This paper describes a method for scheduling the events of a switched system to achieve an optimal performance. The approach has guarantees on convergence and computational complexity that parallel derivative-based iterative optimization but in the infinite dimensional, integer constrained setting of mode scheduling. In comparison to methods relying on mixed integer programming, the presented approach does not require a priori discretizations of time or state. Furthermore, in comparison to embedding and relaxation methods, every iteration of the algorithm returns a dynamically feasible solution. A large class of problems call for optimal mode scheduling. This paper considers a vehicle tracking problem and a high dimensional multimachine power network synchronization problem. For the power network example, both single horizon and receding horizon approaches prevent instability of the network, and the receding horizon approach does so at near real-time speeds on a single processor.
Power network regulation is presented as a benchmark problem for assessing and developing switched-mode optimal control approaches like mode scheduling, sliding window scheduling and modal design. Power network evolution modeled by the swing equations and coupled with controllable switching components is a nonlinear, high-dimensional problem. The proposed benchmark problem is the 54 generator IEEE 118 Bus Test Case composed of 106 states. Open questions include scalability in state and number of modes of operation, as well as real-time implementation, reliability, hysteresis, and timing constr…
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…
In this paper, a hierarchical distributed method consisting of two iterative procedures is proposed for optimal electric vehicle charging scheduling (EVCS) in the distribution grids. In the proposed method, the distribution system operator (DSO) aims at reducing the grid loss while satisfying the power flow constraints. This is achieved by a consensus-based iterative procedure with the EV aggregators (Aggs) located in the grid buses. The goal of aggregators, which are equipped with the battery energy storage (BES), is to reduce their electricity cost by optimal control of BES and EVs. As Aggs'…
We consider a single-hop switched queueing network. Amongst a plethora of applications, these networks have been used to model wireless networks and input queued switches. The MaxWeight scheduling policies have proved popular, chiefly, because they are throughput optimal and do not require explicit estimation of arrival rates. In this article, we prove the same throughput optimality property for a generalization of the MaxWeight policy called the MaxWeight-(α,g) policy. These throughput optimal, myopic scheduling policies allow for scheduling choices similar to those found in bandwidth sharing…
We consider the allocation of spectral and power resources to the mobiles (i.e., user equipment (UE)) in a cell every subframe (1 ms) for the Long Term Evolution (LTE) orthogonal frequency division multiple access (OFDMA) cellular network. To enable scheduling based on packet delays, we design a novel mechanism for inferring the packet delays approximately from the buffer status reports (BSR) transmitted by the UEs; the BSR reports only contain queue length information. We then consider a constrained optimization problem with a concave objective function - schedulers such as those based on uti…
We consider a switched network, a fairly general constrained queueing network model that has been used successfully to model the detailed packet-level dynamics in communication networks, such as input-queued switches and wireless networks. The main operational issue in this model is that of deciding which queues to serve, subject to certain constraints. In this paper, we study qualitative performance properties of the well known $α$-weighted scheduling policies. The stability, in the sense of positive recurrence, of these policies has been well understood. We establish exponential upper bounds…
This paper considers the problem of real-time mode scheduling in linear time-varying switched systems subject to a quadratic cost functional. The execution time of hybrid control algorithms is often prohibitive for real-time applications and typically may only be reduced at the expense of approximation accuracy. We address this trade-off by taking advantage of system linearity to formulate a projection-based approach so that no simulation is required during open-loop optimization. A numerical example shows how the proposed open-loop algorithm outperforms methods employing common numerical inte…
The problem of multi-area interchange scheduling under system uncertainty is considered. A new scheduling technique is proposed for a multi-proxy bus system based on stochastic optimization that captures uncertainty in renewable generation and stochastic load. In particular, the proposed algorithm iteratively optimizes the interface flows using a multidimensional demand and supply functions. Optimality and convergence are guaranteed for both synchronous and asynchronous scheduling under nominal assumptions.
