Switching logic synthesis for reachability

Abstract

We consider the problem of driving a system from some initial configuration to a desired configuration while avoiding some unsafe configurations. The system to be controlled is a dynamical system that can operate in different modes. The goal is to synthesize the logic for switching between the modes so that the desired reachability property holds.In this paper, we first present a sound and complete inference rule for proving reachability properties of single mode continuous dynamical systems. Next, we present an inference rule for proving controlled reachability in multi-modal continuous dynamical systems. From a constructive proof of controlled reachability, we show how to synthesize the desired switching logic. We show that our synthesis procedure is sound and produces only non-zeno hybrid systems.In practice, we perform a constructive proof of controlled reachability by solving an Exists-Forall formula in the theory of reals. We present an approach for solving such formulas that combines symbolic and numeric solvers. We demonstrate our approach on some examples. All results extend naturally to the case when, instead of reachability, interest is in until properties.

Formal verification of hybrid systems

“…Illustrative examples of this new view of synthesis include programming by examples for spreadsheet transformations in Microsoft Excel [27], and sketching of bit-streaming programs using program skeletons [51]. We believe that these ideas emerging in the programming languages community should be explored in the context of design of hybrid systems to integrate synthesis in a pragmatic way in the design cycle (see [53] for recent work on synthesizing switching conditions in hybrid automata).…”

Automated synthesis of symbolic instruction encodings from I/O samples

“…A central theme of all these techniques is to express the synthesis problem as a search problem over a restricted space. The restricted space is defined either using a template [24,25], or using a sketch [21,22], or using a set of building blocks [9,13], or using a restricted language [8,12]. The synthesis techniques used in this paper are inspired from and build upon this prior work.…”

Verification and synthesis using real quantifier elimination

“…In a recent paper [29], we used qepcad to solve ∃∀ formulas arising from certificate-based synthesis. This paper builds upon [29] by proposing certificate-based analysis as a uniform approach for verification and synthesis, presenting several different benchmarks, and solving them using a combination of symbolic tools for quantifier elimination and simplification. Recently, Anai [1] used a combination of numerical methods (sum-of-squares) and symbolic quantifier elimination methods to solve problems arising in control, and such an integration is left for future work here.…”