An algorithm for minimum energy control
Algorithm for fixed time minimum energy discrete optimal control problems of linear plants with convex constraints imposed on terminal state
Deparis, M.↗
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An algorithm for a general class of routing problems derived from Huygens' principle
If a set of N points or nodes with a nonnegative cost associated with each ordered pair is known, it is desired to find a path from one given node to another given node which minimizes the cost sum. An algorithm is presented which yields a global minimum solution after at most N - 1 iterations or on a typical large third-generation computer, after 1 hour of computation time for a 10,000-node problem. The rapid-access data storage capacity demanded by the algorithm is approximately 3N words for costs read in from slow-access storage or 2N words for calculable costs. The time-storage requirements of the algorithm known to the authors. When the problem is viewed as a discretized optimal control problem, after N-1 iterations, an optimal control or node transition is established for each of the N nodes or states; thus, the algorithm can be applied to situations were there may be errors in the control that necessitate a closed loop control that necessitate a closed loop control philosophy.
Avis, L. M.↗
Digital adaptive controllers using second order models with transport lag
Design of a discrete optimal regulator requires the a priori knowledge of a mathematical model for the system of interest. Because a second-order model with transport lag is very amenable to control computations and because this type of model has been used previously to represent certain high order single input-single output processes, an adaptive controller was designed based upon adjustment of controls computed for such a model. An extended Kalman filter was utilized for tracking the model parameters which were subsequently used to update a set of optimal control gains. Favorable results were obtained in applying this procedure to the control of several examples including a ninth order nonlinear process.
Joshi, S.↗
On the optimal minimum order observer-based compensator and the limited state variable feedback controller
Four design problems are considered: two on the optimal minimum order observer-based compensator design and two on the optimal limited state variable feedback controller. The problem of designing an optimal discrete time linear time-invariant observer-based compensator for the regulation of an n dimensional linear discrete time time-invariant plant with m independent outputs is considered. This is a stochastic design problem to the extent that the initial plant state is assumed to be a random vector with known first and second order statistics. The compensator parameters are obtained by minimizing the expectation, with respect to the initial conditions, of the standard cost, quadratic in the state and control vectors with the inclusion of cross terms.
Llorens-Ortiz, B.↗
The human operator in manual preview tracking /an experiment and its modeling via optimal control/
A manual preview tracking experiment and its results are presented. The preview drastically improves the tracking performance compared to zero-preview tracking. Optimal discrete finite preview control is applied to determine the structure of a mathematical model of the manual preview tracking experiment. Variable parameters in the model are adjusted to values which are consistent to the published data in manual control. The model with the adjusted parameters is found to be well correlated to the experimental results.
Tomizuka, M.↗
Application of an adaptive blade control algorithm to a gust alleviation system
The feasibility of an adaptive control system designed to alleviate helicopter gust induced vibration was analytically investigated for an articulated rotor system. This control system is based on discrete optimal control theory, and is composed of a set of measurements (oscillatory hub forces and moments), an identification system using a Kalman filter, a control system based on the minimization of the quadratic performance function, and a simulation system of the helicopter rotor. The gust models are step and sinusoidal vertical gusts. Control inputs are selected at the gust frequency, subharmonic frequency, and superharmonic frequency, and are superimposed on the basic collective and cyclic control inputs. The response to be reduced is selected to be that at the gust frequency because this is the dominant response compared with sub- and superharmonics. Numerical calculations show that the adaptive blade pitch control algorithm satisfactorily alleviates the hub gust response. Almost 100% reduction of the perturbation thrust response to a step gust and more than 50% reduction to a sinusoidal gust are achieved in the numerical simulations.
Saito, S.↗
Application of an adaptive blade control algorithm to a gust alleviation system
The feasibility of an adaptive control system designed to alleviate helicopter gust induced vibration was analytically investigated for an articulated rotor system. This control system is based on discrete optimal control theory, and is composed of a set of measurements (oscillatory hub forces and moments), an identification system using a Kalman filter, a control system based on the minimization of the quadratic performance function, and a simulation system of the helicopter rotor. The gust models are step and sinusoidal vertical gusts. Control inputs are selected at the gust frequency, subharmonic frequency, and superharmonic frequency, and are superimposed on the basic collective and cyclic control inputs. The response to be reduced is selected to be that at the gust frequency because this is the dominant response compared with sub- and superharmonics. Numerical calculations show that the adaptive blade pitch control algorithm satisfactorily alleviates the hub gust response. Almost 100 percent reduction of the perturbation thrust response to a step gust and more than 50 percent reduction to a sinusoidal gust are achieved in the numerical simulations.
