Bang-bang Controls Research Articles

A numerical example of optimal bang-bang controls

The problem of computing optimal bang-bang controls for a nonlinear control system is discussed. It is shown that the method of replacing the optimal bang-bang control problem by a parameter optimization problem leads to an efficient algorithm. The problem of bringing a rotating rigid body to rest in minimum time is used to illustrate the theory. In this example, the parameter optimization problem reduces to a one-dimensional search.

Optimal bang-bang controls that maximize the probability of hitting a target manifold†

The optimal bang-bang control problem is considered as one of maximizing the probability that the state hits a target manifold before the outer boundary of a safe region in the control interval [0, T]; hitting the outer boundary corresponds to a breakdown of the control system, and T may or may not be finite. It is assumed that the dynamics of the controlled system can be expressed by a linear stochastic differential equation, and that all the state variables are accessible for direct measurements. Dynamic programming formulation leads to an initial and boundary value problem for the Bellman equation. A discussion is given for a simple scalar system. The initial and boundary value problem for a second-order plant 1/s 2 is solved by use of the finite-difference method. Some optimal switching curves are also demonstrated for different target manifolds.

An Introduction to Optimal Control Theory

Abstract : The report presents an introduction to some of the concepts and results currently popular in optimal control theory. The introduction is intended for someone acquainted with ordinary differential equations and real variables, but with no prior knowledge of control theory. The material covered includes the problems of controllability, controllability using special (e.g., bang-bang) controls, the geometry of linear time optimal processes, general existence of optimal controls, and the Pontryagin maximum principle. (Author)

On performance sensitivity of optimal control systems†

Formulae for the differential, with respect to plant parameters of an optimized performance index (performance sensitivity), are extended to include hard (instantaneous) as well as soft (isoperimetric) constraints on the control. In particular, this extends to discontinuous and bang-bang controls the Pagurek-Witscnhausen result on the equality of such differentials for open and closed-loop optimal systems

Stochastic bang-bang controls that maximize the expectation of first passage time†

The stochastic bang-bang control problem of maximizing the expectation of the first passage time of the state to the boundary of a certain safe region is considered. It is assumed that the dynamics of the system is described by a linear stochastic differential equation. By use of dynamic programming, the problem is reduced to a boundary-value problem of Dirichlet type for the Bellman equation. A difference scheme is applied in order to obtain the numerical solution of the boundary-value problem. It is found that for first-order systems the difference scheme gives excellent numerical results. Some switching curves are also obtained for a second-order plant l/s 2 with additive Gaussian white noises.

バング-バング制御と正規および正則条件

バング-バング制御と正規および正則条件