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Results for “Minimax problem”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

An application of a linear programing technique to nonlinear minimax problems

A differential correction technique for solving nonlinear minimax problems is presented. The basis of the technique is a linear programing algorithm which solves the linear minimax problem. By linearizing the original nonlinear equations about a nominal solution, both nonlinear approximation and estimation problems using the minimax norm may be solved iteratively. Some consideration is also given to improving convergence and to the treatment of problems with more than one measured quantity. A sample problem is treated with this technique and with the least-squares differential correction method to illustrate the properties of the minimax solution. The results indicate that for the sample approximation problem, the minimax technique provides better estimates than the least-squares method if a sufficient amount of data is used. For the sample estimation problem, the minimax estimates are better if the mathematical model is incomplete.

Schiess, J. R.↗
NASA NTRS1988

Chebyshev minimax problems for skip trajectories

The dimensionless equations of motion for hypersonic flight in the upper layer of the atmosphere are presented. The necessary conditions for the Chebyshev minimax problems are provided. Some important properties concerning the peak heating rate, the peak dynamic pressure and the peak altitude drop for a skip trajectory are discussed. As application of the theory, the problem of minimizing the peak altitude drop is solved. The numerical results support the theory that the nearly-grazing trajectory is useful in reducing the peak heating rate and the peak dynamic pressure.

Vinh, N. X.↗
DOE OSTI2024

Robust cooperative control strategy for a platoon of connected and autonomous vehicles against sensor errors and control errors simultaneously in a real-world driving environment

In a real-world driving environment, a platoon of connected and autonomous vehicles (CAVs) is subject to many internal and external disturbances, resulting in uncertain vehicle dynamics. In general, the disturbances can be categorized into two types: disturbances due to vehicle sensor errors (e.g., GPS error) and disturbances due to vehicle control errors (e.g., actuator delay). In the literature, many control strategies have been proposed to improve the robustness of the CAV platoon against uncertain vehicle dynamics induced by these disturbances. However, most of these strategies only consider one type of disturbance and cannot tackle both types of disturbances simultaneously. Furthermore, they are designed to maximize the benefits of each vehicle in the platoon independently, which can deteriorate the performance of the platoon. Here, to address these problems, this study proposes a robust cooperative control (RCC) strategy to maneuver the vehicles in the platoon cooperatively to counteract the impacts of both types of disturbances. The RCC strategy is developed based on a minimax problem, where the maximization subproblem seeks to find the worst inputs for the uncertainty terms in the vehicle dynamics equation to minimize the platoon performance, while the minimization subproblem seeks to find the optimal control decisions for all subsequent vehicles to maximize the platoon performance in the worst case. To solve the minimax problem, this study proposes a globally convergent solution algorithm. It can solve the minimax problem very efficiently to enable real time deployment of the RCC strategy. Numerical application indicates that compared to the existing methods, the RCC strategy can dramatically improve the robustness of the CAV platoon against the uncertain vehicle dynamics induced by both vehicle state detection errors and vehicle control errors. Therefore, it can maneuver the CAV platoon safely and efficiently in a real-world driving environment.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2021

Tuning Multigrid Methods with Robust Optimization and Local Fourier Analysis

Local Fourier analysis is a useful tool for predicting and analyzing the performance of many efficient algorithms for the solution of discretized PDEs, such as multigrid and domain decomposition methods. The crucial aspect of local Fourier analysis is that it can be used to minimize an estimate of the spectral radius of a stationary iteration, or the condition number of a preconditioned system, in terms of a symbol representation of the algorithm. In practice, this is a “minimax” problem, minimizing with respect to solver parameters the appropriate measure of work, which involves maximizing over the Fourier frequency. Often, several algorithmic parameters may be determined by local Fourier analysis in order to obtain efficient algorithms. Analytical solutions to minimax problems are rarely possible beyond simple problems; the status quo in local Fourier analysis involves grid sampling, which is prohibitively expensive in high dimensions. In this paper, we propose and explore optimization algorithms to solve these problems efficiently. Finally, several examples, with known and unknown analytical solutions, are presented to show the effectiveness of these approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Reinforcement Learning-based Output Structured Feedback for Distributed Multi-Area Power System Frequency Control