Saito, S.↗
Application of variable-gain output feedback for high-alpha control
This paper describes a variable-gain optimal discrete output-feedback design approach that is applied to a nonlinear flight regime covering a wide angle-of-attack range that includes stall and poststall. The paper includes brief descriptions of the variable-gain formulation, the discrete-control structure and flight equations used to apply the design approach, and the high performance airplane model used in the application. Both linear and nonlinear analyses are shown for a longitudinal four-model design case with angles of attack of 5, 15, 35, and 60 deg.
Ostroff, Aaron J.↗
Application of variable-gain output feedback for high-alpha control
A variable-gain, optimal, discrete, output feedback design approach that is applied to a nonlinear flight regime is described. The flight regime covers a wide angle-of-attack range that includes stall and post stall. The paper includes brief descriptions of the variable-gain formulation, the discrete-control structure and flight equations used to apply the design approach, and the high performance airplane model used in the application. Both linear and nonlinear analysis are shown for a longitudinal four-model design case with angles of attack of 5, 15, 35, and 60 deg. Linear and nonlinear simulations are compared for a single-point longitudinal design at 60 deg angle of attack. Nonlinear simulations for the four-model, multi-mode, variable-gain design include a longitudinal pitch-up and pitch-down maneuver and high angle-of-attack regulation during a lateral maneuver.
Ostroff, Aaron J.↗
Minimizing distortion and internal forces in truss structures by simulated annealing
Inaccuracies in the length of members and the diameters of joints of large space structures may produce unacceptable levels of surface distortion and internal forces. Here, two discrete optimization problems are formulated, one to minimize surface distortion (DSQRMS) and the other to minimize internal forces (FSQRMS). Both of these problems are based on the influence matrices generated by a small-deformation linear analysis. Good solutions are obtained for DSQRMS and FSQRMS through the use of a simulated annealing heuristic.
Kincaid, Rex K.↗
Randomly Sampled-Data Control Systems
The purpose is to solve the Linear Quadratic Regulator (LQR) problem with random time sampling. Such a sampling scheme may arise from imperfect instrumentation as in the case of sampling jitter. It can also model the stochastic information exchange among decentralized controllers to name just a few. A practical suboptimal controller is proposed with the nice property of mean square stability. The proposed controller is suboptimal in the sense that the control structure is limited to be linear. Because of i. i. d. assumption, this does not seem unreasonable. Once the control structure is fixed, the stochastic discrete optimal control problem is transformed into an equivalent deterministic optimal control problem with dynamics described by the matrix difference equation. The N-horizon control problem is solved using the Lagrange's multiplier method. The infinite horizon control problem is formulated as a classical minimization problem. Assuming existence of solution to the minimization problem, the total system is shown to be mean square stable under certain observability conditions. Computer simulations are performed to illustrate these conditions.
Han, Kuoruey↗
A Parallel Approach To Optimum Actuator Selection With a Genetic Algorithm
Recent discoveries in smart technologies have created a variety of aerodynamic actuators which have great potential to enable entirely new approaches to aerospace vehicle flight control. For a revolutionary concept such as a seamless aircraft with no moving control surfaces, there is a large set of candidate locations for placing actuators, resulting in a substantially larger number of combinations to examine in order to find an optimum placement satisfying the mission requirements. The placement of actuators on a wing determines the control effectiveness of the airplane. One approach to placement Maximizes the moments about the pitch, roll, and yaw axes, while minimizing the coupling. Genetic algorithms have been instrumental in achieving good solutions to discrete optimization problems, such as the actuator placement problem. As a proof of concept, a genetic has been developed to find the minimum number of actuators required to provide uncoupled pitch, roll, and yaw control for a simplified, untapered, unswept wing model. To find the optimum placement by searching all possible combinations would require 1,100 hours. Formulating the problem and as a multi-objective problem and modifying it to take advantage of the parallel processing capabilities of a multi-processor computer, reduces the optimization time to 22 hours.
