Stefan Streif

Stochastic nonlinear model predictive control with probabilistic constraints

Stochastic uncertainties are ubiquitous in complex dynamical systems and can lead to undesired variability of system outputs and, therefore, a notable degradation of closed-loop performance. This paper investigates model predictive control of nonlinear dynamical systems subject to probabilistic parametric uncertainties. A nonlinear model predictive control framework is presented for control of the probability distribution of system states while ensuring the satisfaction of constraints with some desired probability levels. To obtain a computationally tractable formulation for real control applications, polynomial chaos expansions are utilized to propagate the probabilistic parametric uncertainties through the system model. The paper considers individual probabilistic constraints, which are converted explicitly into convex second-order cone constraints for a general class of probability distributions. An algorithm is presented for receding horizon implementation of the finite-horizon stochastic optimal control problem. The capability of the stochastic model predictive control approach in terms of shaping the probability distribution of system states and fulfilling state constraints in a stochastic setting is demonstrated for optimal control of polymorphic transformation in batch crystallization.

Identification of Archaea-specific chemotaxis proteins which interact with the flagellar apparatus

BackgroundArchaea share with bacteria the ability to bias their movement towards more favorable locations, a process known as taxis. Two molecular systems drive this process: the motility apparatus and the chemotaxis signal transduction system. The first consists of the flagellum, the flagellar motor, and its switch, which allows cells to reverse the rotation of flagella. The second targets the flagellar motor switch in order to modulate the switching frequency in response to external stimuli. While the signal transduction system is conserved throughout archaea and bacteria, the archaeal flagellar apparatus is different from the bacterial one. The proteins constituting the flagellar motor and its switch in archaea have not yet been identified, and the connection between the bacterial-like chemotaxis signal transduction system and the archaeal motility apparatus is unknown.ResultsUsing protein-protein interaction analysis, we have identified three proteins in Halobacterium salinarum that interact with the chemotaxis (Che) proteins CheY, CheD, and CheC2, as well as the flagella accessory (Fla) proteins FlaCE and FlaD. Two of the proteins belong to the protein family DUF439, the third is a HEAT_PBS family protein. In-frame deletion strains for all three proteins were generated and analyzed as follows: a) photophobic responses were measured by a computer-based cell tracking system b) flagellar rotational bias was determined by dark-field microscopy, and c) chemotactic behavior was analyzed by a swarm plate assay. Strains deleted for the HEAT_PBS protein or one of the DUF439 proteins proved unable to switch the direction of flagellar rotation. In these mutants, flagella rotate only clockwise, resulting in exclusively forward swimming cells that are unable to respond to tactic signals. Deletion of the second DUF439 protein had only minimal effects. HEAT_PBS proteins could be identified in the chemotaxis gene regions of all motile haloarchaea sequenced so far, but not in those of other archaeal species. Genes coding for DUF439 proteins, however, were found to be integral parts of chemotaxis gene regions across the archaeal domain, and they were not detected in other genomic context.ConclusionAltogether, these results demonstrate that, in the archaeal domain, previously unrecognized archaea-specific Che proteins are essential for relaying taxis signaling to the flagellar apparatus.

Photonic crystal light collectors in fish retina improve vision in turbid water.

Seeing in the Dark Elephantnose fish are known to use electrosensing to navigate their murky freshwater environment. However, unlike some other animals from dark environments, they have retained their eyes and some dependence on vision. While most vertebrate vision optimizes either photon catch (for increased light capture) or visual acuity, Kreysing et al. (p. 1700) show that the unique structures of the grouped retinae found in the eyes of this species matches rod and cone sensitivity, which allows for the simultaneous use of both types of photoreceptors over a large range of dim light intensities. Layering cones on top of rods allows the elephantnose fish to see low-contrast objects in a murky environment. Despite their diversity, vertebrate retinae are specialized to maximize either photon catch or visual acuity. Here, we describe a functional type that is optimized for neither purpose. In the retina of the elephantnose fish (Gnathonemus petersii), cone photoreceptors are grouped together within reflecting, photonic crystal–lined cups acting as macroreceptors, but rod photoreceptors are positioned behind these reflectors. This unusual arrangement matches rod and cone sensitivity for detecting color-mixed stimuli, whereas the photoreceptor grouping renders the fish insensitive to spatial noise; together, this enables more reliable flight reactions in the fish’s dim and turbid habitat as compared with fish lacking this retinal specialization.

ADMIT: a toolbox for guaranteed model invalidation, estimation and qualitative-quantitative modeling

Summary: Often competing hypotheses for biochemical networks exist in the form of different mathematical models with unknown parameters. Considering available experimental data, it is then desired to reject model hypotheses that are inconsistent with the data, or to estimate the unknown parameters. However, these tasks are complicated because experimental data are typically sparse, uncertain, and are frequently only available in form of qualitative if–then observations. ADMIT (Analysis, Design and Model Invalidation Toolbox) is a MatLabTM-based tool for guaranteed model invalidation, state and parameter estimation. The toolbox allows the integration of quantitative measurement data, a priori knowledge of parameters and states, and qualitative information on the dynamic or steady-state behavior. A constraint satisfaction problem is automatically generated and algorithms are implemented for solving the desired estimation, invalidation or analysis tasks. The implemented methods built on convex relaxation and optimization and therefore provide guaranteed estimation results and certificates for invalidity. Availability: ADMIT, tutorials and illustrative examples are available free of charge for non-commercial use at http://ifatwww.et.uni-magdeburg.de/syst/ADMIT/ Contact: stefan.streif@ovgu.de