Load frequency control (LFC) is a key factor to maintain the stable frequency in multi-area power systems. As the modern power systems evolve from centralized to decentralized paradigm, LFC needs to consider the decentralized scheme that considers limited information from the information-exchange graph for the generator control of each interconnected area. This paper aims to solve a data-driven constrained LQR problem with mean-variance risk constraints and output structured feedback, and applies this framework to solve the LFC problem in multi-area power systems. By reformulating the constrained optimization problem into a minimax problem, the stochastic gradient descent max-oracle (SGDmax) algorithm with zero-order policy gradient (ZOPG) is adopted to find the optimal feedback gain from the learning, while guaranteeing the convergence. In addition, to improve the adaptation of the proposed learning method to new or varying models, we construct an emulator grid that approximates the dynamics of a physical grid and performs training based on this model. Once the feedback gain is obtained from the emulator grid, it is applied to the physical grid with a robustness test to check whether the controller from the approximated emulator applies to the actual system. Numerical tests show that the obtained feedback controller can successfully control the frequency of each area, while mitigating the uncertainty from the loads, with reliable robustness that ensures the adaptability of the obtained feedback gain to the actual physical grid.

Kwon, Kyung-bin↗
NASA NTRS1987

Optimization and guidance of abort landing trajectories in a windshear

The abort landing problem for flight trajectories in the presence of windshear is considered with reference to flight in a vertical plane. The optimal trajectory (OT) problem is a minimax problem or Chebyshev problem of optimal control which can be converted into a Bolza problem through suitable transformations. Numerical results for several combinations of windshear intensities and initial altitudes are presented. A guidance trajectory (GT) law is implemented in feedback control form, subject to prescribed bounds on the angle of attack and its time derivative. Simplified guidance trajectories (SGT) are then considered, leading to a safe target altitude guidance. Conclusions derived for strong-to-severe windshear conditions include GT and SGT preserving the basic properties of OT, and the peak altitude drop of GT and SGT being less than that of the constant pitch trajectory and the maximum angle-of-attack trajectory.

Miele, A.↗
NASA NTRS1992

Design of bearings for rotor systems based on stability

Design of rotor systems incorporating stable behavior is of great importance to manufacturers of high speed centrifugal machinery since destabilizing mechanisms (from bearings, seals, aerodynamic cross coupling, noncolocation effects from magnetic bearings, etc.) increase with machine efficiency and power density. A new method of designing bearing parameters (stiffness and damping coefficients or coefficients of the controller transfer function) is proposed, based on a numerical search in the parameter space. The feedback control law is based on a decentralized low order controller structure, and the various design requirements are specified as constraints in the specification and parameter spaces. An algorithm is proposed for solving the problem as a sequence of constrained 'minimax' problems, with more and more eigenvalues into an acceptable region in the complex plane. The algorithm uses the method of feasible directions to solve the nonlinear constrained minimization problem at each stage. This methodology emphasizes the designer's interaction with the algorithm to generate acceptable designs by relaxing various constraints and changing initial guesses interactively. A design oriented user interface is proposed to facilitate the interaction.

Dhar, D.↗
DOE OSTI2023

Risk-Constrained Reinforcement Learning for Inverter-Dominated Power System Controls

Here, this paper develops a risk-aware controller for grid-forming inverters (GFMs) to minimize large frequency oscillations in GFM inverter-dominated power systems. To tackle the high variability from loads/renewables, we incorporate a mean-variance risk constraint into the classical linear quadratic regulator (LQR) formulation for this problem. The risk constraint aims to bound the time-averaged cost of state variability and thus can improve the worst-case performance for large disturbances. The resulting risk-constrained LQR problem is solved through the dual reformulation to a minimax problem, by using a reinforcement learning (RL) method termed as stochastic gradient-descent with max-oracle (SGDmax). In particular, the zero-order policy gradient (ZOPG) approach is used to simplify the gradient estimation using simulated system trajectories. Numerical tests conducted on the IEEE 68-bus system have validated the convergence of our proposed SGDmax for GFM model and corroborate the effectiveness of the risk constraint in improving the worst-case performance while reducing the variability of the overall control cost.

