The filtering equations revisited

The problem of nonlinear filtering has engendered a surprising number of mathematical techniques for its treatment. A notable example is the change-of--probability-measure method originally introduced by Kallianpur and Striebel to derive the filtering equations and the Bayes-like formula that bears their names. More recent work, however, has generally preferred other methods. In this paper, we reconsider the change-of-measure approach to the derivation of the filtering equations and show that many of the technical conditions present in previous work can be relaxed. The filtering equations are established for general Markov signal processes that can be described by a martingale-problem formulation. Two specific applications are treated

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Reduction of affine systems on polytopes

Consider an affine system with a polytope as state set. State trajectories are terminated when they reach a facet of the polytope and attempt to exit. The realization problem is considered based on the behavior of the system, i.e. the set of input-output trajectories on time-intervals of either finite or infinite length. The state set can be affinely reduced due to non-observability if and only if a subspace of the classical unobservable subspace, characterized using the normal vectors of the exit facets, is nontrivial

Maximally permissive coordinated distributed supervisory control of nondeterministic discrete-event systems

In supervisor synthesis for discrete-event systems achieving nonblockingness is a major challenge for a large system. To overcome it we present an approach to synthesize a deterministic coordinated distributed supervisor under partial observation, where the plant is modeled by a collection of nondeterministic finite-state automata and the requirement is modeled by a collection of deterministic finite-state automata. Then we provide a sufficient condition to ensure the maximal permissiveness of a coordinated distributed supervisor generated by the proposed synthesis approach. (C) 2012 Elsevier Ltd. All rights reserve

Control to facet by piecewise-affine output feedback

The control-to-facet problem plays an important role in the design of feedback controllers for piecewise-affine hybrid systems on polytopes. In the litera- ture, necessary and sufficient conditions for solvability by static state feedback exist. In this paper, we extend these results to the case of continuous piecewise-affine out- put feedback. For the construction of a controller, a triangulation of the output polytope is made, that satisfies additional conditions, to guarantee compatibility with the induced subdivision of the state polytope. In the state feedback case, the use of this special type of triangulations was not required

Control to facet by piecewise-affine output feedback

The control-to-facet problem plays an important role in the design of feedback controllers for piecewise-affine hybrid systems on polytopes. In the literature, necessary conditions and sufficient conditions for solvability by static state feedback exist. In this paper, we extend these results to the case of continuous piecewise-affine static output feedback. For the construction of a controller, a triangulation of the output polytope is made which satisfies additional conditions to guarantee compatibility with the induced subdivision of the state polytope. In the state feedback case, the use of this special type of triangulation is not required

The synthesis of time optimal supervisors by using heaps-of-pieces

In many practical applications we are asked to compute a nonblocking supervisor that not only complies with some prescribed safety and liveness requirements but also achieve a certain time optimal performance such as throughput. In this paper we first introduce the concept of supremal minimum-time controllable sublanguage and define a minimumtime supervisory control problem, where the plant is modeled as a finite collection of finite-state automata, whose events are associated with weights, which represent their respective execution time. Then we show that the supremal minimum-time controllable sublanguage can be obtained by a terminable algorithm, where the execution time of each string is computed by using a technique extended from the theory of heaps-of-pieces

Coordinated distributed supervisory control

In supervisor synthesis achieving nonblockingness is a major computational challenge when a target system consists of a large number of local components. To overcome this difficulty we propose a coordinated distributed supervisor synthesis approach, where specifications are enforced by local supervisors. To avoid conflicting among local supervisors, coordinators are created based on automaton abstraction

Supervisory control of partially observed weighted discrete-event systems

When the Ramadge-Wonham supervisory control paradigm is applied to practical problems, it is desirable to require a closed-loop system be finitely coreachable in the sense that a marker state can be reached within a finite number of transitions regardless of the current state. Furthermore, considering that actions in a real system usually carry costs, it is desirable to synthesize a supervisor that incurs only a minimum cost. Pursuing finite coreachability with a minimum cost is the main motivation for developing a theory about optimal supervisory control of weighted discrete-event systems in the literature. In this paper we follow the same line of optimal supervisory control but with a new focus on partial observation, which is common in practical applications. We first define three finitely-weighted supervisory control problems, namely (1) to decide the existence of a finitely-weighted controllable and normal sublanguage; (2) to compute a finitely-weighted controllable and normal sublanguage, when the answer to Problem (1) is affirmative; (3) to compute the supremal minimum-weighted controllable and normal sublanguage, when the answer to Problem (1) is affirmative. Then we provide concrete algorithms to solve them