55,948 research outputs found
Computing the Projected Reachable Set of Stochastic Biochemical Reaction Networks Modelled by Switched Affine Systems
No full textA fundamental question in systems biology is what
combinations of mean and variance of the species present in
a stochastic biochemical reaction network are attainable by
perturbing the system with an external signal. To address this
question, we show that the moments evolution in any generic network
can be either approximated or, under suitable assumptions,
computed exactly as the solution of a switched affine system.
We then propose a new method to approximate the reachable
set of such switched affine system. A remarkable feature of our
approach is that it allows one to easily compute projections of the
reachable set for pairs of moments of interest, without requiring
the computation of the full reachable set, which can be prohibitive
for large networks. As a second contribution, we also show how to
select the external signal in order to maximize the probability of
reaching a target set. To illustrate the method we study a renown
model of controlled gene expression and we derive estimates of
the reachable set, for the protein mean and variance, that are
more accurate than those available in the literature and consistent
with experimental data
On the use of hyperplane methods to compute the reachable set of controlled stochastic biochemical reaction networks
No full textA compression learning perspective to scenario based optimization
No full textWe investigate the connections between compression learning and scenario based optimization. We consider different constrained optimization problems affected by uncertainty represented by means of scenarios and show that the issue of providing guarantees on the probability of constraint violation reduces to a learning problem for an appropriately chosen algorithm that enjoys compression learning properties. The compression learning perspective provides a unifying framework for scenario based optimization and allows us to revisit the scenario approach and the probabilistically robust design, a recently developed technique based on a mixture of randomized and robust optimization. Our analysis shows that all optimization problems we consider here, even though they are of different type, share certain similarities, which translates on similar feasibility properties of their solutions
Compression learning for chance constrained stochastic MPC
No full textMotivated by chance constrained optimisation problems that arise in stochastic model predictive control we investigate the connections between compression learning and scenario based optimisation. We discuss how compression learning provides powerful insight into a fundamental property that ensures optimal solutions to optimisation problems formulated using a finite number of realisations of the uncertainty will also be feasible for other, unseen instances of the uncertainty. This property, known as -consistency-, roughly translates to the requirement that a fixed cardinality subset of the scenarios used to generate the optimal solution are enough to encode all the information needed to reconstruct the solution; all remaining scenarios are in a sense redundant. Computationally the catch of course is it is impossible to know a-priori which of the scenarios will be essential and which not. Moreover, the -unnecessary- scenarios are not wasted even in theory: Their presence is what provides the confidence level with which we can make the statement that the solution is feasible for unseen uncertainty instances. We demonstrate this connection through chance constrained optimisation programs based on a combination of scenarios and robust optimisation
Reachability analysis for switched affine systems and its application to controlled stochastic biochemical reaction networks
No full textUnder suitable assumptions, the moments of a controlled stochastic biochemical reaction network can be computed as the solution of a switched affine system. Motivated by this application, we propose a new method to approximate projections of the reachable set of a switched affine system onto a plane of interest. Our method does not require the computation of the full reachable set, thus allowing us to efficiently analyze the moments of a species of interest in arbitrarily large biochemical networks. To illustrate the benefits of the proposed method we consider a controlled gene expression model involving two species: the mRNA and the corresponding protein. The proposed approach can be used to estimate the reachable set of the protein mean and variance, under less stringent assumptions than those adopted in the literature. Specifically, we address the cases of multiple controlled reactions and heterogeneous population
On the Connection Between Compression Learning and Scenario Based Single-Stage and Cascading Optimization Problems
Full text linkWe investigate the connections between compression learning and scenario based optimization. We first show how to strengthen, or relax the consistency assumption at the basis of compression learning and provide novel learnability conditions for the underlying algorithms. We then consider different constrained optimization problems affected by uncertainty represented by means of scenarios. We show that the compression learning perspective provides a unifying framework for scenario based optimization, since the issue of providing guarantees on the probability of constraint violation reduces to a learning problem for an appropriately chosen algorithm that satisfies some consistency assumption. To illustrate this, we revisit the scenario approach within the developed context. Moreover, using the compression learning machinery we provide novel results on the probability of constraint violation for the class of cascading optimization problems
Mean Field Modeling of Large-Scale Energy Systems
No full textThis work proposes mean field game-type models for two instances of large- scale energy systems, namely plug-in electric vehicles and thermostatically controlled loads. Theoretical and numerical analysis show that both systems possess an equilibrium configuration which is optimal for the individuals and beneficial for the overall population
Constrained linear quadratic deterministic mean field control: Decentralized convergence to Nash equilibria in large populations of heterogeneous agents
No full textThis paper considers the linear quadratic deterministic mean field control problem for large populations of heterogeneous agents, subject to convex state and input constraints, and coupled via a quadratic cost function which depends on the average population state. To control the optimal responses of the rational agents to a Nash equilibrium, we propose feedback iterative solutions based on operator theory arguments. Contrary to the state of the art, global convergence is ensured, under mild sufficient conditions on the matrices defining the cost functions, and not on the convex constraints
Mean field constrained charging policy for large populations of Plug-in Electric Vehicles
No full textConstrained charging control of large populations of Plug-in Electric Vehicles (PEVs) is addressed using mean field game theory. We consider PEVs as heterogeneous agents, with different charging constraints (plug-in times and deadlines). The agents minimize their own charging cost, but are weakly coupled by the common electricity price. We propose an iterative algorithm that, in the case of an infinite population, converges to the Nash equilibrium associated with a related decentralized optimization problem. In this way we approximate the centralized optimal solution, which in the unconstrained case fills the overnight power demand valley, via a decentralized procedure. The benefits of the proposed formulation in terms of convergence behavior and overall charging cost are illustrated through numerical simulations
- …
