Controller synthesis for hybrid systems with linear vector fields

Manon, P.; Valentin, Claire

doi:10.1109/isic.1999.796623

Cited by 10 publications

(5 citation statements)

References 4 publications

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“…First, based on the property of interest, synthesis work broadly falls into one of two categories. The first category finds controllers that meet some liveness specifications, such as synthesizing a trajectory to drive a hybrid system from an initial state to a desired final state [22,19], while also minimizing some cost metric [6]. The second category finds controllers that meet some safety specification; see [1] for detailed related work in this category.…”

Section: Related Workmentioning

confidence: 99%

Synthesizing Switching Logic to Minimize Long-Run Cost

Jha¹,

Seshia²,

Tiwari³

2011

Preprint

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Given a multi-modal dynamical system, optimal switching logic synthesis involves generating the conditions for switching between the system modes such that the resulting hybrid system satisfies a quantitative specification. We formalize and solve the problem of optimal switching logic synthesis for quantitative specifications over long run behavior. Our paper generalizes earlier work on synthesis for safety. We present an approach for specifying quantitative measures using reward and penalty functions, and illustrate its effectiveness using several examples. Each trajectory of the system, and each state of the system, is associated with a cost. Our goal is to synthesize a system that minimizes this cost from each initial state. We present an automated technique to synthesize switching logic for such quantitative measures. Our algorithm works in two steps. For a single initial state, we reduce the synthesis problem to an unconstrained numerical optimization problem which can be solved by any offthe-shelf numerical optimization engines. In the next step, optimal switching condition is learnt as a generalization of the optimal switching states discovered for each initial state. We prove the correctness of our technique and demonstrate the effectiveness of this approach with experimental results.

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Section: Related Workmentioning

confidence: 99%

Synthesizing Switching Logic to Minimize Long-Run Cost

Jha¹,

Seshia²,

Tiwari³

2011

Preprint

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“…RELATED WORK Past work on synthesis of switching logic can be broadly classified into two categories depending on the goals of synthesis. The first category finds controllers that meet some liveness specifications, such as synthesizing a trajectory to drive a hybrid system from an initial state to a desired final state [8], [10]. The second category finds controllers that meet some safety specification [2].…”

Section: E Performancementioning

confidence: 99%

Synthesizing switching logic for safety and dwell-time requirements

Jha

Gulwani

Seshia

et al. 2010

Proceedings of the 1st ACM/IEEE International Conference on Cyber-Physical Systems

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Abstract-Cyber-physical systems (CPS) can be usefully modeled as hybrid automata combining the physical dynamics within modes with discrete switching behavior between modes. CPS designs must satisfy safety and performance requirements. While the dynamics within each mode is usually defined by the physical plant, the tricky design problem often involves getting the switching logic right. In this paper, we present a new approach to assist designers by synthesizing the switching logic, given a partial system model, using a combination of fixpoint computation, numerical simulation, and machine learning. Our technique begins with an overapproximation of the guards on transitions between modes. In successive iterations, the over-approximations are refined by eliminating points that will cause the system to reach unsafe states, and such refinement is performed using numerical simulation and machine learning. In addition to safety requirements, we synthesize models to satisfy dwell-time constraints, which impose upper and/or lower bounds on the amount of time spent within a mode. We demonstrate using case studies that our technique quickly generates intuitive system models and that dwell-time constraints can help to tune the performance of a design.

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“…The first category finds controllers that meet some liveness specifications, such as synthesizing a trajectory to drive a hybrid system from an initial state to a desired final state [17,16]. The second category finds controllers that meet some safety specification.…”

Section: Related Workmentioning

confidence: 99%

Switching logic synthesis for reachability

Taly

Tiwari

2010

Proceedings of the Tenth ACM International Conference on Embedded Software

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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.

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Controller synthesis for hybrid systems with linear vector fields

Cited by 10 publications

References 4 publications

Synthesizing Switching Logic to Minimize Long-Run Cost

Synthesizing Switching Logic to Minimize Long-Run Cost

Synthesizing switching logic for safety and dwell-time requirements

Switching logic synthesis for reachability

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