A feedback approach to bifurcation analysis in biochemical networks with many parameters

Feedback circuits in biochemical networks which underly cellular signaling pathways are important elements in creating complex behavior. A specific aspect thereof is how stability of equilibrium points depends on model parameters. For biochemical networks, which are modelled using many parameters, it is typically very difficult to estimate the influence of parameters on stability. Finding parameters which result in a change in stability is a key step for a meaningful bifurcation analysis. We describe a method based on well known approaches from control theory, which can locate parameters leading to a change in stability. The method considers a feedback circuit in the biochemical network and relates stability properties to the control system obtained by loop--breaking. The method is applied to a model of a MAPK cascade as an illustrative example

Final-State Constrained Optimal Control via a Projection Operator Approach

In this paper we develop a numerical method to solve nonlinear optimal control problems with final-state constraints. Specifically, we extend the PRojection Operator based Netwon's method for Trajectory Optimization (PRONTO), which was proposed by Hauser for unconstrained optimal control problems. While in the standard method final-state constraints can be only approximately handled by means of a terminal penalty, in this work we propose a methodology to meet the constraints exactly. Moreover, our method guarantees recursive feasibility of the final-state constraint. This is an appealing property especially in realtime applications in which one would like to be able to stop the computation even if the desired tolerance has not been reached, but still satisfy the constraints. Following the same conceptual idea of PRONTO, the proposed strategy is based on two main steps which (differently from the standard scheme) preserve the feasibility of the final-state constraints: (i) solve a quadratic approximation of the nonlinear problem to find a descent direction, and (ii) get a (feasible) trajectory by means of a feedback law (which turns out to be a nonlinear projection operator). To find the (feasible) descent direction we take advantage of final-state constrained Linear Quadratic optimal control methods, while the second step is performed by suitably designing a constrained version of the trajectory tracking projection operator. The effectiveness of the proposed strategy is tested on the optimal state transfer of an inverted pendulum

On stability and stabilization of periodic discrete-time systems with an application to satellite attitude control

An alternative stability analysis theorem for nonlinear periodic discrete-time systems is presented. The developed theorem offers a trade-off between conservatism and complexity of the corresponding stability test. In addition, it yields a tractable stabilizing controller synthesis method for linear periodic discrete-time systems subject to polytopic state and input constraints. It is proven that in this setting, the proposed synthesis method is strictly less conservative than available tractable synthesis methods. The application of the derived method to the satellite attitude control problem results in a large region of attraction

Data-driven distributed MPC of dynamically coupled linear systems

In this paper, we present a data-driven distributed model predictive control (MPC) scheme to stabilise the origin of dynamically coupled discrete-time linear systems subject to decoupled input constraints. The local optimisation problems solved by the subsystems rely on a distributed adaptation of the Fundamental Lemma by Willems et al., allowing to parametrise system trajectories using only measured input-output data without explicit model knowledge. For the local predictions, the subsystems rely on communicated assumed trajectories of neighbours. Each subsystem guarantees a small deviation from these trajectories via a consistency constraint. We provide a theoretical analysis of the resulting non-iterative distributed MPC scheme, including proofs of recursive feasibility and (practical) stability. Finally, the approach is successfully applied to a numerical example

An Offline-Sampling SMPC Framework with Application to Automated Space Maneuvers

In this paper, a sampling-based Stochastic Model Predictive Control algorithm is proposed for discrete-time linear systems subject to both parametric uncertainties and additive disturbances. One of the main drivers for the development of the proposed control strategy is the need of real-time implementability of guidance and control strategies for automated rendezvous and proximity operations between spacecraft. The paper presents considers the validation of the proposed control algorithm on an experimental testbed, showing how it may indeed be implemented in a realistic framework. Parametric uncertainties due to the mass variations during operations, linearization errors, and disturbances due to external space environment are simultaneously considered. The approach enables to suitably tighten the constraints to guarantee robust recursive feasibility when bounds on the uncertain variables are provided, and under mild assumptions, asymptotic stability in probability of the origin can be established. The offline sampling approach in the control design phase is shown to reduce the computational cost, which usually constitutes the main limit for the adoption of Stochastic Model Predictive Control schemes, especially for low-cost on-board hardware. These characteristics are demonstrated both through simulations and by means of experimental results

Mechanism of PP2A-mediated IKK beta dephosphorylation: a systems biological approach.

BACKGROUND: Biological effects of nuclear factor-kappaB (NF kappaB) can differ tremendously depending on the cellular context. For example, NF kappaB induced by interleukin-1 (IL-1) is converted from an inhibitor of death receptor induced apoptosis into a promoter of ultraviolet-B radiation (UVB)-induced apoptosis. This conversion requires prolonged NF kappaB activation and is facilitated by IL-1 + UVB-induced abrogation of the negative feedback loop for NF kappaB, involving a lack of inhibitor of kappaB (I kappaB alpha) protein reappearance. Permanent activation of the upstream kinase IKK beta results from UVB-induced inhibition of the catalytic subunit of Ser-Thr phosphatase PP2A (PP2Ac), leading to immediate phosphorylation and degradation of newly synthesized I kappaB alpha. RESULTS: To investigate the mechanism underlying the general PP2A-mediated tuning of IKK beta phosphorylation upon IL-1 stimulation, we have developed a strictly reduced mathematical model based on ordinary differential equations which includes the essential processes concerning the IL-1 receptor, IKK beta and PP2A. Combining experimental and modelling approaches we demonstrate that constitutively active, but not post-stimulation activated PP2A, tunes out IKK beta phosphorylation thus allowing for I kappaB alpha resynthesis in response to IL-1. Identifiability analysis and determination of confidence intervals reveal that the model allows reliable predictions regarding the dynamics of PP2A deactivation and IKK beta phosphorylation. Additionally, scenario analysis is used to scrutinize several hypotheses regarding the mode of UVB-induced PP2Ac inhibition. The model suggests that down regulation of PP2Ac activity, which results in prevention of I kappaB alpha reappearance, is not a direct UVB action but requires instrumentality. CONCLUSION: The model developed here can be used as a reliable building block of larger NF kappa B models and offers comprehensive simplification potential for future modeling of NF kappa B signaling. It gives more insight into the newly discovered mechanisms for IKK deactivation and allows for substantiated predictions and investigation of different hypotheses. The evidence of constitutive activity of PP2Ac at the IKK complex provides new insights into the feedback regulation of NF kappa B, which is crucial for the development of new anti-cancer strategies