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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A practical approach to determine minimal quantum gate durations using amplitude-bounded quantum controls

Here, we present an iterative scheme to estimate the minimal duration in which a quantum gate can be realized while satisfying hardware constraints on the control pulse amplitudes. The scheme performs a sequence of unconstrained numerical optimal control cycles that each minimize the gate fidelity for a given gate duration alongside an additional penalty term for the control pulse amplitudes. After each cycle, the gate duration is adjusted based on the inverse of the resulting maximum control pulse amplitudes by re-scaling the dynamics to a new duration where control pulses satisfy the amplitude constraints. Those scaled controls then serve as an initial guess for the next unconstrained optimal control cycle, using the adjusted gate duration. We provide multiple numerical examples that each demonstrate fast convergence of the scheme toward a gate duration that is close to the quantum speed limit, given the control pulse amplitude bound. The proposed technique is agnostic to the underlying system and control Hamiltonian models, as well as the target unitary gate operation, making the time-scaling iteration an easy to implement and practically useful scheme for reducing the durations of quantum gate operations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

Optimal discrete-time LQR problems for parabolic systems with unbounded input: Approximation and convergence

An abstract approximation and convergence theory for the closed-loop solution of discrete-time linear-quadratic regulator problems for parabolic systems with unbounded input is developed. Under relatively mild stabilizability and detectability assumptions, functional analytic, operator techniques are used to demonstrate the norm convergence of Galerkin-based approximations to the optimal feedback control gains. The application of the general theory to a class of abstract boundary control systems is considered. Two examples, one involving the Neumann boundary control of a one-dimensional heat equation, and the other, the vibration control of a cantilevered viscoelastic beam via shear input at the free end, are discussed.

Rosen, I. G.↗
NASA NTRS1991

Aerospace plane guidance using time-scale decomposition - A geometric approach

A method is proposed for developing the necessary guidance logic to steer single-stage vehicles into orbit. The minimum-fuel ascent problem is first considered to analyze the effects of dynamic pressure, acceleration, and heating constraints on guidance systems to thereby develop the guidance logic. The optimal solution consists of behavior with two time scales, and the control law is used to develop near-optimal guidance. The solution uses the slow manifold to delineate the control for minimum-fuel reduced-order trajectory and a separate control for tracking the optimal reduced-order trajectory. A family of fast manifolds is then employed to resolve the tracking problem via the feedback linearization methodology from nonlinear geometric control theory. The two-time-scale decomposition is found to produce a near-optimal ascent by tracking the applicable state-constraint boundary, as well as to simplify the control-design task.

Van Buren, Mark A.↗
NASA NTRS1972

Lie theory and control systems defined on spheres

It is shown that in constructing a theory for the most elementary class of control problems defined on spheres, some results from the Lie theory play a natural role. To understand controllability, optimal control, and certain properties of stochastic equations, Lie theoretic ideas are needed. The framework considered here is the most natural departure from the usual linear system/vector space problems which have dominated control systems literature. For this reason results are compared with those previously available for the finite dimensional vector space case.

Brockett, R. W.↗
NASA NTRS1976

Stimulation of a turbofan engine for evaluation of multivariable optimal control concepts

The development of control systems for jet engines requires a real-time computer simulation. The simulation provides an effective tool for evaluating control concepts and problem areas prior to actual engine testing. The development and use of a real-time simulation of the Pratt and Whitney F100-PW100 turbofan engine is described. The simulation was used in a multi-variable optimal controls research program using linear quadratic regulator theory. The simulation is used to generate linear engine models at selected operating points and evaluate the control algorithm. To reduce the complexity of the design, it is desirable to reduce the order of the linear model. A technique to reduce the order of the model; is discussed. Selected results between high and low order models are compared. The LQR control algorithms can be programmed on digital computer. This computer will control the engine simulation over the desired flight envelope.

Seldner, K.↗
NASA NTRS1976

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.↗
NASA NTRS1978

The 14th Annual Conference on Manual Control

Human operator dynamics during actual manual control or while monitoring the automatic control systems involved in air-to-air tracking, automobile driving, the operator of undersea vehicles, and remote handling are examined. Optimal control models and the use of mathematical theory in representing man behavior in complex man machine system tasks are discussed with emphasis on eye/head tracking and scanning; perception and attention allocation; decision making; and motion simulation and effects.

Source record↗
NASA NTRS1983

Dynamics and control of forward swept wing aircraft

Aspects of non-zero differential game theory with application to multivariable control synthesis and optimal linear control law design using optimum parameter sensitivity analysis are discussed.

