Toward generalized control theory
Generalized control theory, discussing optimization and table classifying control theory fields
Ho, Y.-C.↗
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A state-of-the-art review of transportation systems evaluation techniques relevant to air transportation, volume 1
Mathematical and philosophical approaches are presented for evaluation and implementation of ground and air transportation systems. Basic decision processes are examined that are used for cost analyses and planning (i.e, statistical decision theory, linear and dynamic programming, optimization, game theory). The effects on the environment and the community that a transportation system may have are discussed and modelled. Algorithmic structures are examined and selected bibliographic annotations are included. Transportation dynamic models were developed. Citizen participation in transportation projects (i.e, in Maryland and Massachusetts) is discussed. The relevance of the modelling and evaluation approaches to air transportation (i.e, airport planning) is examined in a case study in St. Louis, Missouri.
Haefner, L. E.↗
State elimination for mixed‐integer optimal control of partial differential equations by semigroup theory
Abstract Mixed‐integer optimal control problems governed by partial differential equations (MIPDECOs) are powerful modeling tools but also challenging in terms of theory and computation. We propose a highly efficient state elimination approach for MIPDECOs that are governed by partial differential equations that have the structure of an abstract ordinary differential equation in function space. This allows us to avoid repeated calculations of the states for all time steps, and our approach is applied only once before starting the optimization. The presentation of theoretical results is complemented by numerical experiments.
97 MATHEMATICS AND COMPUTING↗
Linear Disturbance Amplification Over Blunted Flat Plates in High-Speed Flows
Modal and nonmodal instability characteristics of cylindrically blunted flat plates with varying leading edge radii are described for Mach 4 and Mach 6 freestream conditions. The selection of leading edge radii and freestream parameters is informed by experimental conditions. The investigation of this 2D problem provides a slow entropy layer swallowing which allows for an isolated development of perturbations seeded upstream within different wall-normal regions of the flow. At both Mach numbers, a decrease in modal instability amplification was seen as the leading edge radius was increased. Nonmodal analysis reveals amplifying perturbations in the boundary layer as well as in the entropy layer. The medium bluntness regime exhibits the strongest amplification of nonmodal disturbances that is nonmonotonic in character. Small amplitude boundary forcing at the plate surface or volumetric forcing at various wall-normal heights was used to account for receptivity effects. While wall forcing effectively induced modal instabilities, only an actuation above the boundary layer captured disturbances that amplify within the entropy layer. The optimal nonmodal theory’s entropy-layer disturbance evolution exhibited outstanding agreement with controlled forcing, including receptivity effects. The evolution of entropy-layer disturbances from the optimal nonmodal theory showed excellent agreement with the results of receptivity to controlled forcing. Therefore, the nonmodal optimal growth analysis may provide a useful as well as efficient technique to identify the complete disturbance spectrum in blunt hypersonic configurations, where both modal and nonmodal disturbances can amplify in the boundary-layer and entropy-layer regions.
Boundary layer transition↗
Linear Disturbance Amplification Over Blunted Flat Plates in High-Speed Flows
Modal and nonmodal instability characteristics of cylindrically blunted flat plates with varying leading edge radii are described for Mach 4 and Mach 6 freestream conditions. The selection of leading edge radii and freestream parameters is informed by experimental conditions. The investigation of this 2D problem provides a slow entropy layer swallowing which allows for an isolated development of perturbations seeded upstream within different wall-normal regions of the flow. At both Mach numbers, a decrease in modal instability amplification was seen as the leading edge radius was increased. Nonmodal analysis reveals amplifying perturbations in the boundary layer as well as in the entropy layer. The medium bluntness regime exhibits the strongest amplification of nonmodal disturbances that is nonmonotonic in character. Small amplitude boundary forcing at the plate surface or volumetric forcing at various wall-normal heights was used to account for receptivity effects. While wall forcing effectively induced modal instabilities, only an actuation above the boundary layer captured disturbances that amplify within the entropy layer. The optimal nonmodal theory’s entropy-layer disturbance evolution exhibited outstanding agreement with controlled forcing, including receptivity effects. The evolution of entropy-layer disturbances from the optimal nonmodal theory showed excellent agreement with the results of receptivity to controlled forcing. Therefore, the nonmodal optimal growth analysis may provide a useful as well as efficient technique to identify the complete disturbance spectrum in blunt hypersonic configurations, where both modal and nonmodal disturbances can amplify in the boundary-layer and entropy-layer regions.
