On Optimal Control of a Class of Partially Observed Discrete Event Systems

We are interested in a new class of optimal control problems for discrete event systems. We adopt the formalism of supervisory control theory (Proc. IEEE 77(1) (198O 89 and model the system as a finite state machine (FSM). Our control problem is characterized by the presence of uncontrollable as well as unobservable events, the notion of occurrence and control costs for events and a worst-case objective function. We first derive an observer for the partially unobservable FSM, which allows us to construct an approximation of the unobservable trajectory costs. We then de#ne the performance measure on this observer rather than on the original FSM itself. We then use the algorithm presented in Sengupta and Lafortune (SIAM J. Control Optim. 36(2)(19987 to synthesize an optimal submachine of the C-observer. This submachine leads to the desired supervisor for the system

Quantitatively-Optimal Communication Protocols for Decentralized Supervisory Control of Discrete-Event Systems

In this thesis, decentralized supervisory control problems which cannot be solved without some communication among the controllers are studied. Recent work has focused on finding minimal communication sets (events or state information) required to satisfy the specifications. A quantitative analysis for the decentralized supervisory control and communication problem is pursued through which an optimal communication strategy is obtained. Finding an optimal strategy for a controller in the decentralized control setting is challenging because the best strategy depends on the choices of other controllers, all of whom are also trying to optimize their own strategies. A locally-optimal strategy is one that minimizes the cost of the communication protocol for each controller. Two important solution concepts in game theory, namely Nash equilibrium and Pareto optimality, are used to analyze optimal interactions in multi-agent systems. These concepts are adapted for the decentralized supervisory control and communication problem. A communication protocol may help to realize the exact control solution in decentralized supervisory control problem; however, the cost may be high. In certain circumstances, it can be advantageous, from a cost perspective, to reduce communication, but incur a penalty for synthesizing an approximate control solution. An exploration of the trade-off between the cost and accuracy of a decentralized discrete-event control solution with synchronously communicating controllers in a multi-objective optimization problem is presented. A widely-used evolutionary algorithm (NSGA-II) is adapted to examine the set of Pareto-optimal solutions that arise for this family of decentralized discrete-event systems (DES). The decentralized control problem is synthesized first by considering synchronous communication among the controllers. In practice, there are non-negligible delays in communication channels which lead to undesirable effects on controller decisions. Recent work on modeling communication delay between controllers only considers the case when all observations are communicated. When this condition is relaxed, it may still be possible to formulate communicating decentralized controllers that can solve the control problem with reduced communications. Instead of synthesizing reduced communication protocols under bounded delay, a procedure is developed for testing protocols designed for synchronous communications (where not all observations are communicated) for their robustness under conditions when only an upper bound for channel delay is known. Finally a decentralized discrete-event control problem is defined in timed DES (TDES) with known upper-bound for communication delay. It is shown that the TDES control problem with bounded delay communication can be converted to an equivalent problem with no delay in communication. The latter problem can be solved using the algorithms proposed for untimed DES with synchronous communication

From Security Enforcement to Supervisory Control in Discrete Event Systems: Qualitative and Quantitative Analyses

Cyber-physical systems are technological systems that involve physical components that are monitored and controlled by multiple computational units that exchange information through a communication network. Examples of cyber-physical systems arise in transportation, power, smart manufacturing, and other classes of systems that have a large degree of automation. Analysis and control of cyber-physical systems is an active area of research. The increasing demands for safety, security and performance improvement of cyber-physical systems put stringent constraints on their design and necessitate the use of formal model-based methods to synthesize control strategies that provably enforce required properties. This dissertation focuses on the higher level control logic in cyber-physical systems using the framework of discrete event systems. It tackles two classes of problems for discrete event systems. The first class of problems is related to system security. This problem is formulated in terms of the information flow property of opacity. In this part of the dissertation, an interface-based approach called insertion/edit function is developed to enforce opacity under the potential inference of malicious intruders that may or may not know the implementation of the insertion/edit function. The focus is the synthesis of insertion/edit functions that solve the opacity enforcement problem in the framework of qualitative and quantitative games on finite graphs. The second problem treated in the dissertation is that of performance optimization in the context of supervisory control under partial observation. This problem is transformed to a two-player quantitative game and an information structure where the game is played is constructed. A novel approach to synthesize supervisors by solving the game is developed. The main contributions of this dissertation are grouped into the following five categories. (i) The transformation of the formulated opacity enforcement and supervisory control problems to games on finite graphs provides a systematic way of performing worst case analysis in design of discrete event systems. (ii) These games have state spaces that are as compact as possible using the notion of information states in each corresponding problem. (iii) A formal model-based approach is employed in the entire dissertation, which results in provably correct solutions. (iv) The approaches developed in this dissertation reveal the interconnection between control theory and formal methods. (v) The results in this dissertation are applicable to many types of cyber-physical systems with security-critical and performance-aware requirements.PHDElectrical and Computer EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/150002/1/jiyiding_1.pd