Guidance, flight mechanics and trajectory optimization. Volume 7 - The Pontryagin maximum principle
Maxima-minima theory, Pontryagin principle, and calculus of variations for optimal trajectory and control analysis
Mc Intyre, J. E.↗
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Approximate Feedback Control for a System With Memory
Report presents algorithm for calculating feedback gain for control of hereditary dynamical systems with control delay. Problem is to approximate optimal feedback gain that minimizes cost function of state and control. Theory applicable to design of controllers for mechanical systems subject to thermal deformation, electrical systems with delay, electrical systems with plasma components, and other systems that exhibit memory.
Milman, Mark H.↗
Discrete Event Supervisory Control Applied to Propulsion Systems
The theory of discrete event supervisory (DES) control was applied to the optimal control of a twin-engine aircraft propulsion system and demonstrated in a simulation. The supervisory control, which is implemented as a finite-state automaton, oversees the behavior of a system and manages it in such a way that it maximizes a performance criterion, similar to a traditional optimal control problem. DES controllers can be nested such that a high-level controller supervises multiple lower level controllers. This structure can be expanded to control huge, complex systems, providing optimal performance and increasing autonomy with each additional level. The DES control strategy for propulsion systems was validated using a distributed testbed consisting of multiple computers--each representing a module of the overall propulsion system--to simulate real-time hardware-in-the-loop testing. In the first experiment, DES control was applied to the operation of a nonlinear simulation of a turbofan engine (running in closed loop using its own feedback controller) to minimize engine structural damage caused by a combination of thermal and structural loads. This enables increased on-wing time for the engine through better management of the engine-component life usage. Thus, the engine-level DES acts as a life-extending controller through its interaction with and manipulation of the engine s operation.
Litt, Jonathan S.↗
Floquet-engineered fast SNAP gates in weakly coupled circuit-QED systems
Superconducting cavities with high quality factors, coupled to a fixed-frequency transmon, provide a state-of-the-art platform for quantum information storage and manipulation. The commonly used selective number-dependent arbitrary phase ( SNAP ) gate faces significant challenges in ultrahigh-coherence cavities, where the weak dispersive shifts necessary for preserving high coherence typically result in prolonged gate times. Here, in this work, we propose a protocol to achieve high-fidelity SNAP gates that are orders of magnitude faster than the standard implementation, surpassing the speed limit set by the bare dispersive shift. We achieve this enhancement by dynamically amplifying the dispersive coupling via sideband interactions, followed by quantum optimal control on the Floquet-engineered system. We also present a unified perturbation theory that explains both the gate acceleration and the associated benign drive-induced decoherence, corroborated by Floquet-Markov simulations. These results pave the way for the experimental realization of high-fidelity, selective control of weakly coupled, high-coherence cavities, and expanding the scope of optimal control techniques to a broader class of Floquet quantum systems.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Elements of calculus of variations and optimum control theory
Basic similarities in calculus of variations and optimum control theory for rocket flight between two points
VARIATIONAL CALCULUS↗
Planning and executing motions for multibody systems in free-fall
The purpose of this research is to develop an end-to-end system that can be applied to a multibody system in free-fall to analyze its possible motions, save those motions in a database, and design a controller that can execute those motions. A goal is for the process to be highly automated and involve little human intervention. Ideally, the output of the system would be data and algorithms that could be put in ROM to control the multibody system in free-fall. The research applies to more than just robots in space. It applies to any multibody system in free-fall. Mathematical techniques from nonlinear control theory were used to study the nature of the system dynamics and its possible motions. Optimization techniques were applied to plan motions. Image compression techniques were proposed to compress the precomputed motion data for storage. A linearized controller was derived to control the system while it executes preplanned trajectories.
Cameron, Jonathan M.↗
Information Theory Applied to Decision Making Structures
Decision making structures, such as control boards, process information on many topics as they select options for the system and project. The decisions are based on the information known to the board members and presenters (subject matter experts) and shared at the board during discussion. This information flow through this process can be modelled using information theory. Information theory provides a mathematical basis to understand the flow of information through the decision making process and the information needed for a particular decision. Information theory also provides the mathematical relationships on which to base the optimal decision making structure for a specific system development and organizational structure. Since decision making bodies provide control for the system or project, control theory can be used to construct a decision making model. This provides a starting point for adding cognitive science models. Information processing by each individual board participant can be represented through cognitive processes which are integrated across the board participants through information theory relationship. The set theory view of information theory provides a structure in which to look at the relationships between the participants in a decision making structure.
