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Synthesis of quantized feedback control software for discrete time linear hybrid systems
, 2010
"... Abstract. We present an algorithm that given a Discrete Time Linear Hybrid System H returns a correctbyconstruction software implementation K for a (near time optimal) robust quantized feedback controller for H along with the set of states on which K is guaranteed to work correctly (controllable ..."
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Cited by 16 (15 self)
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Abstract. We present an algorithm that given a Discrete Time Linear Hybrid System H returns a correctbyconstruction software implementation K for a (near time optimal) robust quantized feedback controller for H along with the set of states on which K is guaranteed to work correctly (controllable region). Furthermore, K has a Worst Case Execution Time linear in the number of bits of the quantization schema. 1
Automatatheoretic Decision of Timed Games
, 2013
"... The solution of games is a key decision problem in the context of verification of open systems and program synthesis. Given a game graph and a specification, we wish to determine if there exists a strategy of the protagonist that allows to select only behaviors fulfilling the specification. In this ..."
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Cited by 13 (3 self)
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The solution of games is a key decision problem in the context of verification of open systems and program synthesis. Given a game graph and a specification, we wish to determine if there exists a strategy of the protagonist that allows to select only behaviors fulfilling the specification. In this paper, we consider timed games, where the game graph is a timed automaton and the specification is given by formulas of the temporal logics Ltl and Ctl. We present an automatatheoretic approach to solve the addressed games, extending to the timed framework a successful approach to solve discrete games. The main idea of this approach is to translate the timed automaton A, modeling the game graph, into a tree automaton AT accepting all trees that correspond to a strategy of the protagonist. Then, given an automaton corresponding to the specification, we intersect it with the tree automaton AT and check for the nonemptiness of the resulting automaton. Our approach yields a decision algorithm running in exponential time for Ctl and in double exponential time for Ltl. The obtained algorithms are optimal in the sense that their computational complexity matches the known lower bounds.
Crossing the bridge between similar games ⋆
"... Abstract. Specifications and implementations of complex physical systems tend to differ as low level effects such as sampling are often ignored when high level models are created. Thus, the low level models are often not exact refinements of the high level specification. However, they are similar to ..."
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Cited by 4 (1 self)
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Abstract. Specifications and implementations of complex physical systems tend to differ as low level effects such as sampling are often ignored when high level models are created. Thus, the low level models are often not exact refinements of the high level specification. However, they are similar to those. To bridge the gap between those models, we study robust simulation relations for hybrid systems. We identify a family of robust simulation relations that allow for certain bounded deviations in the behavior of a system specification and its implementation in both values of the system variables and timings. We show that for this relaxed version of simulation a broad class of logical properties is preserved. The question whether two systems are in simulation relation can be reduced to a reach avoid problem for hybrid games. We provide a sufficient condition under which a winning strategy for these games exists.
A Complete Axiomatization of Differential Game Logic for Hybrid Games
, 2013
"... not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution or government. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) We introduce differential game logic (dGL) for speci ..."
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Cited by 3 (3 self)
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not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution or government. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) We introduce differential game logic (dGL) for specifying and verifying properties of hybrid games, i.e. games on hybrid systems combining discrete and continuous dynamics. Unlike hybrid systems, hybrid games allow choices in the system dynamics to be resolved adversarially by different players with different objectives. The logic dGL can be used to study the existence of winning strategies for such hybrid games. We present a simple sound and complete axiomatization of dGL relative to the fixpoint logic of differential equations. We prove hybrid games to be determined and their winning regions to require higher closure ordinals and we identify separating Hybrid systems [Hen96] are dynamical systems combining discrete dynamics and continuous dynamics, which are important, e.g., for modeling how computers control physical systems. Hybrid systems combine difference equations and differential equations with conditional switching, nondeterminism,
Playing Hybrid Games with KeYmaera ⋆
"... Abstract. We propose a new logic, called differential dynamic game logic (dDGL), that adds several game constructs on top of differential dynamic logic (dL) so that it can be used for hybrid games. The logic dDGL is a conservative extension of dL, which we exploit for our implementation of dDGL in t ..."
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Cited by 2 (2 self)
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Abstract. We propose a new logic, called differential dynamic game logic (dDGL), that adds several game constructs on top of differential dynamic logic (dL) so that it can be used for hybrid games. The logic dDGL is a conservative extension of dL, which we exploit for our implementation of dDGL in the theorem prover KeYmaera. We provide rules for extending the dL sequent proof calculus to handle the dDGL constructs by identifying analogs to operators of dL. We have implemented dDGL in an extension of KeYmaera and verified a case study in which a robot satisfies a joint safety and liveness objective in a factory automation scenario, in which the factory may perform interfering actions independently.
Differential game logic
 CoRR
, 2014
"... Differential game logic (dGL) is a logic for specifying and verifying properties of hybrid games, i.e. games that combine discrete, continuous, and adversarial dynamics. Unlike hybrid systems, hybrid games allow choices in the system dynamics to be resolved adversarially by different players with di ..."
