Direct applications of mathematical programming techniques in numerical solutions of optimal control problems are reviewed The types of control systems discussed include linear, nonlinear, continuous- and discrete-time, deterministic, stochastic, and distributed-parameter systems The areas of application include aerospace trajectory optimization and rendezvous problems, computer control of processes, and nuclear reactor control problems A classified bibliography is included

Applications of mathematical programming techniques in optimal control: A survey

This is a review of the investigations into the field of optimum shock and vibration isolation, including the mathematical foundations of both optimal open-loop and optimal feedback isolation systems. This survey covers the literature from the initial studies to the present.

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Review: Optimal Shock and Vibration Isolation

The following paper discusses the optimal control of these systems, characterized by a set of n first-order state equations, in which performance is measured by Chebyshev-type functional over the state trajectory. The determination of control functions that minimize the maximum value of a given state function over the trajectory interval is shown to follow directly from the development of a differential minimax cost. The differential minimax cost allows the problem to be formulated as a coordinate minimization in the cost-augmented state space, and leads to the consideration of a set of suboptimal problems whose solutions are shown to converge to the required minimax control. The modifications required for the application of standard variational techniques to the reformulated problem are also discussed. The main result of this study is the demonstration of equivalence between the Chebyshev-type control problem and a more conventional Mayer-type formulation.

Optimal control with minimax cost

The problem of controlling the spatial power distribution in a reactor core under changing load conditions is formulated as a nonlinear optimization problem. The one-dimensional distributed core model is approximated by using finite differences to obtain a set of nonlinear ordinary differential equations. Linear programming is then used in an iterative scheme to determine the optimum control rod strategy.

A Nonlinear Dynamic Optimization Technique for Controlling Xenon Induced Oscillations in Large Nuclear Reactors

Optimization of Shock Isolation Systems

A standard linear programming code may be used to compute optimal trajectories for a linear discrete-time system with respect to a minimax criterion on either state or control trajectories. Arbitrary linear constraints, equality or inequality, constant or time-varying, may be placed on linear combinations of the state or control variables along their trajectories or at a fixed terminal time. An important feature of the method is that the dimension of the linear programming problem is independent of the dimension of the state space but depends entirely on the numbers of control variables, constraints, and time intervals. Optimal trajectories for a 21st- order system have been calculated in a few minutes of computer time.

Optimal control trajectories with minimax objective functions by linear programming

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Optimal control trajectories with minimax objective functions by linear programming