Rogers, James L.↗
Actuator Placement Via Genetic Algorithm for Aircraft Morphing
This research continued work that began under the support of NASA Grant NAG1-2119. The focus of this effort was to continue investigations of Genetic Algorithm (GA) approaches that could be used to solve an actuator placement problem by treating this as a discrete optimization problem. In these efforts, the actuators are assumed to be "smart" devices that change the aerodynamic shape of an aircraft wing to alter the flow past the wing, and, as a result, provide aerodynamic moments that could provide flight control. The earlier work investigated issued for the problem statement, developed the appropriate actuator modeling, recognized the importance of symmetry for this problem, modified the aerodynamic analysis routine for more efficient use with the genetic algorithm, and began a problem size study to measure the impact of increasing problem complexity. The research discussed in this final summary further investigated the problem statement to provide a "combined moment" problem statement to simultaneously address roll, pitch and yaw. Investigations of problem size using this new problem statement provided insight into performance of the GA as the number of possible actuator locations increased. Where previous investigations utilized a simple wing model to develop the GA approach for actuator placement, this research culminated with application of the GA approach to a high-altitude unmanned aerial vehicle concept to demonstrate that the approach is valid for an aircraft configuration.
Crossley, William A.↗
Congruence Approximations for Entrophy Endowed Hyperbolic Systems
Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.
Barth, Timothy J.↗
Scalable Approaches to Selecting Key Entities in Large Networked Infrastructure Systems
This work aims at bringing advances in discrete optimization algorithms to solving practical engineering problems at scale. Often times, in many engineering design problems, there is a need to select a small set of influential or representative elements from a large ground set of entities in an optimal fashion. Submodular optimization provides for a formal way to solve such problems. Common examples with infrastructure systems involve sensor placement and identification of key entities with certain objectives. However, scaling these approaches to large infrastructure systems can be challenging because of the high computational complexity of the overall framework that include the optimization algorithms as well as high-complexity compute-oracles that provide the necessary objective function values. In this work, we explore a well-studied and widely-applicable paradigm, namely leader-selection in a multi-agent networked setting in the context of scalable methodologies. We demonstrate novel frameworks that utilize variations of accelerated submodular optimization algorithms along with linear-algebraic methods that can help accelerate the oracle computations. We further explore this combination in conjunction with graph partitioning paradigms to take advantage of the accelerated algorithms in a distributed setting. Finally we demonstrate the key findings on a practical problem in an operational setting. For this, we leverage an example road network with approximately 18k nodes and 27k edges in a traffic control application, where we seek a limited number of k=200 key intersections. This problem can be solved in a serial setting in just under 5 hours providing more than 2 orders of magnitude speed-up over methods that do not consider acceleration techniques.
Visweswara Sathanur, Arun↗
The discrete complementary variational principle and optimal control systems
A discrete complementary variational principle is developed and applied to linear and nonlinear discrete-time optimal control systems. Using the variational approach, a primal-dual relationship is established. This relationship provides a precise measure of system suboptimality independent of any a priori knowledge of the optimal solution.
Chan, W. L.↗
A Framework for the Optimization of Discrete-Event Simulation Models
With the growing use of computer modeling and simulation, in all aspects of engineering, the scope of traditional optimization has to be extended to include simulation models. Some unique aspects have to be addressed while optimizing via stochastic simulation models. The optimization procedure has to explicitly account for the randomness inherent in the stochastic measures predicted by the model. This paper outlines a general purpose framework for optimization of terminating discrete-event simulation models. The methodology combines a chance constraint approach for problem formulation, together with standard statistical estimation and analyses techniques. The applicability of the optimization framework is illustrated by minimizing the operation and support resources of a launch vehicle, through a simulation model.
Joshi, B. D.↗
Language model-accelerated deep symbolic optimization
Symbolic optimization methods have been used to solve varied challenging and relevant problems such as symbolic regression and neural architecture search. However, the current state of the art typically learns each problem from scratch and is unable to leverage pre-existing knowledge and datasets that are available for many applications. Here, inspired by the similarity between sequence representations learned in natural language processing and the formulation of symbolic optimization as a discrete sequence optimization problem, we propose language model-accelerated deep symbolic optimization (LA-DSO), a method that leverages language models to learn symbolic optimization solutions more efficiently. We demonstrate LA-DSO in two tasks: symbolic regression, which allows us to perform extensive experimentation due to its low computation requirements, and computational antibody optimization, which shows that our proposal accelerates learning in challenging real-world problems.
97 MATHEMATICS AND COMPUTING↗