Watson, Michael D.↗
Information Theory Applied to Decision Making Structures
Decision making structures, such as control boards, process information on many topics as they select options for the system and project. The decisions are based on the information known to the board members and presenters (subject matter experts) and shared at the board during discussion. This information flow through this process can be modelled using information theory. Information theory provides a mathematical basis to understand the flow of information through the decision making process and the information needed for a particular decision. Information theory also provides the mathematical relationships on which to base the optimal decision making structure for a specific system development and organizational structure. Since decision making bodies provide control for the system or project, control theory can be used to construct a decision making model. This provides a starting point for adding cognitive science models. Information processing by each individual board participant can be represented through cognitive processes which are integrated across the board participants through information theory relationship. The set theory view of information theory provides a structure in which to look at the relationships between the participants in a decision making structure.
Watson, Michael D.↗
Collectives for Multiple Resource Job Scheduling Across Heterogeneous Servers
Efficient management of large-scale, distributed data storage and processing systems is a major challenge for many computational applications. Many of these systems are characterized by multi-resource tasks processed across a heterogeneous network. Conventional approaches, such as load balancing, work well for centralized, single resource problems, but breakdown in the more general case. In addition, most approaches are often based on heuristics which do not directly attempt to optimize the world utility. In this paper, we propose an agent based control system using the theory of collectives. We configure the servers of our network with agents who make local job scheduling decisions. These decisions are based on local goals which are constructed to be aligned with the objective of optimizing the overall efficiency of the system. We demonstrate that multi-agent systems in which all the agents attempt to optimize the same global utility function (team game) only marginally outperform conventional load balancing. On the other hand, agents configured using collectives outperform both team games and load balancing (by up to four times for the latter), despite their distributed nature and their limited access to information.
Tumer, K.↗
Practical optimal flight control system design for helicopter aircraft. Volume 1: Technical Report
A method by which modern and classical theory techniques may be integrated in a synergistic fashion and used in the design of practical flight control systems is presented. A general procedure is developed, and several illustrative examples are included. Emphasis is placed not only on the synthesis of the design, but on the assessment of the results as well.
Hofmann, L. G.↗
Minimum-energy control of a class of electrically driven vehicles.
A minimum-energy controller is designed and built for a class of electrically driven vehicles according to the theoretical concepts determined by the application of modern control theory. Theoretical results are obtained by making several justifiable assumptions in the dynamical equations of the system and solving the resulting stochastic optimal control problem by Bellman's dynamic programming technique. Several practical and economical considerations are taken into account for the mechanization of the minimum-energy control law.
Sahinkaya, Y. E.↗
Total energy-rate feedback for automatic glide-slope tracking during wind-shear penetration
Low-altitude wind shear is recognized as an infrequent but significant hazard to all aircraft during the take-off and landing phases of flight. A total energy-rate sensor was developed for measuring the specific total energy rate of an airplane with respect to the air mass. Control-system designs, both with and without energy-rate feedback, for the approach to landing of a transport airplane through a severe-wind-shear and gust environment are presented in order to evaluate this application of the sensor. A system model incorporates wind-shear-dynamics equations with the airplane equations of motion to permit analysis of the control systems under various wind-shear conditions. The control systems are designed using optimal-output feedback and are analyzed using frequency-domain control-theory techniques. Control-system performance is evaluated using a complete nonlinear simulation of the airplane combined with a severe-wind-shear and gust data package. This evaluation is concerned with control system stability and regulation capability only.
