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...

The problem of maximizing the duration of open loop operation of a perturbed linear time invariant system, while keeping performance errors within bound, is considered. It was shown in an earlier article that the optimal control for this problem is purely bang-bang if an associated switching function is non-zero almost everywhere. Sufficient conditions are derived in this article to guarantee t...

A principal technical result of this paper is that the onedimensional heat equation with boundary control is exactly null-controllable with control restricted to an arbitrary set E ⊂ [0, T ] of positive measure. A general abstract argument is presented to show that this implies the ‘bangbang’ property for time-optimal controls — i.e., such a control can take only extreme values of (the hull of)...

In this paper, we study a time optimal internal control problem governed by the heat equation in Ω × [0,∞). In the problem, the target set S is nonempty in L(Ω), the control set U is closed, bounded and nonempty in L(Ω) and control functions are taken from the set Uad = {u(·, t) : [0,∞) → L(Ω) measurable; u(·, t) ∈ U, a.e. in t }. We first establish a certain null controllability for the heat e...

<p style='text-indent:20px;'>In this paper, we propose a time-delayed HIV/AIDS-PrEP model which takes into account the delay on pre-exposure prophylaxis (PrEP) distribution and adherence by uninfected persons that are in high risk of HIV infection, analyze impact number individuals with infection. We prove existence stability two equilibrium points, for any positive time delay. After, an ...

where ƒ and g are smooth vector fields. Admissible controls are arbitrary measurable functions with values in [—1,4-1] and a trajectory of the system corresponding to a control u( ) is an absolutely continuous curve such that x(t) — f{x(t)) + u(t)g(x(t)) holds almost everywhere. In every optimal control problem the question of regularity of the solutions comes up naturally. The standard existen...

We consider the time optimal control problem, with a point target, for a class of infinite dimensional systems with a dynamics governed by an abstract Schrödinger type equation. The main results establish a Pontryagyn type maximum principle and give sufficient conditions for the bangbang property of optimal controls. The results are then applied to some systems governed by partial differential ...

This paper studies structural properties of the optimal resource allocation policy for singlequeue systems. Jobs arrive at a service facility and are sent one by one to a pool of computing resources for parallel processing. The facility poses a constraint on the maximum expected sojourn time of a job. A central decision maker allocates the servers dynamically to the facility. We consider two mo...

A multigrid scheme for the solution of constrained optimal control problems discretized by finite differences is presented. This scheme is based on a new relaxation procedure that satisfies the given constraints pointwise on the computational grid. In applications, the cases of distributed and boundary control problems with box constraints are considered. The efficient and robust computational ...

The control problem of time-optimal, rest-to-rest slewing of a flexible spacecraft through a large angle is considered. The flexible spacecraft is modeled as a linear, elastic, undamped, nongyroscopic system suitable for analysis of planar rotational maneuvers. Minimum-time open-loop planar maneuvers are studied. The control histories are found to be bang-bang with multiple switches in each con...