Boundary layer transition↗
Exponential Improvements in the Simulation of Lattice Gauge Theories Using Near-Optimal Techniques
We report a first-of-its-kind analysis on post-Trotter simulation of U(1), SU(2), and SU(3) lattice gauge theories including fermions in arbitrary spatial dimension. We provide explicit circuit constructions as well as T-gate counts and logical qubit counts for Hamiltonian simulation. We find a reduction of up to 25 orders of magnitude in space-time volume over Trotter methods for simulations of non-Abelian lattice gauge theories relevant to the standard model. This improvement results from our algorithm having polynomial scaling with the number of colors in the gauge theory, achieved by utilizing oracle constructions relying on the sparsity of physical operators, in contrast to the exponential scaling seen in state-of-the-art Trotter methods, which employ explicit mappings onto Pauli operators. Our work demonstrates that the use of advanced algorithmic techniques leads to dramatic reductions in the cost of simulating fundamental interactions, bringing it in step with resources required for first-principles quantum simulation of chemistry.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Some optimal considerations in attitude control systems
The conventional six-engine reaction control jet relay attitude control law with deadband is shown to be a good linear approximation to a weighted time-fuel optimal control law. Techniques for evaluating the value of the relative weighting between time and fuel for a particular relay control law is studied along with techniques to interrelate other parameters for the two control laws. Vehicle attitude control laws employing control moment gyros are then investigated. Steering laws obtained from the expression for the reaction torque of the gyro configuration are compared to a total optimal attitude control law that is derived from optimal linear regulator theory. This total optimal attitude control law has computational disadvantages in the solving of the matrix Riccati equation. Several computational algorithms for solving the matrix Riccati equation are investigated with respect to accuracy, computational storage requirements, and computational speed.
Boland, J. S., III↗
Helicopter optimal descent and landing after power loss
An optimal control solution is obtained for the descent and landing of a helicopter after the loss of power in level flight. The model considers the helicopter vertical velocity, horizontal velocity, and rotor speed; and it includes representations of ground effect, rotor inflow time lag, pilot reaction time, rotor stall, and the induced velocity curve in the vortex ring state. The control (rotor thrust magnitude and direction) required to minimize the vertical and horizontal velocity at contact with the ground is obtained using nonlinear optimal control theory. It is found that the optimal descent after power loss in hover is a purely vertical flight path. Good correlation, even quantitatively, is found between the calculations and (non-optimal) flight test results.
Johnson, W.↗
Riccati group invariants of linear hamiltonian systems
The action of the Riccati group on the Riccati differential equation is associated with the action of a subgroup of the symplectic group on a set of hamiltonian matrices. Within this framework various sets of canonical forms are developed for the matrix coefficients of the Riccati differential equation. The canonical forms presented are valid for arbitrary Kronecker indices, and it is shown that the Kronecker indices are invariants for this group action. These canonical forms are useful for studying problems arising in the areas of optimal decentralized control and the spectral theory of optimal control problems.
Garzia, M. R.↗
Attitude control system testing on SCOLE
This paper presents implementation of two control policies on SCOLE (Space Control Laboratory Experiment), a laboratory apparatus representing an offset-feed antenna attached to the Space Shuttle by a flexible mast. In the first case, the flexible mast was restrained by cables, permitting modeling of SCOLE as a rigid-body. Starting from an arbitrary state, SCOLE was maneuvered to a specified terminal state using rigid-body minimum-time control law. In the second case, the so called single step optimal control (SSOC) theory is applied to suppress vibrations of the flexible mast mounted as a cantilever beam. Based on the SSOC theory, two parameter optimization algorithms were developed.
Shenhar, J.↗
Optimal Angle of Attack Control for Aerocapture Maneuvers
Recent investigations of aerocapture maneuvers have considered direct force control as a promising alternative to bank angle control. By modulating the angle of attack and sideslip angle independently, the longitudinal and lateral channels can be decoupled and thus solved separately. However, the optimal angle of attack profile for minimizing post-atmospheric propellant expenditure was previously unknown. This research applies principles of optimal control theory to numerically solve for the optimal angle of attack profile for control of the longitudinal channel. Direct methods are first employed to discretize the angle of attack profile and show that an optimal solution follows a nearly bang-bang (full lift up then full lift down) structure under a variety of conditions along the flight path angle corridor. To corroborate these results, indirect methods were also applied to scope the Optimal Control Problem (OCP) as a Two Point Boundary Value Problem (2P-BVP) which could then be solved numerically. The indirect optimization results aligned closely with the direct results, providing further evidence that a bang-bang structure provides a good approximation for the optimal angle of attack profile for aerocapture maneuvers using direct force control.