Belcastro, C. M.↗
Advances and trends in structures and dynamics; Proceedings of the Symposium, Washington, DC, October 22-25, 1984
Among the topics discussed are developments in structural engineering hardware and software, computation for fracture mechanics, trends in numerical analysis and parallel algorithms, mechanics of materials, advances in finite element methods, composite materials and structures, determinations of random motion and dynamic response, optimization theory, automotive tire modeling methods and contact problems, the damping and control of aircraft structures, and advanced structural applications. Specific topics covered include structural design expert systems, the evaluation of finite element system architectures, systolic arrays for finite element analyses, nonlinear finite element computations, hierarchical boundary elements, adaptive substructuring techniques in elastoplastic finite element analyses, automatic tracking of crack propagation, a theory of rate-dependent plasticity, the torsional stability of nonlinear eccentric structures, a computation method for fluid-structure interaction, the seismic analysis of three-dimensional soil-structure interaction, a stress analysis for a composite sandwich panel, toughness criterion identification for unidirectional composite laminates, the modeling of submerged cable dynamics, and damping synthesis for flexible spacecraft structures.
Noor, A. K.↗
Modeling and control of flexible structures
This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.
Gibson, J. S.↗
Constrained minimization of smooth functions using a genetic algorithm
The use of genetic algorithms for minimization of differentiable functions that are subject to differentiable constraints is considered. A technique is demonstrated for converting the solution of the necessary conditions for a constrained minimum into an unconstrained function minimization. This technique is extended as a global constrained optimization algorithm. The theory is applied to calculating minimum-fuel ascent control settings for an energy state model of an aerospace plane.
Moerder, Daniel D.↗
Neural Flight Control System
The Neural Flight Control System (NFCS) was developed to address the need for control systems that can be produced and tested at lower cost, easily adapted to prototype vehicles and for flight systems that can accommodate damaged control surfaces or changes to aircraft stability and control characteristics resulting from failures or accidents. NFCS utilizes on a neural network-based flight control algorithm which automatically compensates for a broad spectrum of unanticipated damage or failures of an aircraft in flight. Pilot stick and rudder pedal inputs are fed into a reference model which produces pitch, roll and yaw rate commands. The reference model frequencies and gains can be set to provide handling quality characteristics suitable for the aircraft of interest. The rate commands are used in conjunction with estimates of the aircraft s stability and control (S&C) derivatives by a simplified Dynamic Inverse controller to produce virtual elevator, aileron and rudder commands. These virtual surface deflection commands are optimally distributed across the aircraft s available control surfaces using linear programming theory. Sensor data is compared with the reference model rate commands to produce an error signal. A Proportional/Integral (PI) error controller "winds up" on the error signal and adds an augmented command to the reference model output with the effect of zeroing the error signal. In order to provide more consistent handling qualities for the pilot, neural networks learn the behavior of the error controller and add in the augmented command before the integrator winds up. In the case of damage sufficient to affect the handling qualities of the aircraft, an Adaptive Critic is utilized to reduce the reference model frequencies and gains to stay within a flyable envelope of the aircraft.
Gundy-Burlet, Karen↗
Interval Predictor Models for Robust System Identification
This paper proposes a framework for the identification and uncertainty quantification of plant models according to multivariable data. The only restriction imposed upon such models is for their outputs to depend continuously on their parameters. An Interval Predictor Model (IPM) prescribes the parameters of a computational model as a path-connected set thereby making each predicted output an interval-valued function of its inputs. The formulation proposed seeks the parameter set for which the predicted outputs tightly enclose the data. This set, which is modeled as a semi-algebraic set of low-degree polynomials, enables the characterization of possibly strong parameter dependencies commonly found in practice. This uncertainty characterization makes the resulting plant model amenable to robust control approaches using polynomial optimization. Furthermore, we use non-convex scenario theory to assess the reliability of the resulting IPM. This assessment yields a distribution-free upper bound on the probability that future data will fall outside the predicted intervals.
interval↗
PAYCOS: A new multidisciplinary analysis program for hypersonic vehicle design
The Payload Conceptual Sizing Code (PAYCOS), a new multidisciplinary computer program for use in the conceptual development phase of hypersonic lifting vehicles (HV's), is described. The program allows engineers to rapidly determine the feasibility of an HV concept and then improve upon the concept by means of optimization theory. The code contains analysis modules for aerodynamics, thermodynamics, mass properties, flight stability, controls, loads, structures, and packaging. Motivation for the code lies with the increased complexity of HV's over their body-of-revolution ballistic predecessors. With these new shapes, the need to rapidly screen out poor concepts and actively develop new and better concepts is an even more crucial part of the early design process. Preliminary results are given which demonstrate the optimization capabilities of the code.
Stubbe, J. R.↗