Anne-Kathrin Schmuck

Asynchronous l-complete approximations

Abstract This paper extends the l -complete approximation method developed for time invariant systems to a larger system class, ensuring that the resulting approximation can be realized by a finite state machine. To derive the new abstraction method, called asynchronous l -complete approximation, an asynchronous version of the well-known concepts of state property, memory span and l -completeness is introduced, extending the behavioral systems theory in a consistent way.

Reducing an Operational Supervisory Control Problem by Decomposition for Deterministic Pushdown Automata

Abstract The purpose of Supervisory Control Theory (SCT) is to synthesize a controller for a plant and a specification such that the desired closed-loop behavior is enforced. Effective solvers have been constructed in the past for the setting of plants and specifications modeled by Deterministic Finite Automata (DFA). We extend the domain of the specification to Deterministic Pushdown Automata (DPDA) and verify an effective solver (up to two basic building blocks which ensure controllability and blockfreeness, effectively solved for this setting in two companion papers). We verify the enforcement of desired operational criteria, which are, in contrast to the setting of DFA, partly oblivious to the (un)marked language of the closed loop. Our general approach trivially covers the setting of DFA and can be reused and adapted to develop effective solvers for other settings as the realizability of solutions to the supervisory control problem (SCP) is considered on an Abstract: level.

Extending Supervisory Controller Synthesis to Deterministic Pushdown Automata Enforcing Controllability Least Restrictively

Abstract In this paper a step towards the generalization of supervisory control theory to situations where the specification is modeled by a deterministic pushdown automaton (DPDA) is provided. In particular, this paper presents an algorithm to calculate the largest controllable marked sublanguage of a given deterministic context free language (DCFL) by least restrictively removing controllability problems in a DPDA realization of this DCFL. It also provides a counterexample which shows that the algorithm by Griffin (2008) intended to solve the considered problem is not minimally restrictive.

Comparing asynchronous l-complete approximations and quotient based abstractions

This paper is concerned with a detailed comparison of two different abstraction techniques for the construction of finite state symbolic models for controller synthesis of hybrid systems. Namely, we compare quotient based abstractions (QBA) with different realizations of strongest (asynchronous) l-complete approximations (SAlCA). Even though the idea behind their construction is very similar, we show that they are generally incomparable both in terms of behavioral inclusion and similarity relations. We therefore derive necessary and sufficient conditions for QBA to coincide with particular realizations of SAlCA. Depending on the original system, either QBA or SAlCA can be a tighter abstraction.

Simulation and bisimulation over multiple time scales in a behavioral setting

This paper introduces a new behavioral system model with distinct external and internal signals possibly evolving on different time scales. This allows to capture abstraction processes or signal aggregation in the context of control and verification of large scale systems. For this new system model different notions of simulation and bisimulation are derived, ensuring that they are, respectively, preorders and equivalence relations for the system class under consideration.

Compositional construction of finite state abstractions for stochastic control systems

Controller synthesis techniques for continuous systems with respect to temporal logic specifications typically use a finite-state symbolic abstraction of the system. Constructing this abstraction for the entire system is computationally expensive, and does not exploit natural decompositions of many systems into interacting components. We have recently introduced a new relation, called (approximate) disturbance bisimulation for compositional symbolic abstraction to help scale controller synthesis for temporal logic to larger systems. In this paper, we extend the results to stochastic control systems modeled by stochastic differential equations. Given any stochastic control system satisfying a stochastic version of the incremental input-to-state stability property and a positive error bound, we show how to construct a finite-state transition system (if there exists one) which is disturbance bisimilar to the given stochastic control system. Given a network of stochastic control systems, we give conditions on the simultaneous existence of disturbance bisimilar abstractions to every component allowing for compositional abstraction of the network system.

Supervisory control synthesis for deterministic context free specification languages

This paper describes two steps in the generalization of supervisory control theory to situations where the specification is modeled by a deterministic context free language (DCFL). First, it summarizes a conceptual iterative algorithm from Schneider et al. (2014) solving the supervisory control problem for language models. This algorithm involves two basic iterative functions. Second, the main part of this paper presents an implementable algorithm realizing one of these functions, namely the calculation of the largest controllable marked sublanguage of a given DCFL. This algorithm least restrictively removes controllability problems in a deterministic pushdown automaton realizing this DCFL.

Constructing (Bi)similar finite state abstractions using asynchronous l-complete approximations

This paper constructs a finite state abstraction of a possibly continuous-time and infinite state model in two steps. First, a finite external signal space is added, generating a so called φ-dynamical system. Secondly, the strongest asynchronous l-complete approximation of the external dynamics is constructed. As our main results, we show that (i) the abstraction simulates the original system, and (ii) bisimilarity between the original system and its abstraction holds, if and only if the original system is l-complete and its state space satisfies an additional property.

Supervisory controller synthesis for decomposable deterministic context free specification languages

In this paper we consider a supervisory control problem (SCP) consisting of a regular plant language and a deterministic context free specification language, where the latter can be decomposed into a regular and a deterministic context free part. For this setup we give an implementable algorithm calculating two separate controllers for each part of the specification. We show under which conditions the parallel composition of these controllers solves the original SCP. The latter is done by reducing the problem to a special case of hierarchical decentralized control and using existing results from the literature.