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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 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

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

An algorithm for computing supremal nonblocking state-normal supervisors for nondeterministic systems

Recently supervisor synthesis for nondeterministic systems has gained more and more attention, owing to the potential computational advantage of using nondeterministic automata in modular/distributed synthesis. It is well known that, in the Ramadge/Wonham language-based supervisory control paradigm, the supremal nonblocking normal supervisor always exists (although may be empty) and is computable. In this paper we will show that, for a nondeterministic plant model and a deterministic specification, a similar entity called the supremal nonblocking state-normal supervisor also exists, which coincides with the supremal nonblocking normal supervisor when the plant model becomes deterministic. We then present a concrete algorithm to compute such a supervisor and analyze the relevant computational complexity

Aggregative synthesis of distributed supervisors based on automaton abstraction

Achieving nonblockingness in supervisory control imposes a major challenge when the number of states of a target system is large, often owing to synchronous product of many relatively small local components. To overcome this difficulty, in this paper we first present a distributed supervisory control problem, then provide an aggregative synthesis approach that computes nonblocking distributed supervisors. The key to the success of this approach is a newly developed automaton abstraction technique, that removes irrelevant internal transitions at each synthesis stage so that nonblocking supervisor synthesis can be carried out on relatively small abstracted models

A control problem for hybrid systems with discrete inputs and outputs

We address the control synthesis of hybrid systems with discrete inputs and outputs. The control objective is to ensure that the events of the closed-loop system belong to the language of the control requirements. The controller is sampling-based and it is representable by a finite-state machine. We formalize the control problem and provide a theoretically sound solution based on finite-state abstractions of the symbolic behavior of the plant. In addition, we identify classes of hybrid systems for which a suitable finite-state abstraction can be computed and we sketch the corresponding algorithms

ConPAHS : a software package for control of piecewise-affine hybrid systems

The software package ConPAHS facilitates control design of continuous-time piecewise-affine hybrid systems on polytopes. For the control objective of reaching a particular state from a specified initial state, the output of the package is a piecewise-affine control law. After a short review of the control theory for this problem, the paper presents the functional specification of ConPAHS, the objected oriented software principles used, the program structure, and the design choices. Three examples including simulations are provided to illustrate the use of ConPAHS