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Differential game logic (dGL) is a logic for specifying and verifying properties of hybrid games, i.e. games that combine discrete, continuous, and adversarial dynamics. Unlike hybrid systems, hybrid games allow choices in the system dynamics to be resolved adversarially by different players with different objectives. The logic dGL can be used to study the existence of winning strategies for such hybrid games, i.e. ways of resolving the player’s choices in some way so that he wins by achieving his objective for all choices of the opponent. Hybrid games are determined, i.e. from each state, one player has a winning strategy, yet computing their winning regions may take transfinitely many steps. The logic dGL, nevertheless, has a sound and complete axiomatization relative to any expressive logic. Separating axioms are identified that distinguish hybrid games from hybrid systems. Finally, dGL is proved to be strictly more expressive than the corresponding logic of hybrid systems. 1
Optimal Control with Regular Objectives Using an AbstractionRefinement Approach
"... Abstract—This paper presents a method to synthesize a sequence of control inputs for a discretetime switched linear system equipped with a cost function, such that the controlled system behavior satisfies a lineartime temporal objective with minimal cost. An abstract finite state weighted transit ..."
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Abstract—This paper presents a method to synthesize a sequence of control inputs for a discretetime switched linear system equipped with a cost function, such that the controlled system behavior satisfies a lineartime temporal objective with minimal cost. An abstract finite state weighted transition system is constructed, such that the cost of the optimal control on the abstract system provides an upper bound on the cost of the system is constructed from finite partitions of the state and input spaces by solving certain optimization problems, and a sequence of controllers is obtained by considering a sequence of uniformly refined partitions. Under mild assumptions on the optimal control for the switched system, the costs of the sequence of controllers constructed converges to the cost of the optimal control for the switched system. The abstraction refinement algorithm is implemented in the tool OptCAR. The feasibility of this approach is illustrated on two different examples, by constructing automatically, suboptimal controllers with improving optimal costs. I.
Differential Hybrid Games
, 2014
"... This paper introduces differential hybrid games, which combine differential games with hybrid games. In both kinds of games, two players interact with continuous dynamics. The difference is that hybrid games also provide all the features of hybrid systems and discrete games, but only deterministic ..."
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This paper introduces differential hybrid games, which combine differential games with hybrid games. In both kinds of games, two players interact with continuous dynamics. The difference is that hybrid games also provide all the features of hybrid systems and discrete games, but only deterministic differential equations. Differential games, instead, provide differential equations with input by both players, but not the luxury of hybrid games, such as mode switches and discrete or alternating interaction. This paper augments differential game logic with modalities for the combined dynamics of differential hybrid games. It shows how hybrid games subsume differential games and introduces differential game invariants and differential game variants for proving properties of differential games inductively. This material is based upon work supported by the National Science Foundation under NSF CAREER Award CNS1054246. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution or government. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of any sponsoring institution or government.
Web based Reachability Testing for Hetergeneous Application using Nash Equilibrium
"... Reachability testing is a mixture strategy, combine nondeterministic and deterministic testing accomplishes a test run deterministically up to a definite point and then allow synchronized program to work nondeterministically. A game theoretic approach is the learning approach of mathematical model ..."
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Reachability testing is a mixture strategy, combine nondeterministic and deterministic testing accomplishes a test run deterministically up to a definite point and then allow synchronized program to work nondeterministically. A game theoretic approach is the learning approach of mathematical models of variance and collaboration between intellectual rational decisionmakers. To overcome the conflicts arises in the game theoretic approach, the previous work considered the fault discovery of reachability testing from a game theoretic point of view. But the downside of the previous work is that it supports only homogeneous applications rather than heterogeneous and web applications. Proposal in this work presented a web based reachability testing model encompassing a state of Nash equilibrium for heterogeneous applications. Heterogeneous application comprises of parallel and divertive function which have contributory influence over one another at different instances. The proposal adopts game theoretic approach which supports parallel and diversive functions by maintaining equilibrium state for contra functions. Evaluation of reachability test is conducted on to testify the integrity of newer functions with previous versions of the program. Simulations are conducted with web and heterogeneous application to evaluate the performance of proposed web based reachability testing model for both homogeneous and heterogeneous applications. The reliability of our proposal model shows improvement minimal testing time i.e., nearly 16%, and memory usage i.e nearly 17 % compared to the existing reachability testing methods.
Creative Commons Attribution License. A GameTheoretic approach to Fault Diagnosis of Hybrid Systems∗
"... Physical systems can fail. For this reason the problem of identifying and reacting to faults has received a large attention in the control and computer science communities. In this paper we study the fault diagnosis problem for hybrid systems from a gametheoretical point of view. A hybrid system is ..."
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Physical systems can fail. For this reason the problem of identifying and reacting to faults has received a large attention in the control and computer science communities. In this paper we study the fault diagnosis problem for hybrid systems from a gametheoretical point of view. A hybrid system is a system mixing continuous and discrete behaviours that cannot be faithfully modeled neither by using a formalism with continuous dynamics only nor by a formalism including only discrete dynamics. We use the well known framework of hybrid automata for modeling hybrid systems, and we define a Fault Diagnosis Game on them, using two players: the environment and the diagnoser. The environment controls the evolution of the system and chooses whether and when a fault occurs. The diagnoser observes the external behaviour of the system and announces whether a fault has occurred or not. Existence of a winning strategy for the diagnoser implies that faults can be detected correctly, while computing such a winning strategy corresponds to implement a diagnoser for the system. We will show how to determine the existence of a winning strategy, and how to compute it, for some decidable classes of hybrid automata like ominimal hybrid automata. 1