Proximate Time-Optimal Control of a Harmonic Oscillator
نویسندگان
چکیده
منابع مشابه
Proximate Time-Optimal Control of a Harmonic Oscillator
This paper considers near time-optimal setpoint tracking of a second-order oscillator. First, the time-optimal setpoint tracking feedback law is derived by recasting the problem as a regulator problem in the error coordinates with shifted control limits. This result is used to construct a derated approximation of the optimal control, PTOSω. Initially, the PTOSω is derived for a regulator contro...
متن کاملOptimal Finite-time Control of Positive Linear Discrete-time Systems
This paper considers solving optimization problem for linear discrete time systems such that closed-loop discrete-time system is positive (i.e., all of its state variables have non-negative values) and also finite-time stable. For this purpose, by considering a quadratic cost function, an optimal controller is designed such that in addition to minimizing the cost function, the positivity proper...
متن کاملPropagator for the time-dependent harmonic oscillator.
The propagator for a harmonic oscillator with general time-dependent mass and frequency matrices is constructed from the Van-Vleck/Morette formula. The explicit form of the classical action, and thus of the propagator, is found in terms of infinite series which are solutions to a set of differential equations. Those equations are found independently via the Hamilton-Jacobi equation, and by comp...
متن کاملSliding Mode Proximate Time-optimal Servomechanism
A discrete-time sliding mode proximate time-optimal servomechanism is developed using nonlinear sliding mode tangent to a reference velocity profile. Instead of a strong nonlinear function causing control chattering in discrete-time, a linear control is designed around the sliding surface. The resulting servomechanism delivers a bounded motion about the sliding surface even in the presence of p...
متن کاملEnergy Evolution in Time-Dependent Harmonic Oscillator
The theory of adiabatic invariants has a long history, and very important implications and applications in many different branches of physics, classically and quantally, but is rarely founded on rigorous results. Here we treat the general timedependent one-dimensional harmonic oscillator, whose Newton equation q̈+ω(t)q = 0 cannot be solved in general. We follow the time-evolution of an initial e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Transactions on Automatic Control
سال: 2018
ISSN: 0018-9286,1558-2523
DOI: 10.1109/tac.2017.2759059