Schmidt, D. K.↗
NASA NTRS2003

Optimal Disturbances in Boundary Layers Subject to Streamwise Pressure Gradient

Laminar-turbulent transition in shear flows is still an enigma in the area of fluid mechanics. The conventional explanation of the phenomenon is based on the instability of the shear flow with respect to infinitesimal disturbances. The conventional hydrodynamic stability theory deals with the analysis of normal modes that might be unstable. The latter circumstance is accompanied by an exponential growth of the disturbances that might lead to laminar-turbulent transition. Nevertheless, in many cases, the transition scenario bypasses the exponential growth stage associated with the normal modes. This type of transition is called bypass transition. An understanding of the phenomenon has eluded us to this day. One possibility is that bypass transition is associated with so-called algebraic (non-modal) growth of disturbances in shear flows. In the present work, an analysis of the optimal disturbances/streamwise vortices associated with the transient growth mechanism is performed for boundary layers in the presence of a streamwise pressure gradient. The theory will provide the optimal spacing of the control elements in the spanwise direction and their placement in the streamwise direction.

Tumin, Anatoli↗
NASA NTRS1982

Difference equation state approximations for nonlinear hereditary control problems

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.

Rosen, I. G.↗
NASA NTRS1984

Difference equation state approximations for nonlinear hereditary control problems

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589

Rosen, I. G.↗
NASA NTRS1990

A comparison of time-optimal interception trajectories for the F-8 and F-15

The simulation results of a real time control algorithm for onboard computation of time-optimal intercept trajectories for the F-8 and F-15 aircraft are given. Due to the inherent aerodynamic and propulsion differences in the aircraft, there are major differences in their optimal trajectories. The significant difference in the two aircrafts are their flight envelopes. The F-8's optimal cruise velocity is thrust limited, while the F-15's optimal cruise velocity is at the intersection of the Mach and dynamic pressure constraint boundaries. This inherent difference necessitated the development of a proportional thrust controller for use as the F-15 approaches it's optimal cruise energy. Documented here is the application of singular perturbation theory to the trajectory optimization problem, along with a summary of the control algorithms. Numerical results for the two aircraft are compared to illustrate the performance of the minimum time algorithm, and to compute the resulting flight paths.

Calise, Anthony J.↗
NASA NTRS1980

Alternatives for jet engine control

Alternatives to linear quadratic regulator theory in the linear case are examined along with nonlinear modelling and optimization approaches for global control. Context for the studies has been set by the DYNGEN digital simulator and by models generated for various phases of the F100 Multivariable Control Synthesis Program. With respect to the linear alternatives, the multivariable frequency domain is stressed. Progress is reported in both the direct algebraic approach to exact model matching, by means of stimulating work on the basic computational issues, and in the indirect generalized Nyquist approach. With respect to nonlinear modelling and optimization, the emphasis is twofold: the development of analytical nonlinear models of the jet engine and the use of these models in conjunction with techniques of mathematical programming in order to study global control over nonincremental portions of the flight envelope. The possibility of using tensor methods is explored.

Sain, M. K.↗
NASA NTRS1986

Unified control/structure design and modeling research

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed.

Mingori, D. L.↗
NASA NTRS1989

Integrated control-system design via generalized LQG (GLQG) theory

Thirty years of control systems research has produced an enormous body of theoretical results in feedback synthesis. Yet such results see relatively little practical application, and there remains an unsettling gap between classical single-loop techniques (Nyquist, Bode, root locus, pole placement) and modern multivariable approaches (LQG and H infinity theory). Large scale, complex systems, such as high performance aircraft and flexible space structures, now demand efficient, reliable design of multivariable feedback controllers which optimally tradeoff performance against modeling accuracy, bandwidth, sensor noise, actuator power, and control law complexity. A methodology is described which encompasses numerous practical design constraints within a single unified formulation. The approach, which is based upon coupled systems or modified Riccati and Lyapunov equations, encompasses time-domain linear-quadratic-Gaussian theory and frequency-domain H theory, as well as classical objectives such as gain and phase margin via the Nyquist circle criterion. In addition, this approach encompasses the optimal projection approach to reduced-order controller design. The current status of the overall theory will be reviewed including both continuous-time and discrete-time (sampled-data) formulations.

Bernstein, Dennis S.↗
NASA NTRS1993

Guidance and flight control law development for hypersonic vehicles

During the third reporting period our efforts were focused on a reformulation of the optimal control problem involving active state-variable inequality constraints. In the reformulated problem the optimization is carried out not with respect to all controllers, but only with respect to asymptotic controllers leading to the state constraint boundary. Intimately connected with the traditional formulation is the fact that when the reduced solution for such problems lies on a state constraint boundary, the corresponding boundary layer transitions are of finite time in the stretched time scale. Thus, it has been impossible so far to apply the classical asymptotic boundary layer theory to such problems. Moreover, the traditional formulation leads to optimal controllers that are one-sided, that is, they break down when a disturbance throws the system on the prohibited side of the state constraint boundary.

Calise, A. J.↗