Minimum energy time-optimal control for saturating sampled-data systems
Optimal time regulator for sampled-data fuel control system with input saturation
TIME OPTIMAL CONTROL↗
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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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Optimal Control Allocation for Distributed Electric Propulsion in a Series/Parallel Partial Hybrid Powertrain
The SUbsonic Single Aft eNgine (SUSAN) Electrofan is a NASA concept jet transport aircraft with a 2040 entry-into-service date. It utilizes electrified aircraft propulsion (EAP) to enable propulsive and aerodynamic benefits to reduce fuel usage, emissions, and cost. The powertrain consists of a single thrust producing, boundary layer-ingesting (BLI) turbofan gas turbine engine (GTE) with generators driving a series/parallel partial hybrid EAP system. The architecture includes 16 underwing contrarotating BLI fans, eight on each side, in a mailslot configuration. The 16 fans run on power extracted from the GTE through four 5 MW motor/generators connected to the Low-Pressure Spool, and a single 1 MW motor/generator on the High-Pressure Spool. The distributed fans can be used by the flight control to augment or replace the rudder function. At top of climb, the power extracted from the GTE for the fans is boosted by batteries. The design provides redundancy, and the capacity for boost means that the fans are designed to be able to provide additional thrust when necessary. These features can be leveraged in case of a fan or generator failure. This paper sets up the optimal control problem of setpoint determination for individual fans in the distributed propulsion system, accounting for electrical string efficiencies, saturations, and failures. The solution minimizes power consumption while maintaining thrust and torque on the airframe for maneuvering. Additionally, thrust that would have been lost due to temporary fan speed or power saturation is optimally redistributed to maintain overall desired thrust and torque on the aircraft. The power extraction range constraints derive from the gas turbine engine design and the small amount of variation allowed for the engine to maintain operability. The problem formulation allows the number and location of fan failures for which the thrust and torque can be maintained to be investigated, which has implications for certification. Simulations of a coordinated turn utilizing the distributed electric propulsion for yaw rate control under different failure scenarios demonstrate the robustness of the powertrain design to failures and help define its limitations.
Distributed Electric Propulsion↗
Optimal stochastic control.
Optimal stochastic control of small dynamic systems described by random differential equations, noting selective bibliography on several subjects
Wonham, W. M.↗
A method for optimizing control-free costs in systems with linear controllers.
Optimization of control independent cost functions in multidimensional system with linear controllers
Butman, S.↗
Optimal stochastic control.
Optimal stochastic control, discussing dynamic mathematical models described by differential equations
Wonham, W. M.↗
Computation of optimal singular controls
Optimal singular controls made nonsingular for decreasing epsilon values by adding integral quadratic functional of control to cost functional
Gershwin, S. B.↗
Applications of modern optimal control theory to environmental control of confined spaces and life support systems. I
Optimal temperature control for confined spaces and life support systems, using mathematical models of environmental control systems
Fan, L. T.↗
An optimal control approach to pilot/vehicle analysis and Neal-Smith criteria
The approach of Neal and Smith was merged with the advances in pilot modeling by means of optimal control techniques. While confirming the findings of Neal and Smith, a methodology that explicitly includes the pilot's objective in attitude tracking was developed. More importantly, the method yields the required system bandwidth along with a better pilot model directly applicable to closed-loop analysis of systems in any order.
Bacon, B. J.↗
Function space quasi-Newton algorithms for optimal control problems with bounded controls and singular arcs
Two existing function space algorithms, Davidon and projected gradient, are modified so that they may handle directly control variable inequality constraints. A third quasi-Newton type algorithm developed by C. G. Broyden is extended to optimal control problems. The Broyden algorithm is further modified so that it also may handle directly control variable inequality constraints. These methods along with a pure gradient and two conjugate gradient algorithms are simulated on three relatively simple yet representative bounded control problems, two of which have singular subarcs. Overall the Broyden algorithm was found to be superior. The most notable result of the study was the clear superiority of the Broyden and Davidon algorithms in producing a sharp interior control subarc.
Edge, E. R.↗
Discrete optimal control approach to a four-dimensional guidance problem near terminal areas
Description of a computer-oriented technique to generate the necessary control inputs to guide an aircraft in a given time from a given initial state to a prescribed final state subject to the constraints on airspeed, acceleration, and pitch and bank angles of the aircraft. A discrete-time mathematical model requiring five state variables and three control variables is obtained, assuming steady wind and zero sideslip. The guidance problem is posed as a discrete nonlinear optimal control problem with a cost functional of Bolza form. A solution technique for the control problem is investigated, and numerical examples are presented. It is believed that this approach should prove to be useful in automated air traffic control schemes near large terminal areas.