Active Fault Diagnosis for Nonlinear Systems with Probabilistic Uncertainties

Abstract Stringent requirements on safety and availability of high-performance systems necessitate reliable fault detection and isolation in the event of system failures. This paper investigates active fault diagnosis of nonlinear systems with probabilistic, time-invariant uncertainties of the parameters and initial conditions. A probabilistic model-based approach is presented for the design of auxiliary input signals enhancing fault diagnosability by separation of multiple nonlinear models pertaining to nominal and faulty system operations in the presence of the probabilistic uncertainties. To obtain a computationally tractable formulation, polynomial chaos expansions are used to propagate the probabilistic uncertainties through the system models. The input design problem is formulated in terms of a metric that characterizes the similarity of arbitrarily shaped distributions of the model outputs. An optimal input sequence is generated while considering hard input and state constraints. The simulation results for active diagnosis of multiple faults in a three-tank system indicate the capability of the presented approach to improve fault detectability and isolability under probabilistic uncertainties of the parameters and initial conditions.

Robust Nonlinear Model Predictive Control with Constraint Satisfaction: A Relaxation-based Approach

Abstract A nonlinear model predictive control scheme guaranteeing robust constraint satisfaction is presented. The scheme is applicable to polynomial or rational systems and guarantees that state, terminal, and output constraints are robustly satisfied despite uncertain and bounded disturbances, parameters, and state measurements or estimates. In addition, for a suitably chosen terminal set, feasibility of the underlying optimization problem at a time instance guarantees that the constraints are robustly satisfied for all future time instances. The proposed scheme utilizes a semi-infinite optimization problem reformulated as a bilevel optimization problem: The outer program determines an input minimizing a performance index for a nominal nonlinear system, while several inner programs certify robust constraint satisfaction. We use convex relaxations to deal with the nonlinear dynamics in the inner programs efficiently. A simulation example is presented to demonstrate the approach.

Fast stochastic model predictive control of high-dimensional systems

Probabilistic uncertainties and constraints are ubiquitous in complex dynamical systems and can lead to severe closed-loop performance degradation. This paper presents a fast algorithm for stochastic model predictive control (SMPC) of high-dimensional stable linear systems with time-invariant probabilistic uncertainties in initial conditions and system parameters. Tools and concepts from polynomial chaos theory and quadratic dynamic matrix control inform the development of an input-output formulation for SMPC with output constraints. Generalized polynomial chaos theory is used to enable efficient uncertainty propagation through the high-dimensional system model. Galerkin projection is used to construct the polynomial chaos expansion for a general class of linear differential algebraic equations (DAEs), so that the SMPC algorithm is applicable to both regular and singular/descriptor systems. The fast SMPC approach is applied for control of an end-to-end continuous pharmaceutical manufacturing process with approximately 8000 states. The on-line computational cost of the proposed probabilistic input-output SMPC algorithm is independent of the state dimension and, therefore, alleviates the prohibitive computational costs of control of uncertain systems with large state dimension.

A comparative study of stochastic analysis techniques

Stochastic models are becoming increasingly popular in Systems Biology. They are compulsory, if the stochastic noise is crucial for the behavioural properties to be investigated. Thus, substantial effort has been made to develop appropriate and efficient stochastic analysis techniques. The impressive progress of hardware power and specifically the advent of multicore computers have ameliorated the computational tractability of stochastic models. We report on a comparative study focusing on the three base case techniques of stochastic analysis: exact numerical analysis, approximative numerical analysis, and simulation. For modelling we use extended stochastic Petri nets, which allows us to take advantage of structural information and to complement the stochastic analyses by qualitative analyses, belonging to the standard body of Petri net theory.

A predictive computational model of the kinetic mechanism of stimulus-induced transducer methylation and feedback regulation through CheY in archaeal phototaxis and chemotaxis

BackgroundPhoto- and chemotaxis of the archaeon Halobacterium salinarum is based on the control of flagellar motor switching through stimulus-specific methyl-accepting transducer proteins that relay the sensory input signal to a two-component system. Certain members of the transducer family function as receptor proteins by directly sensing specific chemical or physical stimuli. Others interact with specific receptor proteins like the phototaxis photoreceptors sensory rhodopsin I and II, or require specific binding proteins as for example some chemotaxis transducers. Receptor activation by light or a change in receptor occupancy by chemical stimuli results in reversible methylation of glutamate residues of the transducer proteins. Both, methylation and demethylation reactions are involved in sensory adaptation and are modulated by the response regulator CheY.ResultsBy mathematical modeling we infer the kinetic mechanisms of stimulus-induced transducer methylation and adaptation. The model (deterministic and in the form of ordinary differential equations) correctly predicts experimentally observed transducer demethylation (as detected by released methanol) in response to attractant and repellent stimuli of wildtype cells, a cheY deletion mutant, and a mutant in which the stimulated transducer species is methylation-deficient.ConclusionsWe provide a kinetic model for signal processing in photo- and chemotaxis in the archaeon H. salinarum suggesting an essential role of receptor cooperativity, antagonistic reversible methylation, and a CheY-dependent feedback on transducer demethylation.

Stability for receding-horizon stochastic model predictive control

A stochastic model predictive control (SMPC) approach is presented for discrete-time linear systems with arbitrary time-invariant probabilistic uncertainties and additive Gaussian process noise. Closed-loop stability of the SMPC approach is established by appropriate selection of the cost function. Polynomial chaos is used for uncertainty propagation through system dynamics. The performance of the SMPC approach is demonstrated using the Van de Vusse reactions.