David L. Pepyne

Optimal control of a class of hybrid systems

We present a modeling framework for hybrid systems intended to capture the interaction of event-driven and time-driven dynamics. This is motivated by the structure of many manufacturing environments where discrete entities (termed jobs) are processed through a network of workcenters so as to change their physical characteristics. Associated with each job is a temporal state subject to event-driven dynamics and a physical state subject to time-driven dynamics. Based on this framework, we formulate and analyze a class of optimal control problems for single-stage processes. First-order optimality conditions are derived and several properties of optimal state trajectories (sample paths) are identified which significantly simplify the task of obtaining explicit optimal control policies.

Optimal control of hybrid systems in manufacturing

Hybrid systems combine time-driven and event-driven dynamics. This is a natural framework for manufacturing processes: The physical characteristics of production parts undergo changes at various operations described by time-driven models, while the timing control of operations is described by event-driven models. Accordingly, in the framework we propose, manufactured parts are characterized by physical states (e.g. temperature, geometry) subject to time-driven dynamics and by temporal states (e.g., operation start and stop times) subject to event-driven dynamics. We first provide a tutorial introduction to this hybrid system framework and associated optimal control problems through a single-stage manufacturing process model. We then show how the structure of the problem can be exploited to decompose what is a hard nonsmooth, nonconvex optimization problem into a collection of simpler problems. Next, we present extensions to multistage manufacturing processes for which we develop solution algorithms that make use of Bezier approximation techniques. Emphasis is given to the issue of deriving solutions through efficient algorithms, and some explicit numerical results are included.

Optimal dispatching control for elevator systems during uppeak traffic

In this paper we develop optimal dispatching controllers for elevator systems during uppeak traffic. An uppeak traffic period arises when the bulk of the passenger traffic is moving from the first door up into the building (e.g., the start of a business day in an office building). The cars deliver the passengers and then return empty to the first floor to pick up more passengers. We show that the structure of the optimal dispatching policy minimizing the discounted or average passenger waiting time is a threshold-based policy. That is, the optimal policy is to dispatch an available car from the first floor when the number of passengers inside the car reaches or exceeds a threshold that depends on several factors including the passenger arrival rate, elevator performance capabilities, and the number of elevators available at the first floor. Since most elevator systems have sensors to determine the car locations and the number of passengers in each car, such a threshold policy is easily implemented. Our analysis is based on a Markov decision problem formulation with a batch service queueing model consisting of a single queue served by multiple finite-capacity bulk servers. We use dynamic programming techniques to obtain the structure of the optimal control policy and to derive some of its important properties. Several numerical examples are included to illustrate our results and to compare the optimal threshold policy to some known ad hoc approaches. Finally, since many transportation systems can be modeled as multiserver batch service queueing systems, we expect our results to be useful in controlling those systems as well.

Modeling, Analysis, and Optimal Control of a Class of HybridSystems

We propose a modeling framework for a class of hybrid systems which arise in many manufacturing environments and study related optimal control problems. In this framework, discrete entities have a state characterized by a temporal component whose evolution is described by event-driven dynamics, and a physical component whose evolution is described by time-driven dynamics. As a first step towards developing an optimal control theory for such hybrid systems, we formulate a problem consisting of a single-stage manufacturing process and use calculus of variations techniques to obtain structural properties and an explicit algorithm for deriving optimal policies.

An end-user-responsive sensor network architecture for hazardous weather detection, prediction and response

We present an architecture for a class of systems that perform distributed, collaborative, adaptive sensing (DCAS) of the atmosphere. Since the goal of these DCAS systems is to sense the atmosphere when and where the user needs are greatest, end-users naturally play the central role in determining how system resources (sensor targeting, computation, communication) are deployed. We describe the meteorological command and control components that lie at the heart of our testbed DCAS system, and provide timing measurements of component execution times. We then present a utility-based framework that determines how multiple end-user preferences are combined with policy considerations into utility functions that are used to allocate system resources in a manner that dynamically optimizes overall system performance. We also discuss open challenges in the networking and control of such end-user-driven systems.

Simple explanation of the no free lunch theorem of optimization

The No Free Lunch Theorem of Optimization (NFLT) is an impossibility theorem telling us that a general-purpose universal optimization strategy is impossible, and the only way one strategy can outperform another is if it is specialized to the structure of the specific problem under consideration. In this paper, a framework is presented for conceptualizing optimization problems that leads to useful insights and a simple explanation of the NFLT.

Vulnerability assessment and allocation of protection resources in power systems

In electrical power grids, there exists the potential for disturbances, even small ones, to trigger cascading collapse and blackout of large portions of the grid. In this paper we propose a simple cascading collapse model. The purpose of the model is to identify topological and component differences that can be exploited for the allocation of protection resources and in designing preventive maintenance schedules. Numerical examples are given to illustrate how the model can be used for protection enhancements and in designing preventive maintenance schedules that reduce vulnerabilities due to hidden failures.

Closed-loop architecture for distributed collaborative adaptive sensing of the atmosphere: meteorological command and control

Distributed Collaborative Adaptive Sensing (DCAS) of the atmosphere is a new paradigm for detecting and predicting hazardous weather using a dense network of short-range, low-powered radars to sense the lowest few kilometres of the earths atmosphere. DCAS systems are collaborative in that the beams from multiple radars are actively coordinated in a sense-and-respond manner to achieve greater sensitivity, precision and resolution than possible with a single radar. DCAS systems are adaptive in that the radars and their associated computing and communications infrastructure are dynamically reconfigured in response to changing weather conditions and end-user needs. This paper describes an end-to-end DCAS architecture and evaluates the performance of the system in an operational testbed with actual weather events and end-user considerations driving the system. Our results demonstrate how the architecture is capable of real-time data processing, optimisation of radar control and sensing of the atmosphere in a manner that maximises end-user utility.

Optimal control of a two-stage hybrid manufacturing system model

Extending previous work for an optimal control problem of a single-stage system, we consider a two-stage manufacturing system where each job has a physical state characterized by time-driven dynamics and a temporal state by event-driven dynamics. We derive necessary conditions for optimality and develop some new algorithms for explicit solution of the problem that make use of Bezier approximation techniques. In addition, we establish some properties of the optimal control sequence that have interesting implications.

Design and implementation of an adaptive dispatching controller for elevator systems during uppeak traffic

We design a dispatching controller for elevator systems during uppeak passenger traffic with the ability to adapt to changing operating conditions. The design of this controller is motivated by our previous paper (1997) where we proved that for a queuing model of the uppeak dispatching problem a threshold policy is optimal (in the sense of minimizing the average passenger waiting time) with threshold parameters that depend on the passenger arrival rate. The controller, which we call the concurrent estimation dispatching algorithm (CEDA), uses concurrent estimation techniques for discrete-event systems. The CEDA allows us to observe the elevator system while it operates under some arbitrary thresholds, and concurrently estimate, in an unobtrusive way, what the waiting time would have been had the system operated under a set of different thresholds. These concurrently estimated waiting times are used to adapt the operating thresholds to match the elevator service rate to a changing passenger arrival rate. Implementation issues relating to the limited state information provided by actual elevator systems are resolved in a way that maintains modest computational requirements and avoids the need for supplemental sensors beyond those already typically provided. Numerical performance results show the advantages of the CEDA over currently used dispatching algorithms for uppeak.