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Results for “Optimal Control 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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Finite element solution of optimal control problems with state-control inequality constraints

It is demonstrated that the weak Hamiltonian finite-element formulation is amenable to the solution of optimal control problems with inequality constraints which are functions of both state and control variables. Difficult problems can be treated on account of the ease with which algebraic equations can be generated before having to specify the problem. These equations yield very accurate solutions. Owing to the sparse structure of the resulting Jacobian, computer solutions can be obtained quickly when the sparsity is exploited.

Bless, Robert R.↗
NASA NTRS1973

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.↗
NASA NTRS1976

Function-space quasi-Newton algorithms for optimal control problems with bounded controls and singular arcs

Two existing function-space quasi-Newton algorithms, the Davidon algorithm and the projected gradient algorithm, are modified so that they may handle directly control-variable inequality constraints. A third quasi-Newton-type algorithm, developed by Broyden, is extended to optimal control problems. The Broyden algorithm is further modified so that it may handle directly control-variable inequality constraints. From a computational viewpoint, dyadic operator implementation of quasi-Newton methods is shown to be superior to the integral kernel representation. The quasi-Newton methods, along with the steepest descent method and two conjugate gradient algorithms, are simulated on three relatively simple (yet representative) bounded control problems, two of which possess singular subarcs. Overall, the Broyden algorithm was found to be superior. The most notable result of the simulations was the clear superiority of the Broyden and Davidon algorithms in producing a sharp singular control subarc.

Edge, E. R.↗
NASA NTRS1976

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.↗
NASA NTRS1983

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.↗
NASA NTRS1979

Nonlinear singularly perturbed optimal control problems with singular arcs

Singular perturbation techniques are studied for dealing with singular arc problems by analyzing a relatively low-order but otherwise general system. This system encompasses many flight mechanic problems including Goddard's problem and a version of the minimum time-to-climb problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem.

Ardema, M. D.↗
NASA NTRS1974

Control of Finite-State, Finite Memory Stochastic Systems

A generalized problem of stochastic control is discussed in which multiple controllers with different data bases are present. The vehicle for the investigation is the finite state, finite memory (FSFM) stochastic control problem. Optimality conditions are obtained by deriving an equivalent deterministic optimal control problem. A FSFM minimum principle is obtained via the equivalent deterministic problem. The minimum principle suggests the development of a numerical optimization algorithm, the min-H algorithm. The relationship between the sufficiency of the minimum principle and the informational properties of the problem are investigated. A problem of hypothesis testing with 1-bit memory is investigated to illustrate the application of control theoretic techniques to information processing problems.

Sandell, Nils R.↗