We formulate and solve the H-SARA Problem, a Vehicle Routing and Appointment Scheduling Problem motivated by home services management. We assume that travel times, service durations, and customer cancellations are stochastic. We use a two-stage process that first generates teams and routes using a VRP Solver with optional extensions and then uses an MC Scheduler that determines expected arrival times by teams at customers. We further introduce two different models of cancellation and their associated impacts on routing and scheduling. Finally, we introduce the Route Fracture Metaheuristic that…
This paper deals with Networked Control Systems (NCSs) whose shared networks have limited communication capacity and are prone to data losses. We assume that among (N) plants, only (M < N) plants can communicate with their controllers at any time instant. In addition, a control input, at any time instant, is lost in a channel with a probability (p). Our contributions are threefold. First, we identify necessary and sufficient conditions on the open-loop and closed-loop dynamics of the plants that ensure existence of purely time-dependent periodic scheduling sequences under which stability of ea…
We consider a family of discrete time multihop switched queueing networks where each packet moves along a fixed route. In this setting, BackPressure is the canonical choice of scheduling policy; this policy has the virtues of possessing a maximal stability region and not requiring explicit knowledge of traffic arrival rates. BackPressure has certain structural weaknesses because implementation requires information about each route, and queueing delays can grow super-linearly with route length. For large networks, where packets over many routes are processed by a queue, or where packets over a …
This paper proposes an optimization strategy to assist utility operators to recover power distribution systems after large outages. Specifically, a mixed-integer linear programming (MILP) model is developed for co-optimizing crews, resources, and network operations. The MILP model coordinates damage isolation, network reconfiguration, distributed generator re-dispatch, and crew/resource logistics. In addition, a framework for integrating different types of photovoltaic (PV) systems in the restoration process is developed.} We consider two different types of crews, namely, line crews for damage…
Platooning of vehicles is a promising approach for reducing fuel consumption, increasing vehicle safety, and using road space more efficiently. We consider the important but difficult problem of assigning optimal routes and departure schedules to a collection of vehicles. We propose an iterative route-then-schedule heuristic for centralized planning that quickly converges to high-quality solutions. We also propose and analyze a collection of valid inequalities for the individual problems of assigning vehicles to routes and scheduling the times that vehicles traverse their routes. These inequal…
In this work, we present a new iterative exact solution algorithm for the weighted fair sequences problem, which is a recently introduced NP-hard sequencing problem with applications in diverse areas such as TV advertisement scheduling, periodic machine maintenance and real-time scheduling. In the problem we are given an upper bound on the allowed solution sequence length and a list of symbols. For each symbols, there is a positive weight and a number, which gives the minimum times the symbol has to occur in a feasible solution sequence. The goal is to find a feasible sequence, which minimizes…
Many optimization techniques evaluate solutions consecutively, where the next candidate for evaluation is determined by the results of previous evaluations. For example, these include iterative methods, "black box" optimization algorithms, simulated annealing, evolutionary algorithms and tabu search, to name a few. When solving an optimization problem, these algorithms evaluate a large number of solutions, which raises the following question: Is it possible to learn something about the optimum using these solutions? In this paper, we define this "learning" question in terms of a logistic regre…
This paper presents an iterative algorithm to compute a Robust Control Invariant (RCI) set, along with an invariance-inducing control law, for Linear Parameter-Varying (LPV) systems. As the real-time measurements of the scheduling parameters are typically available, in the presented formulation, we allow the RCI set description along with the invariance-inducing controller to be scheduling parameter dependent. The considered formulation thus leads to parameter-dependent conditions for the set invariance, which are replaced by sufficient Linear Matrix Inequality (LMI) conditions via Polya's rel…
Process Planning and Scheduling (PPS) is an essential and practical topic but a very intractable problem in manufacturing systems. Many research use iterative methods to solve such problems; however, they cannot achieve satisfactory results in both quality and computational speed. Other studies formulate scheduling problems as a graph coloring problem (GCP) or its extensions, but these formulations are limited to certain types of scheduling problems. In this paper, we propose a novel approach to formulate a general type of the PPS problem with resource allocation and process planning integrate…
A high number of electric vehicles (EVs) in the transportation sector necessitates an advanced scheduling framework for e-mobility ecosystem operation as a whole in order to overcome range anxiety and create a viable business model for charging stations (CSs). The framework must account for the stochastic nature of all stakeholders' operations, including EV drivers, CSs, and retailers and their mutual interactions. In this paper, a three-layer joint distributionally robust chance-constrained (DRCC) model is proposed to plan grid-to-vehicle (G2V) and vehicle-to-grid (V2G) operation in day-ahead…
