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A second-order variational method for discrete-time optimal control problems.
Discrete time optimal control problems solved by second order variational algorithm, developing recurrence relations for perturbation equations
On the Problem of Approximate Synthesis of Optimal Controls
Time optimal feedback control using extension of Hermes approximation theorem
An iterative technique for the computation of time optimal controls.
Iterative solution of time optimal control boundary value problem resulting from application of Pontryagin maximum principle
Time-optimal control of a bounded phase- coordinate process. II - High-order systems with multiple control inputs.
Time optimal control of bounded phase coordinate problem associated with large booster autopilot design, noting oscillatory system with two control inputs
DETERMINING THE SWITCHING CRITERION FOR TIME-OPTIMAL CONTROL
Switching criterion for time-optimal control
Sufficiency in linear time optimal control.
Sufficient conditions for linear time optimal control system on compact real intervals in Euclidean n space
ON THE UNIQUENESS OF TIME-OPTIMAL CONTROL FOR LINEAR PROCESSES
Uniqueness of time-optimal control for linear processes
AN APPLICATION OF TIME OPTIMAL CONTROL TO A FLEXIBLE LAUNCH VEHICLE
Application of time optimal control to a flexible launch vehicle - pitch controller
The use of a movable telescoping end mass system for the time-optimal control of spinning spacecraft
The time-optimal control of a spin-stabilized spacecraft with a movable telescoping appendage (boom) is considered analytically and numerically. The motion of a control mass at the end of the boom is determined such that the terminal time will be minimized for two-axis control of a symmetric spacecraft. The equations of rotational motion are linearized about the desired state of spin about the symmetry axis. The equations for the transverse angular velocity components have the form of a coupled two dimensional harmonic oscillator with boom motion as a control force. The control function which brings the system to the desired state is known to be a series of positive and negative pulses. If the initial state is such that the system can be driven to rest in a single switch, the responses, switching and final times, and required boom motion may be determined analytically. Some typical numerical results based on these solutions are discussed.
Variable time optimal control
Computational algorithms and techniques for solving variable time optimal control problems
Closed-loop, approximately time-optimal control of linear systems.
Closed-loop approximately time optimal control of linear systems based on eignevector scalar product solutions to Hamilton-Jacobi equation
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.
Synthesis of time-optimal control of a second- order nonlinear process.
Time optimal control of soft spring showing switching locus changes
Time-optimal control of gravity gradient satellites with disturbances
Time optimal control of gravity gradient satellites with disturbances
Synthesis of a time optimal control for a second order nonlinear process
Time optimal control for nonlinear second order system containing positive parameter and measurable control function
Two examples in the time optimal control theory of distributed parameter systems.
The behavior of hyperbolic and parabolic partial differential equations is contrasted by studying the point-to-point time-optimal control problem for the equation of heat conduction and the equation of motion of a vibrating string. A maximal principle is obtained for the time-optimal control of the one-dimensional heat equation, and it is proven that time optimal controls are weakly bang-bang. The bang-bang principle is proven to be invalid for hyperbolic equations because of the finite speed of wave propagation. In the case of boundary value control of the vibrating spring, the latter is demonstrated by deriving an explicit formula for the time optimal control.
A time optimal control study of a second-order linear system with delay.
Time optimal control function and optimal trajectories solved for second order linear system with constant time delay