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

Multiuser Switched Diversity Scheduling Schemes

Multiuser switched-diversity scheduling schemes were recently proposed in order to overcome the heavy feedback requirements of conventional opportunistic scheduling schemes by applying a threshold-based, distributed, and ordered scheduling mechanism. The main idea behind these schemes is that slight reduction in the prospected multiuser diversity gains is an acceptable trade-off for great savings in terms of required channel-state-information feedback messages. In this work, we characterize the achievable rate region of multiuser switched diversity systems and compare it with the rate region of full feedback multiuser diversity systems. We propose also a novel proportional fair multiuser switched-based scheduling scheme and we demonstrate that it can be optimized using a practical and distributed method to obtain the feedback thresholds. We finally demonstrate by numerical examples that switched-diversity scheduling schemes operate within 0.3 bits/sec/Hz from the ultimate network capacity of full feedback systems in Rayleigh fading conditions.Comment: Accepted at IEEE Transactions on Communications, to appear 2012, funded by NPRP grant 08-577-2-241 from QNR

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

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

Derivation of near-optimal pump schedules for water distribution by simulated annealing

The scheduling of pumps for clean water distribution is a partially discrete non-linear problem with many variables. The scheduling method described in this paper typically produces costs within 1% of a linear program-based solution, and can incorporate realistic non-linear costs that may be hard to incorporate in linear programming formulations. These costs include pump switching and maximum demand charges. A simplified model is derived from a standard hydraulic simulator. An initial schedule is produced by a descent method. Two-stage simulated annealing then produces solutions in a few minutes. Iterative recalibration ensures that the solution agrees closely with the results from a full hydraulic simulation