An abstract ‘ bang - bang principle ’ and time - optimal boundary control of the heat equation 1

نویسندگان

  • Victor J. Mizel
  • Thomas I. Seidman
چکیده

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) the constraint set — without imposing any condition regarding the target state, in contrast to previous results.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Using Modified IPSO-SQP Algorithm to Solve Nonlinear Time Optimal Bang-Bang Control Problem

In this paper, an intelligent-gradient based algorithm is proposed to solve time optimal bang-bang control problem. The proposed algorithm is a combination of an intelligent algorithm called improved particle swarm optimization algorithm (IPSO) in the first stage of optimization process together with a gradient-based algorithm called successive quadratic programming method (SQP) in the second s...

متن کامل

COMPARISON BETWEEN MINIMUM AND NEAR MINIMUM TIME OPTIMAL CONTROL OF A FLEXIBLE SLEWING SPACECRAFT

In this paper, a minimum and near-minimum time optimal control laws are developed and compared for a rigid space platform with flexible links during an orientating maneuver with large angle of rotation. The control commands are considered as typical bang-bang with multiple symmetrical switches, the time optimal control solution for the rigid-body mode is obtained as a bang-bang function and app...

متن کامل

A Bang - Bang Principle of Time Optimal Internal Controls of the Heat Equation ∗

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...

متن کامل

Near-Minimum Time Optimal Control of Flexible Spacecraft during Slewing Maneuver

The rapid growth of space utilization requires extensive construction, and maintenance of space structures and satellites in orbit. &#10This will, in turn, substantiate application of robotic systems in space. In this paper, a near-minimum-time optimal control law is developed for a rigid space platform with flexible links during an orientating maneuver with large angle of rotation. The time op...

متن کامل

Time Optimal Control of the Heat Equation with Pointwise Control Constraints

Time optimal control problems for an internally controlled heat equation with pointwise control constraints are studied. By making use of Pontryagin’s maximum principle and a special kind of property for nontrivial solutions of the heat equation, we derive a bangbang property for time optimal control. Using the bang-bang property and establishing certain connections between timeand norm optimal...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007