Design and analysis of fuzzy schedulers using ... - Semantic Scholar
1999 Third International Conference on Knowledge-BasedIntelligent Information Engineeing Systems, 3 I It Aug- Id Sept 1999, Adelaide, Australia
Design and Analysis of Fuzzy Schedulers using Fuzzy Lyapunov Synthesis Michael Margaliot Gideon Langholz Department of Electrical Engineering - Systems Tel Aviv University, Israel 69978 michaelm,[email protected] Keywords: fuzzy scheduling, fuzzy Lyapunov synthesis, computing with words.
Abstract Recently, the authors suggested a new approach to the design offuzzy control rules. The method, referred to as fuzzy Lyapunov synthesis, extends classical Lyapunov synthesis to the domain of "computing with words", and allows the systematic, instead of heuristic, design and analysis of fuzzy controllers given linguistic information about the plant. In this papes we use the fuzzy Lyapunov synthesis method to design and analyze the rule-base of a fuzzy scheduler. We show thatfuzzy rules, previously suggested based on heuristics, can be derived systematically and, therefore, that the entire process can be
automated. This may lead to a novel "computingwith words '' algorithm: the input is linguistic information concerning the "plant'' and the "control" objective, and the output is a suitable fuzzy rule-base.
ulers, where scheduler 1 is considered better than scheduler 2 if it yields a smaller value of the performance measure. Hence, the scheduling problem is to find a scheduler that stabilizes the system while minimizing the performance measure. Scheduling a fixed number of parts with known arrival and processing times is referred to as static scheduling. On the other hand, if at time t the scheduler determines which part-type to process next based on quantities that are known at time t (e.g., the current state of the machines' buffers), then the scheduling is referred to as dynamic scheduling. Perkins and Kumar [5] showed that the problem of dynamic scheduling can be handled in a distributed manner, that is, the scheduling decisions of machine Mi are based only on the properties and the current state of machine Mi regardless of the other machines in the system. Thus, the problem can be decomposed into a set of independent single-machinescheduling problems.
1 Introduction Consider a manufacturing system consisting of several machines that process parts of different types. Parts of type i (i = 1,2, ...,P ) must be processed in order by a series of machines, say machine Mi, for Ti,il seconds, then machine Mi, for ~ i , i , seconds, and so on until machine Mi, where the production of the parts is completed. Because each of the machines can only process one part at a time, each machine must also contain a buffer, for each part-type it inputs, which stores the parts that entered the machine and are waiting to be processed. A scheduler is an algorithm that specifies the order in which the machines should process the waiting parts. To assure adequate performance, schedulers must also guarantee that the buffer levels in the machines remain bounded. A scheduler that guarantees this property is called stable. Various performance measures (e.g.. the average load of the buffers) can be used to rate different sched-
, .
Figure 1. scheduler
Machine
Single-machine
.
,
dynamic
Fig. 1 depicts the organization of a single-machine dynamic scheduler. Here, x ( t ) = ( z l ( t )... z p ( t ) ) , where zi(t) is the level of buffer zi at time t , and i* is the index of the part-type to process next. Note
207
1999 Third International Conference on Knowledge-BasedIntelligent information Engineeing Systems, 31'' Aug-1" Sept 1999, Adelaide, Australia
C < 00, for all t > 0, then the scheduler is called sta-
that the scheduler can be considered as a closed-loop decision-maker or controller. Passino and Yurkovich [4] studied a singlemachine dynamic fuzzy scheduler governed by a set of fuzzy rules derived based on the heuristics: At time t, choose to process part-type: i* = a r g m g x ( x i ( t ) ) . Hence, a typical rule in this case is a (for a machine with three buffers):
ble. Clearly, a necessary condition for the existence of a stable scheduler is:
Design and Analysis of Fuzzy Schedulers using Fuzzy Lyapunov Synthesis Michael Margaliot Gideon Langholz Department of Electrical Engineering - Systems Tel Aviv University, Israel 69978 michaelm,[email protected] Keywords: fuzzy scheduling, fuzzy Lyapunov synthesis, computing with words.
Abstract Recently, the authors suggested a new approach to the design offuzzy control rules. The method, referred to as fuzzy Lyapunov synthesis, extends classical Lyapunov synthesis to the domain of "computing with words", and allows the systematic, instead of heuristic, design and analysis of fuzzy controllers given linguistic information about the plant. In this papes we use the fuzzy Lyapunov synthesis method to design and analyze the rule-base of a fuzzy scheduler. We show thatfuzzy rules, previously suggested based on heuristics, can be derived systematically and, therefore, that the entire process can be
automated. This may lead to a novel "computingwith words '' algorithm: the input is linguistic information concerning the "plant'' and the "control" objective, and the output is a suitable fuzzy rule-base.
ulers, where scheduler 1 is considered better than scheduler 2 if it yields a smaller value of the performance measure. Hence, the scheduling problem is to find a scheduler that stabilizes the system while minimizing the performance measure. Scheduling a fixed number of parts with known arrival and processing times is referred to as static scheduling. On the other hand, if at time t the scheduler determines which part-type to process next based on quantities that are known at time t (e.g., the current state of the machines' buffers), then the scheduling is referred to as dynamic scheduling. Perkins and Kumar [5] showed that the problem of dynamic scheduling can be handled in a distributed manner, that is, the scheduling decisions of machine Mi are based only on the properties and the current state of machine Mi regardless of the other machines in the system. Thus, the problem can be decomposed into a set of independent single-machinescheduling problems.
1 Introduction Consider a manufacturing system consisting of several machines that process parts of different types. Parts of type i (i = 1,2, ...,P ) must be processed in order by a series of machines, say machine Mi, for Ti,il seconds, then machine Mi, for ~ i , i , seconds, and so on until machine Mi, where the production of the parts is completed. Because each of the machines can only process one part at a time, each machine must also contain a buffer, for each part-type it inputs, which stores the parts that entered the machine and are waiting to be processed. A scheduler is an algorithm that specifies the order in which the machines should process the waiting parts. To assure adequate performance, schedulers must also guarantee that the buffer levels in the machines remain bounded. A scheduler that guarantees this property is called stable. Various performance measures (e.g.. the average load of the buffers) can be used to rate different sched-
, .
Figure 1. scheduler
Machine
Single-machine
.
,
dynamic
Fig. 1 depicts the organization of a single-machine dynamic scheduler. Here, x ( t ) = ( z l ( t )... z p ( t ) ) , where zi(t) is the level of buffer zi at time t , and i* is the index of the part-type to process next. Note
207
1999 Third International Conference on Knowledge-BasedIntelligent information Engineeing Systems, 31'' Aug-1" Sept 1999, Adelaide, Australia
C < 00, for all t > 0, then the scheduler is called sta-
that the scheduler can be considered as a closed-loop decision-maker or controller. Passino and Yurkovich [4] studied a singlemachine dynamic fuzzy scheduler governed by a set of fuzzy rules derived based on the heuristics: At time t, choose to process part-type: i* = a r g m g x ( x i ( t ) ) . Hence, a typical rule in this case is a (for a machine with three buffers):
ble. Clearly, a necessary condition for the existence of a stable scheduler is:
