Linear stochastic optimal control and estimation
Problem is defined as that of designing controls for linear time invariant system, which is disturbed by white noise, in such a way as to minimize quadratic performance index.
Geyser, L. C.↗
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Results for “stochastic optimal control”
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Linear stochastic optimal control and estimation problem
Problem involves design of controls for linear time-invariant system disturbed by white noise. Solution is Kalman filter coupled through set of optimal regulator gains to produce desired control signal. Key to solution is solving matrix Riccati differential equation. LSOCE effectively solves problem for wide range of practical applications. Program is written in FORTRAN IV for batch execution and has been implemented on IBM 360.
Geyser, L. C.↗
Some problems and some recent results in stochastic control.
Stochastic optimal control applications in dynamic programming for linear and nonlinear systems
DYNAMIC PROGRAMMING↗
On the application of deterministic optimization methods to stochastic control problems
A technique is presented by which deterministic optimization techniques, for example, the maximum principle of Pontriagin, can be applied to stochastic optimal control problems formulated around linear systems with Gaussian noises and general cost criteria. Using this technique, the stochastic nature of the problem is suppressed but for two expectation operations, the optimization being deterministic. The use of the technique in treating problems with quadratic and nonquadratic costs is illustrated.
Kramer, L. C.↗
On the application of deterministic optimization methods to stochastic control problems.
A technique is presented by which one can apply the Minimum Principle of Pontryagin to stochastic optimal control problems formulated around linear systems with Gaussian noises and general cost criteria. Using this technique, the stochastic nature of the problem is suppressed but for two expectation operations, the optimization being essentially deterministic. The technique is applied to systems with quadratic and non-quadratic costs to illustrate its use.
Kramer, L. C.↗
Optimal Discounted Stochastic Control for Diffusion Processes
Optimal cost discounted stochastic control for diffusion processes
Kushner, H. J.↗
On the separation theorem of stochastic control.
Optimal control and filtering problem for stochastic linear dynamic system reduced to independent equations
Wonham, W. M.↗
Sufficient conditions for the optimality of a stochastic control.
Sufficient conditions for optimal stochastic control of diffusion processes governed by vector equations satisfying local Lipschitz conditions
OPTIMAL CONTROL↗
A computational approach to optimal control of stochastic saturating systems.
Stochastic saturating systems optimal control computation, considering attitude control and tracking system design by elliptical differential equation of dynamic programming
Cashman, W. F.↗
On the status of optimal control and stability for stochastic systems.
Optimal control and stability for stochastic systems, viewing linear diffusion models based upon Gaussian-Markov process as finite dimensional linear system driven by white noise
SYSTEM STABILITY↗
Optimization of stochastic control processes with respect to probability on entering a target manifold
Optimization of stochastic control processes with respect to probability of entering target manifold in specific time interval
Luh, J. Y. S.↗
On stochastic control and optimal measurement strategies
The control of stochastic dynamic systems is studied with particular emphasis on those which influence the quality or nature of the measurements which are made to effect control. Four main areas are discussed: (1) the meaning of stochastic optimality and the means by which dynamic programming may be applied to solve a combined control/measurement problem; (2) a technique by which it is possible to apply deterministic methods, specifically the minimum principle, to the study of stochastic problems; (3) the methods described are applied to linear systems with Gaussian disturbances to study the structure of the resulting control system; and (4) several applications are considered.
Kramer, L. C.↗
A Unified Statistical Rain-Attenuation Model for Communication Link Fade Predictions and Optimal Stochastic Fade Control Design Using a Location-Dependent Rain-Statistic Database
A static and dynamic rain-attenuation model is presented which describes the statistics of attenuation on an arbitrarily specified satellite link for any location for which there are long-term rainfall statistics. The model may be used in the design of the optimal stochastic control algorithms to mitigate the effects of attenuation and maintain link reliability. A rain-statistics data base is compiled, which makes it possible to apply the model to any location in the continental U.S. with a resolution of 0-5 degrees in latitude and longitude. The model predictions are compared with experimental observations, showing good agreement.
Manning, Robert M.↗
Optimal control of saturating systems with stochastic inputs
Optimal control of nonlinear saturating systems with stochastic inputs
NONLINEAR SYSTEM↗
Application of quadratic optimization to supersonic inlet control
The application of linear stochastic optimal control theory to the design of the control system for the air intake (inlet) of a supersonic air-breathing propulsion system is discussed. The controls must maintain a stable inlet shock position in the presence of random airflow disturbances and prevent inlet unstart. Two different linear time invariant control systems are developed. One is designed to minimize a nonquadratic index, the expected frequency of inlet unstart, and the other is designed to minimize the mean square value of inlet shock motion. The quadratic equivalence principle is used to obtain the best linear controller that minimizes the nonquadratic performance index. The two systems are compared on the basis of unstart prevention, control effort requirements, and sensitivity to parameter variations.
Lehtinen, B.↗
Stochastic time-optimal control problems
Two types of stochastic time-optimal controls in a one-dimensional setting are considered. Multidimensional problems, in the case of complete state information available and the system modeled by stochastic differential equations, are studied under the formulation of minimizing the expected transient-response time. The necessary condition of optimality is the satisfaction for the value function of a parabolic partial differential equation with boundary conditions. The sufficient condition of optimality is also provided, based on Dynkin's formula. Finally, three examples are given.
Zhang, W.↗
Optimal stationary control of linear systems with control-dependent noise
Optimal stochastic control investigated for linear systems with driving noise intensity proportional to control input
Kleinman, D. L.↗
Analytical and experimental performance of optimal controller designs for a supersonic inlet
The techniques of modern optimal control theory were applied to the design of a control system for a supersonic inlet. The inlet control problem was approached as a linear stochastic optimal control problem using as the performance index the expected frequency of unstarts. The details of the formulation of the stochastic inlet control problem are presented. The computational procedures required to obtain optimal controller designs are discussed, and the analytically predicted performance of controllers designed for several different inlet conditions is tabulated. The experimental implementation of the optimal control laws is described, and the experimental results obtained in a supersonic wind tunnel are presented. The control laws were implemented with analog and digital computers. Comparisons are made between the experimental and analytically predicted performance results. Comparisons are also made between the results obtained with continuous analog computer controllers and discrete digital computer versions.
Zeller, J. R.↗