17,148 research outputs found
Algorithm for Optimal Mode Scheduling in Switched Systems
This paper considers the problem of computing the schedule of modes in a
switched dynamical system, that minimizes a cost functional defined on the
trajectory of the system's continuous state variable. A recent approach to such
optimal control problems consists of algorithms that alternate between
computing the optimal switching times between modes in a given sequence, and
updating the mode-sequence by inserting to it a finite number of new modes.
These algorithms have an inherent inefficiency due to their sparse update of
the mode-sequences, while spending most of the computing times on optimizing
with respect to the switching times for a given mode-sequence. This paper
proposes an algorithm that operates directly in the schedule space without
resorting to the timing optimization problem. It is based on the Armijo step
size along certain Gateaux derivatives of the performance functional, thereby
avoiding some of the computational difficulties associated with discrete
scheduling parameters. Its convergence to local minima as well as its rate of
convergence are proved, and a simulation example on a nonlinear system exhibits
quite a fast convergence
Consistent Approximations for the Optimal Control of Constrained Switched Systems
Though switched dynamical systems have shown great utility in modeling a
variety of physical phenomena, the construction of an optimal control of such
systems has proven difficult since it demands some type of optimal mode
scheduling. In this paper, we devise an algorithm for the computation of an
optimal control of constrained nonlinear switched dynamical systems. The
control parameter for such systems include a continuous-valued input and
discrete-valued input, where the latter corresponds to the mode of the switched
system that is active at a particular instance in time. Our approach, which we
prove converges to local minimizers of the constrained optimal control problem,
first relaxes the discrete-valued input, then performs traditional optimal
control, and then projects the constructed relaxed discrete-valued input back
to a pure discrete-valued input by employing an extension to the classical
Chattering Lemma that we prove. We extend this algorithm by formulating a
computationally implementable algorithm which works by discretizing the time
interval over which the switched dynamical system is defined. Importantly, we
prove that this implementable algorithm constructs a sequence of points by
recursive application that converge to the local minimizers of the original
constrained optimal control problem. Four simulation experiments are included
to validate the theoretical developments
Stabilizing Scheduling Policies for Networked Control Systems
This paper deals with the problem of allocating communication resources for
Networked Control Systems (NCSs). We consider an NCS consisting of a set of
discrete-time LTI plants whose stabilizing feedback loops are closed through a
shared communication channel. Due to a limited communication capacity of the
channel, not all plants can exchange information with their controllers at any
instant of time. We propose a method to find periodic scheduling policies under
which global asymptotic stability of each plant in the NCS is preserved. The
individual plants are represented as switched systems, and the NCS is expressed
as a weighted directed graph. We construct stabilizing scheduling policies by
employing cycles on the underlying weighted directed graph of the NCS that
satisfy appropriate contractivity conditions. We also discuss algorithmic
design of these cycles
Reliability of Dynamic Load Scheduling with Solar Forecast Scenarios
This paper presents and evaluates the performance of an optimal scheduling
algorithm that selects the on/off combinations and timing of a finite set of
dynamic electric loads on the basis of short term predictions of the power
delivery from a photovoltaic source. In the algorithm for optimal scheduling,
each load is modeled with a dynamic power profile that may be different for on
and off switching. Optimal scheduling is achieved by the evaluation of a
user-specified criterion function with possible power constraints. The
scheduling algorithm exploits the use of a moving finite time horizon and the
resulting finite number of scheduling combinations to achieve real-time
computation of the optimal timing and switching of loads. The moving time
horizon in the proposed optimal scheduling algorithm provides an opportunity to
use short term (time moving) predictions of solar power based on advection of
clouds detected in sky images. Advection, persistence, and perfect forecast
scenarios are used as input to the load scheduling algorithm to elucidate the
effect of forecast errors on mis-scheduling. The advection forecast creates
less events where the load demand is greater than the available solar energy,
as compared to persistence. Increasing the decision horizon leads to increasing
error and decreased efficiency of the system, measured as the amount of power
consumed by the aggregate loads normalized by total solar power. For a
standalone system with a real forecast, energy reserves are necessary to
provide the excess energy required by mis-scheduled loads. A method for battery
sizing is proposed for future work.Comment: 6 pager, 4 figures, Syscon 201
An energy-efficient distributed dynamic bandwidth allocation algorithm for Passive Optical Access Networks
The rapid deployment of passive optical access networks (PONs) increases the global energy consumption of networking infrastructure. This paper focuses on the minimization of energy consumption in Ethernet PONs (EPONs). We present an energy-efficient, distributed dynamic bandwidth allocation (DBA) algorithm able to power off the transmitter and receiver of an optical network unit (ONU) when there is no upstream or downstream traffic. Our main contribution is combining the advantages of a distributed DBA (namely, a smaller packet delay compared to centralized DBAs, due to less time being needed to allocate the transmission slot) with energy saving features (that come at a price of longer delays due to the longer queue waiting times when transmitters are switched off). The proposed algorithm analyzes the queue size of the ONUs in order to switch them to doze/sleep mode when there is no upstream/downstream traffic in the network, respectively. Our results show that we minimized the ONU energy consumption across a wide range of network loads while keeping delay bounded.Postprint (published version
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