J.H. van Schuppen

Decentralized failure diagnosis for discrete-event systems with costly communication between diagnosers

Reliable supervisory control of engineering systems requires failure diagnosis algorithms for discrete-event systems. For large, modularly designed plants, such as communication networks, robustness considerations and limitations on the communication between local sensors lead to decentralized implementations of failure diagnosis algorithms. A trade-off has to be made between the speed of diagnosis and the cost of communication and computation. An algorithm is proposed for decentralized failure diagnosis with asymmetric communication in which Diagnoser 2 also estimates the observer state of Diagnoser 1 and sends only that subset of failure states which is relevant for the other diagnoser when this is useful for Diagnoser 1s control task of failure detection and diagnosis. This algorithm can help in suggesting practically implementable heuristic algorithms.

On the optimal control of stochastic systems with an exponential-of-integral performance index

Abstract In this paper a theory of optimal control is developed for stochastic systems whose performance is measured by the exponential of an integral form. Such a formulation of the cost function is shown to be not only general and useful but also analytically tractable. Starting with very general classes of stochastic systems, optimality conditions are obtained which exploit the multiplicative decomposability of the exponential-of-integral form. Specializing to partially observed systems of stochastic differential equations with Brownian Motion disturbances, optimality conditions are obtained which parallel those for systems with integral costs. Also treated are the special cases of linear systems with exponential of quadratic costs for which explicit optimal controls are obtainable. In addition, several general results of independent interest are obtained, which concern optimality of stochastic systems.

On Kalman filtering for conditionally Gaussian systems with random matrices

Abstract We consider linear stochastic systems with additive white Gaussian noise, with the added generality that the system matrices are random and adapted to the observation process. The main result of this paper is that in order for the standard Kalman filter to generate the conditional mean and conditional covariance of the conditionally Gaussian distributed state, it is sufficient for the random matrices to be finite with probability one at each time instant. This generalizes the best previous results available to date, to our knowledge, which require the more stringent hypothesis that the entries of the random matrices should possess finite second moments at each time instant. A significant application of the results of this paper is to the problem of recursive identification of the unknown parameters of a controlled linear stochastic system. In such problems, the observation matrix is typically generated by complicated nonlinear feedback, as for example in adaptive control, and the finiteness of the second moments is difficult, if not impossible, to establish, while the finiteness with probability one has been established in many applications.

The Synthesis of Time Optimal Supervisors by Using Heaps-of-Pieces

In many practical applications, we need to compute a nonblocking supervisor that not only complies with pre-specified safety requirements but also achieves a certain time optimal performance such as maximum throughput. In this paper, we first present a minimum-makespan supervisor synthesis problem. Then we show that the problem can be solved by a terminable algorithm, where the execution time of each string is computable by the theory of heaps-of-pieces. We also provide a timed supervisory control map that can implement the synthesized minimum-makespan sublanguage.

Coordination control of discrete-event systems

The concept of a coordinator is proposed for control of modular discrete-event systems. The coordinator makes all subsystems conditionally independent generators as defined in the paper. The coordinator receives part of the partial observations of the subsystems and its task is to satisfy the global part of the specification and of the nonblockingness. The complete supervisor then consists of the coordinator, its supervisor, and the local supervisors for the subsystems. An example of control of a distributed discrete-event system shows that a coordinator is necessary for achieving safety and nonblockingness.

Modular Control of Discrete-Event Systems With Coalgebra

Modular supervisory control of discrete-event systems, where the overall system is a synchronous (parallel) product of subsystems, is considered. The main results of this paper are formulations of sufficient conditions for the compatibility between the synchronous product and various operations stemming from supervisory control as supervised product and supremal controllable sublanguages. These results are generalized to the case of modules with partial observations: e.g., modular computation of supremal normal sublanguages is studied. Coalgebraic techniques based on the coinduction proof principle are used in our main results. Sufficient conditions are derived for modular to equal global control synthesis. An algorithmic procedure for checking the new conditions is proposed and the computational benefit of the modular approach is discussed and illustrated by comparing the time complexity of modular and monolithic computation.

Convergence results for continuous-time adaptive stochastic filtering algorithms

Abstract The adaptive stochastic filtering problem for Gaussian processes is considered. The self-tuning synthesis procedure is used to derive two algorithms for this problem. Almost sure convergence for the parameter estimate and the filtering error will be established. The convergence analysis is based on an almost-supermartingale convergence lemma that allows a stochastic Lyapunov-like approach.

Modular Supervisory Control with General Indecomposable Specification Languages

Modular supervisory control of discrete-event systems (DES), where the global DES is composed of local components that run concurrently, is considered. For supervisory control of large-scale modular DES the possibility of performing control-related computations locally (in components) is of utmost importance to computational complexity. Recently we have treated the case, where the specification language is decomposable into local specification languages and is included in the (global) plant language. In this paper the case of general specification languages that are neither necessarily decomposable nor contained in the global plant language is studied. Sufficient conditions are found under which any manipulation with the global plant is avoided for the computation of supremal controllable sublanguages of (global) indecomposable specification languages.

Tuning of Gaussian stochastic control systems

A closed-loop system consisting of a control system and an adaptive controller is called tuning for a specified control objective if the real system and the ideal system defined below achieve the same value for the control objective. The real system is the system consisting of the unknown control system in closed loop with the adaptive controller in which the parameters of the adaptive controller have been determined by identification under feedback or in closed loop. The ideal system is the system consisting of the unknown control system in closed loop with a controller in which the controller has been synthesized with knowledge of the unknown control system and such that the closed-loop system satisfies the control objective. Both the Gaussian stochastic control system with full observations and with partial observations are considered. The approach to the problem is based on stochastic realization theory for Gaussian systems. The control objectives of minimum variance control and pole placement are also given. Necessary conditions for tuning are discussed. >

On Nash equilibrium solutions in stochastic dynamic games

We consider Nash equilibrium solutions in linear, quadratic, Gaussian stochastic differential games where the two players have access to noise-corrupted information. A class of such games is identified for which each player has optimal solutions which are finite-dimensionally implementable. Utilizing these solutions, we propose, for either player, a finite-dimensionally implementable suboptimal solution to the general linear quadratic, Gaussian zero-sum stochastic differential game where both players have access to differing noise-corrupted observations. This solution possesses the property that it guarantees a computable lower bound for the performance of a player adopting it.