Frequency control↗
NASA NTRS1986

Optimal take-off trajectories in the presence of windshear

The present consideration of takeoff trajectory optimization in eight different fundamental problems involving wind shears assumes that the power setting is held at the maximum value, and that the aircraft is controlled with respect to angle-of-attack. While the first three problems are least-squares ones of the Bolza type, the remaining five are minimax problems of the Chebyshev type which can be converted to Bolza type by means of suitable transformations. All problems are solved on the basis of the dual sequential gradient-restoration algorithm for optimal control problems. The trajectory solutions obtained are superior to constant angle-of-attack trajectories.

Miele, A.↗
NASA NTRS1983

Optimal trajectories for aeroassisted orbital transfer

Consideration is given to classical and minimax problems involved in aeroassisted transfer from high earth orbit (HEO) to low earth orbit (LEO). The transfer is restricted to coplanar operation, with trajectory control effected by means of lift modulation. The performance of the maneuver is indexed to the energy expenditure or, alternatively, the time integral of the heating rate. Firist-order optimality conditions are defined for the classical approach, as are a sequential gradient-restoration algorithm and a combined gradient-restoration algorithm. Minimization techniques are presented for the aeroassisted transfer energy consumption and time-delay integral of the heating rate, as well as minimization of the pressure. It is shown that the eigenvalues of the Jacobian matrix of the differential system is both stiff and unstable, implying that the sequential gradient restoration algorithm in its present version is unsuitable. A new method, involving a multipoint approach to the two-poing boundary value problem, is recommended.

Miele, A.↗
NASA NTRS1987

Optimal trajectories for aeroassisted, noncoplanar orbital transfer. II - LEO-to-LEO transfer

Both classical and minimax problems of optimal control arising in the study of noncoplanar, aeroassisted orbital transfer are considered and are illustrated with the example of LEO-to-LEO transfer. Trajectory control is achieved by modulation of the lift coefficient and the angle of bank. Problems considered include the minimization of the energy required for orbital transfer, maximization of the flight time during the atmospheric portion of the trajectory, and minimization of the peak heating rate. The near-grazing solution is found to be a good compromise between energy and heating requirements.

Miele, A.↗
NASA NTRS1988

Minimax optimal control for atmospheric fly-through trajectories

Necessary conditions for minimax problems with isolated or flat maxima are presented. Some relevant properties concerning the peak heating rate and the peak deceleration during atmospheric entry are discussed. As application of the theory, the problem of minimizing the peak heating rate of a skip trajectory is solved with special emphasis on the discussion of the continuity of the lift control at the point where the maximum occurs along the trajectory.

Lu, P.↗
NASA NTRS1984

Approximate solutions to minimax optimal control problems for aeroassisted orbital transfer

The maneuver considered in the present investigation involves the coplanar transfer of a spacecraft from a high earth orbit (HEO) to a low earth orbit (LEO). HEO can be a geosynchronous earth orbit (GEO). The basic concept utilized involves the hybrid combination of propulsive maneuvers in space and aerodynamic maneuvers in the sensible atmosphere. The considered type of flight is also called synergetic space flight. With respect to the atmospheric part of the maneuver, trajectory control is achieved by means of lift modulation. The Bolza problem of optimal control is stated, and the first-order optimality conditions for this problem are given. The one-arc approach, the two-arc approach, and the three-subarc approach are discussed. Attention is given to the Chebyshev problem of optimal control, details concerning aeroassisted orbital transfer (AOT), AOT optimization problems, and numerical experiments.

Miele, A.↗
NASA NTRS1988

Transformation techniques for minimax optimal control problems and their application to optimal flight trajectories in a windshear - Optimal abort landing trajectories

The optimal-control problem of abort-landing trajectories in the presence of low-altitude wind shear is investigated analytically. The vertical-plane Newtonian motion of a point-mass aircraft in a steady wind field is modeled, and a sequential gradient-restoration algorithm is applied. Numerical results showing the effects of wind-shear intensity, initial altitude, and power-setting rate are presented in extensive graphs and discussed in detail. Optimal trajectories for strong or severe wind shears are found to begin with a descent, followed by level flight and then an ascent after leaving the shear region.

Miele, A.↗