Forward decomposition algorithms for optimal control of a class of hybrid systems

Cho, Young C.; Cassandras, Christos G.; Pepyne, D.L.

doi:10.1002/rnc.595

Cited by 61 publications

(68 citation statements)

References 12 publications

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“…Proof: (By contradiction) Let us assume that jobs and are in the same block of the th machine on the optimal sample path, and . From (10), there are two possible cases: Case 1: : From (31), and from (35), . Case 2:…”

Section: B Controllable Machinesmentioning

confidence: 99%

“…In [8], the task of solving these problems was simplified by exploiting structural properties of the optimal sample path, and it was shown that, despite the fact that the objective function was non-convex and non-differentiable, the optimal sample path was unique. Further exploiting the structural properties of the optimal sample path, "backward-in-time" and "forward-in-time" algorithms based on the decomposition of the original non-convex and non-differentiable optimization problem into sets of smaller convex optimization problems with linear constraints were presented in [9] and [10], respectively. The "forward-in-time" algorithm presented in [10] was then improved by Zhang and Cassandras in [11].…”

mentioning

confidence: 99%

“…Further exploiting the structural properties of the optimal sample path, "backward-in-time" and "forward-in-time" algorithms based on the decomposition of the original non-convex and non-differentiable optimization problem into sets of smaller convex optimization problems with linear constraints were presented in [9] and [10], respectively. The "forward-in-time" algorithm presented in [10] was then improved by Zhang and Cassandras in [11].…”

mentioning

confidence: 99%

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Service Time Optimization of Mixed-Line Flow Shop Systems

Gokbayrak

Selvi

2010

IEEE Trans. Automat. Contr.

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Abstract-We consider deterministic mixed-line flow shop systems that are composed of controllable and uncontrollable machines. Arrival times and completion deadlines of jobs are assumed to be known, and they are processed in the order they arrive at the machines. We model these flow shops as serial networks of queues operating under a non-preemptive first-come-first-served policy, and employ max-plus algebra to characterize the system dynamics. Defining completion-time costs for jobs and service costs at controllable machines, a non-convex optimization problem is formulated where the control variables are the constrained service times at the controllable machines. In order to simplify this optimization problem, under some cost assumptions, we show that no waiting is observed on the optimal sample path at the downstream of the first controllable machine. We also present a method to decompose the optimization problem into convex subproblems. A solution algorithm utilizing these findings is proposed, and a numerical study is presented to evaluate the performance improvement due to this algorithm.

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Section: B Controllable Machinesmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Service Time Optimization of Mixed-Line Flow Shop Systems

Gokbayrak

Selvi

2010

IEEE Trans. Automat. Contr.

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“…In [6], [7], [8], and [9], the hybrid system framework is adopted to analyze a single-stage manufacturing process assuming a deterministic setting, i.e., a known job arrival schedule and controllable service times for all jobs. An efficient algorithm to determine the optimal service times for a class of single-stage systems is presented in [8].…”

Section: Introductionmentioning

confidence: 99%

“…An efficient algorithm to determine the optimal service times for a class of single-stage systems is presented in [8]. In [10], however, a stochastic model of a single-stage manufacturing system is studied, where the job arrivals are represented through a Poisson process with the control variable being the exponential service's process rate.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of a Two-Stage Stochastic Hybrid Manufacturing System with Poisson Arrivals and Exponential Service Times

Gokbayrak

Selvi

Proceedings of the 44th IEEE Conference on Decision and Control

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Abstract-Extending earlier work on single-stage stochastic hybrid system models, we consider a two-stage stochastic hybrid system where the job arrivals are represented through a Poisson process, and the service times required to attain a desired physical state are exponentially distributed dependent on the controllable process rates. For the case where the costs associated with the process rates and the inventory levels are non-decreasing convex, and the process rates take values from finite sets, we show that there exist threshold policies on both inventory levels for selecting the optimal process rates at each station.

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A novel multidimensional penalty‐free approach for constrained optimal control of switched control systems

Sun

Wang

et al. 2020

Intl J Robust & Nonlinear

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In this article, a novel multidimensional penalty-free method is proposed for the optimal control problem of switched control systems with path constraints. First, by introducing a Boolean vector, the switched control system and path constraints are transformed into affine forms. Typically, the complementary constrained method and piecewise constant function are used to relax and approximate the Boolean vector. Moreover, numerical methods are used to solve the approximated constrained optimal control problem (COCP), which relies on a discrete grid of the control function by using a piecewise linear function. Furthermore, the approximated COCP of affine control systems is equivalently transformed into a constrained dynamic parameter optimization problem by a refined time-scaling transformation. Finally, the global convergence of the proposed multidimensional penalty-free algorithm is proved and the feasibility of the algorithm is verified by numerical examples.

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Forward decomposition algorithms for optimal control of a class of hybrid systems

Cited by 61 publications

References 12 publications

Service Time Optimization of Mixed-Line Flow Shop Systems

Service Time Optimization of Mixed-Line Flow Shop Systems

Optimal Control of a Two-Stage Stochastic Hybrid Manufacturing System with Poisson Arrivals and Exponential Service Times

A novel multidimensional penalty‐free approach for constrained optimal control of switched control systems

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