Feedback Refinement Relations for the Synthesis of Symbolic Controllers
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200 citations
Cites background or methods from "Feedback Refinement Relations for t..."
...As a first example we consider a path planning problem, also considered in [20] and [9], for the bicycle dynamics of a SymbolicSet η, z ∈ R+ Ja, bK ⊆ Rn User Input:...
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...The interested reader is referred to [20] for the precise definitions of the various terms and objects....
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...Contrary to other available tools, it supports the construction of symbolic models in the framework of feedback refinement relations and therefore facilitates a rather straightforward controller refinement procedure [20]....
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...Table 1: Comparison of SCOTS with numbers reported in [9] and [20]....
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...Moreover, the controller does not require to include the abstraction as a building block [20]....
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Additional excerpts
...In this methodology, one starts with a continuous dynamical system and an approximation factor ε, and constructs a finite-state abstraction whose trajectories are guaranteed to be within a distance of ε to the original system and vice versa [1]–[4]....
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42 citations
References
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139,059 citations
"Feedback Refinement Relations for t..." refers background in this paper
...However, these models are not abstractions of the plant in the usual sense, and so, typically, a large number of low-level controllers need to be synthesized to actually enforce on the continuous plant the high-level commands generated by the discrete controller [27], [28]....
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...For example, [9]–[11] do not cover uncertainties in plant dynamics, while in [8], [10], [11], [26]–[28] the quantizer is assumed to be deterministic which mandates the state measurement to be precise, without any error; see Section VI-B....
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6,398 citations
Additional excerpts
...Then, there exist t0 ∈ [0, τ ] and a solution ξ̄ : [0, t0[→ R of (22) with input u such that ξ̄|[0,τ ′] = ξ and ξ̄(t) becomes unbounded as t ∈ [0, t0[ approaches t0 [46]....
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4,905 citations
"Feedback Refinement Relations for t..." refers background in this paper
...This class of systems contains a great variety of system descriptions, including common models like transition systems [2], [24] as well as discrete-time control systems [25]....
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1,927 citations