aerocapture↗
A matrix equation arising in statistical filter theory
Solution of Ricatti differential equation arising in statistical filering and optimal control theory
FILTER↗
Surrogate Hessian accelerated structural optimization for stochastic electronic structure theories
In this work, we present an efficient energy-based method for structural optimization with stochastic electronic structure theories, such as diffusion quantum Monte Carlo (DMC). This method is based on robust line-search energy minimization in reduced parameter space, exploiting approximate but accurate Hessian information from a surrogate theory, such as density functional theory. The surrogate theory is also used to characterize the potential energy surface, allowing for simple but reliable ways to maximize statistical efficiency while retaining controllable accuracy. We demonstrate the method by finding the minimum DMC energy structures of the selected flake-like aromatic molecules, such as benzene, coronene, and ovalene, represented by 2, 6, and 19 structural parameters, respectively. In each case, the energy minimum is found within two parallel line-search iterations. The method is near-optimal for a line-search technique and suitable for a broad range of applications. It is easily generalized to any electronic structure method where forces and stresses are still under active development and implementation, such as diffusion Monte Carlo, auxiliary-field Monte Carlo, and stochastic configuration interaction, as well as deterministic approaches such as the random-phase approximation. Accurate and efficient means of geometry optimization could shed light on a broad class of materials and molecules, showing high sensitivity of induced properties to structural variables.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Optimization of an unobscured optical system using vector aberration theory
Excellent results for optimization of one all-reflective system are gained by choosing a limited number of variables as indicated by vector aberration theory. An aberration analysis shown here can be used to extend the method to other systems.
Stacy, John E.↗
Quantum-mechanical communication theory
Quantum mechanical communication theory of optimal receivers, using statistical detection and estimation theory
Gordon, J. P.↗
Drag reduction strategies
previously a description was given of an active control scheme using wall transpiration that leads to a 15% reduction in surface skin friction beneath a turbulent boundary layer, according to direct numerical simulation. In this research brief further details of that scheme and its variants are given together with some suggestions as to how sensor/actuator arrays could be configured to reduce surface drag. The research which is summarized here was performed during the first half of 1994. This research is motivated by the need to understand better how the dynamics of near-wall turbulent flow can be modified so that skin friction is reduced. The reduction of turbulent skin friction is highly desirable in many engineering applications. Experiments and direct numerical simulations have led to an increased understanding of the cycle of turbulence production and transport in the boundary layer and raised awareness of the possibility of disrupting the process with a subsequent reduction in turbulent skin friction. The implementation of active feedback control in a computational setting is a viable approach for the investigation of the modifications to the flow physics that can be achieved. Bewley et al. and Hill describe how ideas from optimal control theory are employed to give 'sub-optimal' drag reduction schemes. The objectives of the work reported here is to investigate in greater detail the assumptions implicit within such schemes and their limitations. It is also our objective to describe how an array of sensors and actuators could be arranged and interconnected to form a 'smart' surface which has low skin friction.
Hill, D. Christopher↗
Integrated design of structures, controls, and materials
In this talk we shall discuss algorithms and CAD tools for the design and analysis of structures for high performance applications using advanced composite materials. An extensive mathematical theory for optimal structural (e.g., shape) design was developed over the past thirty years. Aspects of this theory have been used in the design of components for hypersonic vehicles and thermal diffusion systems based on homogeneous materials. Enhancement of the design methods to include optimization of the microstructure of the component is a significant innovation which can lead to major enhancements in component performance. Our work is focused on the adaptation of existing theories of optimal structural design (e.g., optimal shape design) to treat the design of structures using advanced composite materials (e.g., fiber reinforced, resin matrix materials). In this talk we shall discuss models and algorithms for the design of simple structures from composite materials, focussing on a problem in thermal management. We shall also discuss methods for the integration of active structural controls into the design process.
Blankenship, G. L.↗
Integrated Application of Active Controls (IAAC) technology to an advanced subsonic transport project: Current and advanced act control system definition study, volume 1
An active controls technology (ACT) system architecture was selected based on current technology system elements and optimal control theory was evaluated for use in analyzing and synthesizing ACT multiple control laws. The system selected employs three redundant computers to implement all of the ACT functions, four redundant smaller computers to implement the crucial pitch-augmented stability function, and a separate maintenance and display computer. The reliability objective of probability of crucial function failure of less than 1 x 10 to the -9th power per flight of 1 hr can be met with current technology system components, if the software is assumed fault free and coverage approaching 1.0 can be provided. The optimal control theory approach to ACT control law synthesis yielded comparable control law performance much more systematically and directly than the classical s-domain approach. The ACT control law performance, although somewhat degraded by the inclusion of representative nonlinearities, remained quite effective. Certain high-frequency gust-load alleviation functions may require increased surface rate capability.
Hanks, G. W.↗