily tracked and manipulated by the pilot or converted to control actuator commands for automated operation during autorotation in the case of an autonomous rotorcraft. The formulation of the optimal control problem has been carefully tailored so the solutions resemble those of an expert pilot, accounting for the performance limitations of the rotorcraft and safety concerns.

Bachelder, Edward N.↗

NASA NTRS2019

GOES-17 Advanced Baseline Imager Performance Recovery Summary

The 17th Geostationary Operational Environmental Satellite (GOES-17) was launched on 1 March 2018. The Advanced Baseline Imager (ABI) is the primary instrument on the GOES-R series for weather and environmental monitoring. The GOES-17 ABI (flight model 2) experienced a degradation in its thermal system that limits ABI's ability to shed solar heat load. This limitation resulted in significant reduction in performance after initial turn on with only 3 of 16 spectral channels expected to be available for much of the year. A combined government/vendor team was tasked with optimizing the operation of ABI to recapture as much performance as possible. By modifying the operational configuration and sensor parameters, the team was able to regain over 97% imaging capability.This was accomplished by taking advantage of the considerably flexible nature of ABI's design to adapt its configuration to the new reality and improve capabilities for many of ABI's subsystems. The significant differences in operational configuration, sensor parameter optimization, and algorithm optimization will be discussed as well as their impact on performance and data availability.

Advanced Baseline Imager↗

DOE OSTI2024

Riemannian Optimization Applied to AC Optimal Power Flow: Preprint

The nonlinear, nonconvex AC optimal power flow problem is of growing importance as the nature of the power grid evolves. This problem can be difficult to solve for interior point methods. However, the advent of optimization algorithms over smooth Riemannian manifolds presents an alternative approach. The nonlinear, nonconvex constraints in the AC power flow problem form an embedded submanifold of Euclidean space. In this paper, the authors explore the performance of Riemannian optimization algorithms for the ACOPF problem where the optimization is performed directly on the AC power flow manifold. They demonstrate that these are viable computational alternatives to interior point methods. This is done by using Julia and the packages PowerModels.jl and Manopt.jl.

manifold optimization↗