Citation Context

...rthogonal to and may in the future be combined with abstraction techniques (such as bounding the degree of precision or loosening constraints as in [11]), incorporating robustness [12,8] or slackness =-=[1,2]-=-sExact State Set Representations 427 in models allowing precise abstractions by finite grids under robustness respectively slackness assumptions, counter-example guided abstraction refinement as in [2...

Citation Context

...tic to assume that the controller can interact with its environment continuously and with infinite precision. The inherent discrete nature of a controller of a hybrid system has led to recent efforts =-=[17, 2, 3, 1]-=- towards studying the discrete time behavior of hybrid systems. A similar argument in favor of focusing on discrete time behavior is presented by Henzinger and Kopke [12]. Lazy linear hybrid automata ...

Citation Context

...a solution to (H, I, G). For example, this can be done by giving conditions ensuring that the abstract system satisfies some equivalence relation with respect to the concrete system (e.g. see [17] or =-=[1]-=-). In our approach, the abstraction induced by a quantization is a design constraint rather than a methodological tool, since it depends on the number of bits used by AD/DA conversions. In [15], we gi...

Citation Context

...presentation of a solution to P. For example, this can be done by giving conditions ensuring that the abstract system satisfies some equivalence relation with respect to the concrete system (e.g. see =-=[33,1,25]-=-). To avoid useless computation, our on-the-fly control synthesis algorithm (Sect. 5.2) simultaneously computes the finite abstraction ˆ HΣ and the solution to the control problem ( ˆ HΣ, Î, ˆ G). To ...

Citation Context

...c to assume that the controller can interact with its environment continuously and with infinite precision. 3The inherent discrete nature of a controller of a hybrid system has led to recent efforts =-=[25, 4, 5, 3]-=- towards studying the discrete time behavior of hybrid systems. A similar argument in favor of focusing on discrete time behavior is presented by Henzinger and Kopke [17]. Lazy linear hybrid automata ...

Citation Context

...tic to assume that the controller can interact with its environment continuously and with infinite precision. The inherent discrete nature of a controller of a hybrid system has led to recent efforts =-=[15, 2, 3, 1]-=- toward studying the discrete time behavior of hybrid systems. A similar argument in favor of focusing on discrete time behavior is presented by Henzinger and Kopke [11]. Lazy linear hybrid automata(L...

Citation Context

...1369 II. BACKGROUND In the following the class of LLHA is described. A LLHA is meant to be a model of a closed-loop system consisting of a digital controller interacting with a continuous environment =-=[9]-=-. The controller samples the state of the continuous environment at periodic discrete-time instants. The state of the environment consists of the values of the continuous variables as observed by the ...

Citation Context

...ch uses translations of verification problems into satisfiability problems for theories of real numbers (possibly with exponentiation). Decidability of finite-precision hybrid automata was studied in =-=[1]-=-. In [20, 4, 5], o-minimal hybrid systems are studied; it is shown that for such hybrid systems reachability can be reduced to reachability in finite models due to existence of finite bismulations – t...