Nagarajan, N.↗
Application of an Optimal Control Allocation Scheme with Structural Load and Aero Heating Feedback for a Morphing Inflatable Aerodynamic Decelerator
Precision landing of large payloads on Mars presents a challenge to the Entry, Descent, and Landing (EDL) community. Previous studies indicated that by incorporating the capability for a Hypersonic Inflatable Aerodynamic Decelerator (HIAD) to morph during reentry would result in a more accurate landing footprint by allowing modulation of the lift- to-drag (L/D) vector directly instead of through bank angle control. However, morphing the HIAD shape for trajectory control may expose the HIAD to potential structural loads or aero heating concerns. In this study, the application of an optimal control allocation (OCA) technique was investigated that would to enable the morphing HIAD to maximize trajectory control capabilities while simultaneously keeping the structural loads and aero heating below some thresholds. This concept was demonstrated in a 3 degree-of-freedom (DOF) EDL simulation and provides basis for future research.
Bassett, George Z.↗
Multiobjective Optimization of Low-Energy Trajectories Using Optimal Control on Dynamical Channels
We introduce a computational method to design efficient low-energy trajectories by extracting initial solutions from dynamical channels formed by invariant manifolds, and improving these solutions through variational optimal control. We consider trajectories connecting two unstable periodic orbits in the circular restricted 3-body problem (CR3BP). Our method leverages dynamical channels to generate a range of solutions, and approximates the areto front for impulse and time of flight through a multiobjective optimization of these solutions based on primer vector theory. We demonstrate the application of our method to a libration orbit transfer in the Earth-Moon system.
trajectory design↗
The linear quadratic optimal control problem for infinite dimensional systems over an infinite horizon - Survey and examples
Available published results are surveyed for a special class of infinite-dimensional control systems whose evolution is characterized by a semigroup of operators of class C subscript zero. Emphasis is placed on an approach that clarifies the system-theoretic relationship among controllability, stabilizability, stability, and the existence of a solution to an associated operator equation of the Riccati type. Formulation of the optimal control problem is reviewed along with the asymptotic behavior of solutions to a general system of equations and several theorems concerning L2 stability. Examples are briefly discussed which involve second-order parabolic systems, first-order hyperbolic systems, and distributed boundary control.
Bensoussan, A.↗
Solution algorithms for non-linear singularly perturbed optimal control problems
The applicability and usefulness of several classical and other methods for solving the two-point boundary-value problem which arises in non-linear singularly perturbed optimal control are assessed. Specific algorithms of the Picard, Newton and averaging types are formally developed for this class of problem. The computational requirements associated with each algorithm are analysed and compared with the computational requirement of the method of matched asymptotic expansions. Approximate solutions to a linear and a non-linear problem are obtained by each method and compared.
Ardema, M. D.↗
A real time, FEM based optimal control algorithm and its implementation using parallel processing hardware (transistors) in a microprocessor environment
There is an evident need to discover a means of establishing reliable, implementable controls for systems that are plagued by nonlinear and, or uncertain, model dynamics. The development of a generic controller design tool for tough-to-control systems is reported. The method utilizes a moving grid, time infinite element based solution of the necessary conditions that describe an optimal controller for a system. The technique produces a discrete feedback controller. Real time laboratory experiments are now being conducted to demonstrate the viability of the method. The algorithm that results is being implemented in a microprocessor environment. Critical computational tasks are accomplished using a low cost, on-board, multiprocessor (INMOS T800 Transputers) and parallel processing. Progress to date validates the methodology presented. Applications of the technique to the control of highly flexible robotic appendages are suggested.
Patten, William Neff↗
Optimizing on-ramp merging for connected and automated vehicles: A hierarchical approach using deep reinforcement learning and optimal control
On-ramp merging for Connected and Automated Vehicles (CAVs) presents significant challenges in dynamic traffic environments. Traditional methods and recent learning-based approaches often fail to simultaneously address decision-making complexity and execution precision under fluctuating conditions. This study introduces a novel hierarchical framework that combines: (1) a high-level Deep Reinforcement Learning (DRL) module that coordinates merging sequences through Virtual Traffic Signals (VTS) with Yield/Green phases and (2) a low-level optimal controller generating collision-free speed trajectories via pseudospectral convex optimization. A convolutional autoencoder compresses high-dimensional traffic states to enhance responsiveness. Extensive simulations demonstrate a 12.5% improvement in mainline throughput a 28% reduction in emergency braking events, and 31.66% lower fuel consumption compared to baseline methods. Furthermore, the framework’s effectiveness in coordinating CAV merges highlights its potential for real-world deployment. Future work will extend validation to multi-lane scenarios with mixed traffic and large-scale multiple merging points.
Connected and automated vehicles↗
Simulation of a turbofan engine for evaluation of multivariable optimal control concepts
This paper describes the development and use of a real-time simulation of the F100-PW-100 turbofan engine. The simulation is being used in a multi-variable optimal controls research program using linear quadratic regulatory theory. The simulation is used to generate linear engine models at selected operating points and evaluate the control algorithm. The paper discusses a technique to reduce the order of the model and compares selected results between high and low order models.
Seldner, K.↗
Optimal control of distributed parameter elastic systems
This paper presents an analytical solution to the Riccati equation for self-adjoint systems such as beams, plates, strings and membranes moving in space, and shows how the optimal control law can be implemented using the given solution. It is then shown that there always exists a self-adjoint operator describing the distribution of potential energy if the state space is appropriately augmented. A beam-like gravity-stabilized satellite moving in a circular orbit around the earth is used to illustrate the main results in this paper.
Juang, J.-N.↗