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Nonlinear Controller Algorithmic Analysis And Synthesis

Posted on:2009-01-03Degree:MasterType:Thesis
Country:ChinaCandidate:S W YangFull Text:PDF
GTID:2178360248954499Subject:Computer software and theory
Abstract/Summary:PDF Full Text Request
In this paper, we are interested in developing algorithms for analyzing the hybrid automata, which exhibit nonlinear continuous dynamics, by directly exploring the infinite state space. Inspired by the algorithms developed for the controller synthesis problems for timed systems, we propose synthesis algorithms for finding sets of initial states for the continuous dynamical systems such that some temporal properties, such as safety and liveness properties, are satisfied. The initial sets produce by algorithms are related to some classical concepts for continuous dynamical systems, such as invariant sets and domains of attraction. Level set methods are used for representing reachable sets and tracking the evolution of the boundary of a reachable set since they can be used to effectively represent complex continuous sets and, furthermore, there exist efficient computation methods for computing the evolution of reachable sets for nonlinear dynamic systems. We adopt the level set method for performing the computation in the algorithms. In this method, the representations and operations of state sets are performed in an Eulerian framework, that is, one which the underlying coordinate system remains fixed. This framework makes set operations and more advanced constructive solid geometry operations straightforward to apply. Since the representations and operations of state sets cannot be exact, only approximate results can be produced. However, if the coordinate system is bounded, then the partition of the state space contains only a finite number of representative elements. Hence, the algorithms are guaranteed to terminate. ReachLab, a model-based tool, is developed to enable rapid prototyping of the algorithm, and to allow the use of various computation methods for implementing the algorithm. We implement the synthesis algorithms in ReachLab and perform reachable analysis via Parallel Level Set computation Kernel on a cluster of parallel computing machines. And the computation results for several nonlinear continuous dynamic systems are presented.
Keywords/Search Tags:nonlinear, stability, hybrid automata, level set method, reachability analysis
PDF Full Text Request
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