A discrete event system (DES) is a dynamic system whose state transitions are caused by physical phenomena, called events, occurring abruptly at unknown irregular intervals. Examples include manufacturing systems, computer and communication networks and traffic systems. The supervisory control theory (SCT) is recognized as one of effective tools for the analysis and control of the DESs. In SCT, the control objective is to restrict the plant behavior such that(s.t.) it remains confined within a specific range. Recently, there has also been many studies considering the optimal supervisory control problem (OSCP) in which the control objective is to restrict the system behavior so that a certain cost function defined along the trajectory of the system is optimized. In the OSCP, it is impossible to optimize the system for all aspects. For example, in order to complete a task in short time, we have to consume a lot of energy. Thus, we have to decide what we optimize and then define the cost function which is suitable to our purpose.
In this dissertation, we study optimal control problems for the DESs. First, we formulate the OSCP with the cost function using the disabling costs of the events and the penalties of the states which is useful in the system design. Then, we devise an algorithm to design the optimal nonblocking supervisor to solve the problem. Since the proposed algorithm has polynomial-order computational complexity, we can solve the problem efficiently. Then, we formulate the power distribution network restoration problem to an OSCP and solve it using the proposed algorithm as a case study.
Next, we extend the results to the partial observation cases. In the OSCP under partial observation, the optimal supervisor for the given DES has restrictions that it must makes the controlled system's behavior observable as well as it is a nonblocking supervisor. Although the proposed algorithm to design optimal nonblocking supervisor (ONS) under partial observation doesn't have polynomial-order computational complexity, we can design the ONS systematically with it. In addition, we propose an algorithm to design ONS for the decentralized supervisory control problem. Then, we extend the net cost which is the objective function of the optimal problem so that we can consider all the cost for setting up the control mechanism and sensing mechanism.
For optimization of the system operations, we introduce the multi-constrained optimal supervisory control problem (MOSCP). We propose an algorithm to solve the MOSCP. If we use the algorithm, we can design the suboptimal nonblocking supervisors in ascending order of the cost. Moreover, we can solve the restricted optimal supervisory control problem with the proposed algorithm with a little modifications. The usefulness of the our results for the MOSCP is demonstrated by solving the multi-constrained QoS routing problem efficiently with our results. Using our results, we obtain the higher performance with much shorter calculation time than the existing results developed by others.
Finally, we investigate the OSCP using the enabling costs of the events which is the function of the overheads of the states. The optimal supervisor in this approach has restrictions that it must be an all-marking supervisor. We introduce an exact algorithm to design the optimal all-marking supervisor (OAMS) for the given DES with analysis of the characteristic of the OAMSs. However, since the computational complexity of the exact algorithm is exponential, it is not practical for the DESs with many marker states. Therefore, we devise a heuristic algorithm to design the OAMS. Using the heuristic, we solve the optimal feeder routing problem for the power distribution system planning as a case study. We expect that the proposed heuristic can be used for the network design such as the communication network and the highway system design.
관리제어이론은 생산시스템, 통신망, 교통시스템 등의 복잡한 첨단시스템의 체계적 분석과 제어에 매우 효과적인 이론으로 각광받고 있으며, 관리제어이론에서의 일반적인 제어목적은 시스템의 동작특성을 우리가 원하는 특정범위 이내로 제한시키는 것이었다. 그러나 근래에는 비용함수를 정의하여 비용함수가 최소가 되도록 시스템의 동작특성을 제한하는 최적관리제어기법에 관한 연구가 많이 진행되고 있다. 이에 본 논문에서는 다양한 비용함수를 정의하고 그에 따른 최적관리제어기 설계기법을 제안하였다. 우선, 시스템의 설계단계에서 유용하게 쓰일 수 있도록 하기 위하여 사건들의 억제비용과 상태들의 벌칙비용을 이용한 비용함수를 정의하고 최적비막힘관리제어기 설계기법을 제안하고 제안된 기법의 응용 예로서 전력배전시스템에 고장이 발생한 경우 최적의 복구방안을 찾는 방법을 제시하였다. 또 관측불가능한 사건이 존재하는 경우에도 적용할 수 있도록 제안된 기법을 확장하고, 이를 변형시켜 분산관리제어기법에도 응용이 가능하도록 하였다. 다음으로 시스템의 운영단계에서 유용하게 쓰일 수 있도록 복수개의 비용함수를 고려한 다중제약 최적관리제어문제를 소개하고 복수개의 비용함수가 주어진 제약조건을 모두 만족시키는 관리제어기를 설계할 수 있는 설계기법을 제안하였다. 제안된 기법의 유용성을 검증하기 위해서 다중제약 QoS 라우팅문제를 해결하였으며 모의실험을 통해 기존의 다중제약 QoS 라우팅방법에 비해 훨씬 짧은 시간안에 주어진 모든 QoS 조건을 만족시키는 경로를 찾아낼 수 있음을 보였다. 마지막으로 전력시스템, 고속도로망, 통신망 등의 설계에 유용하게 쓰일 수 있도록 하기 위하여 상태들의 벌칙비용과 이들의 함수로 주어지는 사건의 인가비용을 이용한 비용함수를 정의하고 모든 표기상태들을 초기상태로부터 도달가능하게 하는 관리제어기들 중 최소의 비용함수를 갖는 관리제어기를 설계할 수 있는 설계기법을 제안하였다. 제안된 설계기법의 유용성 검증을 위해 제안된 기법을 송전선의 최적연결 문제에 적용하여 많은 부하들이 존재하는 대규모 송전시스템 설계문제를 효율적으로 해결할 수 있음을 보였다.