classical control methods such as pontryagin maximum principle and bang-bang principle and other methods are not usually useful for solving opti-mal control systems (ocs) specially optimal control of nonlinear systems (ocns). in this paper, we introduce a new approach for solving ocns by using some combination of atomic measures. we define a criterion for controllability of lumped nonlinear con...

We provide sufficient optimality conditions for optimal control problems with bang-bang controls. Building on a structural assumption on the adjoint state, we additionally need a weak second-order condition. This second-order condition is formulated with functions from an extended critical cone, and it is equivalent to a formulation posed on measures supported on the set where the adjoint state...

The distance from the convex hull of the range of an n-dimensional vector-valued measure to the range of that measure is no more than an/2, where a is the largest (one-dimensional) mass of the atoms of the measure. The case a = 0 yields Lyapounov's Convexity Theorem; applications are given to the bisection problem and to the bang-bang principle of optimal control theory.

T.H. Jensen Feedback stabilization of the resistive wall mode is usually accomplished by using linear amplifiers. In this paper a study is made of a possibility of controlling resistive wall modes using switches instead of linear amplifiers, i.e., using bang-bang control. The motivation is that bangbang control systems may be cheaper than conventional feedback systems. A distinct disadvantage o...

We study bang–bang control problems that depend on a parameter p. For a fixed nominal parameter p0, it is assumed that the bang-bang control has finitely many switching points and satisfies second order sufficient conditions (SSC). SSC are formulated and checked in terms of an associated finitedimensional optimization problem w.r.t. the switching points and the free final time. We show that the...

In the paper, we consider ODE driven optimal control problems with bang-bang type extremals. The specific nature of bang-bang controls causes some difficulties in optimality and stability analysis. Usual convexity arguments like (strong) Legendre-Clebsch condition fail to hold, and the control discontinuity has to be taken into account. In recent years, substantial results on secondorder optima...

In this paper, the time and norm optimal control problems of controlled heat equations with a weight function are considered. For the time optimal problems, we study the following two cases: one is for equations with multi-domain control under null controllability, and the other is for equations under approximate null controllability. We prove the solvability, and obtain the bang-bang principle...

A large collection of financial contracts offering guaranteed minimum benefits are often posed as control prob4 lems, in which at any point in the solution domain, a control is able to take any one of an uncountable number of 5 values from the admissible set. Often, such contracts specify that the holder exerts control at a finite number of 6 deterministic times. The existence of an optimal ban...