Control of polynomial dynamical systems on rectangles

We consider the problem of synthesising rate parameters for stochastic biochemical networks so that a given time-bounded CSL property is guaranteed to hold, or, in the case of quantitative properties, the probability of satisfying the property is maximised or minimised. Our method is based on extending CSL model checking and standard uniformisation to parametric models, in order to compute safe bounds on the satisfaction probability of the property. We develop synthesis algorithms that yield answers that are precise to within an arbitrarily small tolerance value. The algorithms combine the computation of probability bounds with the refinement and sampling of the parameter space. Our methods are precise and efficient, and improve on existing approximate techniques that employ discretisation and refinement. We evaluate the usefulness of the methods by synthesising rates for three biologically motivated case studies: infection control for a SIR epidemic model; reliability

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“…By [7,40], the extrema of a multi-affine function defined over a rectangular domain R are found in the vertices of R.…”

Section: Computing Bounds For Unnested Path Formulasmentioning

confidence: 99%

Precise parameter synthesis for stochastic biochemical systems

et al. 2016

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“…To validate the proposed algorithms, we will apply them to examples from [10] and [21] comprising affine and polynomial systems.…”

Section: Examplesmentioning

confidence: 99%

“…It is seen that the vector field points into the simplex at all facets; thus, the problem is solved. We solve the control problems for a polynomial system presented in [21]. In contrast to [21], we consider a simplicial subset of the state space for the design.…”

Section: Affine Systemmentioning

confidence: 99%

“…Control to facet has been considered for different classes of systems: affine systems [8], multi-affine systems [3], and polynomial systems [21]. Additionally, a tool for designing controls that obey temporal logic specifications using the control to facet technique was presented in [12].…”

Section: Introductionmentioning

confidence: 99%

“…Previous works exploit the affine nature of the problem, which allows the synthesis of a control to be reduced to solving linear constraints defined on the vertices of a polyhedral set. To extend the above idea to polynomial vector fields, [21] proposes to transform polynomials into higher dimensional multi-affine functions using blossoming [23].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Control to facet for polynomial systems

Sloth

Wisniewski

2014

Proceedings of the 17th International Conference on Hybrid Systems: Computation and Control

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This paper presents a solution to the control to facet problem for arbitrary polynomial vector fields defined on simplices. The novelty of the work is to use Bernstein coefficients of polynomials for determining certificates of positivity. Specifically, the constraints that are set up for the controller design are solved by searching for polynomials in Bernstein form. This allows the controller design problem to be formulated as a linear programming problem. Examples are provided that demonstrate the efficiency of the method for designing controls for polynomial systems.

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Abstraction of Monotone Systems Based on Feedback Controllers

Sinyakov

Girard

2020

IFAC-PapersOnLine

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Control of polynomial dynamical systems on rectangles

Cited by 5 publications

References 9 publications

Precise parameter synthesis for stochastic biochemical systems

Precise parameter synthesis for stochastic biochemical systems

Control to facet for polynomial systems

Abstraction of Monotone Systems Based on Feedback Controllers

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