A. Agung Julius

Approximate simulation relations for hybrid systems

Abstract Approximate simulation relations have recently been introduced as a powerful tool for the approximation of discrete and continuous systems. In this paper, we extend this notion to hybrid systems. Using the so-called simulation functions, we develop a computationally effective characterization of approximate simulation relations which can be used for hybrid systems approximation. An example of application in the context of safety verification is shown.

Modeling, control and experimental characterization of microbiorobots

In this paper, we describe how motile microorganisms can be integrated with engineered microstructures to develop a micro-bio-robotic system. SU-8 microstructures blotted with swarmer cells of Serratia Marcescens in a monolayer are propelled by the bacteria in the absence of any environmental stimulus. We call such microstructures with bacteria MicroBioRobots (MBRs) and the uncontrolled motion in the absence of stimuli self actuation. Our paper has two primary contributions. First, we demonstrate the control of MBRs using self actuation and DC electric fields, and develop an experimentally validated mathematical model for the MBRs. This model allows us to use self actuation and electrokinetic actuation to steer the MBR to any position and orientation in a planar micro channel. Second, we combine our experimental setup and a feedback control algorithm to steer robots with micrometer accuracy in two spatial dimensions. We describe the fabrication process for MBRs and show experimental results demonstrating actuation and control.

Stochastic Modeling and Control of Biological Systems: The Lactose Regulation System of Escherichia Coli

In this paper, we present a comprehensive framework for stochastic modeling, model abstraction, and controller design for a biological system. The first half of the paper concerns modeling and model abstraction of the system. Most models in systems biology are deterministic models with ordinary differential equations in the concentration variables. We present a stochastic hybrid model of the lactose regulation system of E. coli bacteria that capture important phenomena which cannot be described by continuous deterministic models. We then show that the resulting stochastic hybrid model can be abstracted into a much simpler model, a two-state continuous-time Markov chain. The second half of the paper discusses controller design for a specific architecture. The architecture consists of measurement of a global quantity in a colony of bacteria as an output feedback and manipulation of global environmental variables as control actuation. We show that controller design can be performed on the abstracted (Markov chain) model and implementation on the real model yields the desired result.

Genetic network identification using convex programming

Gene regulatory networks capture interactions between genes and other cell substances, resulting in various models for the fundamental biological process of transcription and translation. The expression levels of the genes are typically measured as mRNA concentration in micro-array experiments. In a so-called genetic perturbation experiment, small perturbations are applied to equilibrium states and the resulting changes in expression activity are measured. One of the most important problems in systems biology is to use these data to identify the interaction pattern between genes in a regulatory network, especially in a large scale network. The authors develop a novel algorithm for identifying the smallest genetic network that explains genetic perturbation experimental data. By construction, our identification algorithm is able to incorporate and respect a priori knowledge known about the network structure. A priori biological knowledge is typically qualitative, encoding whether one gene affects another gene or not, or whether the effect is positive or negative. The method is based on a convex programming relaxation of the combinatorially hard problem of L(0) minimisation. The authors apply the proposed method to the identification of a subnetwork of the SOS pathway in Escherichia coli, the segmentation polarity network in Drosophila melanogaster, and an artificial network for measuring the performance of the method.

The canonical controllers and regular interconnection

We study the control problem from the point of view of the behavioral systems theory. Two controller constructions, called canonical controllers, are introduced. We prove that for linear time-invariant behaviors, the canonical controllers implement the desired behavior if and only if there exists a controller that implements it. We also investigate the regularity of the canonical controllers, and establish the fact that they are maximally irregular. This means a canonical controller is regular if and only if every other controller that implements the desired behavior is regular.

Inferring stable genetic networks from steady-state data

Gene regulatory networks capture the interactions between genes and other cell substances, resulting from the fundamental biological process of transcription and translation. In some applications, the topology of the regulatory network is not known, and has to be inferred from experimental data. The experimental data consist of expression levels of the genes, which are typically measured as mRNA concentrations in micro-array experiments. In a so-called genetic perturbation experiment, small perturbations are applied to equilibrium states and the resulting changes in expression activity are measured. This paper develops novel algorithms that identify a sparse and stable genetic network that explains data obtained from noisy genetic perturbation experiments. Our identification algorithm is based on convex relaxations of the sparsity and stability constraints and can also incorporate a variety of prior knowledge of the network structure. Such knowledge can be either qualitative, specifying positive, negative or no interactions between genes, or quantitative, specifying a range of interaction strengths. Our approach is applied to both synthetic and experimental data, obtained for the SOS pathway in Escherichia coli, and the results show that the stability specification not only ensures consistency with the steady-state assumptions, but also significantly increases the identification performance. Since the method is based on convex optimization, it can be efficiently applied to large scale networks.

Approximate bisimulation for a class of stochastic hybrid systems

We develop a notion of approximate bisimulation for a class of stochastic hybrid systems, namely, the jump linear stochastic systems (JLSS). The idea is based on the construction of the so called stochastic bisimulation function, which quantify the distance between two jump linear stochastic systems. The function is then used to quantify the distance between a given JLSS and its abstraction, and hence quantify the quality of the abstraction. We show that this idea can be applied to simplify safety verification for JLSS. We also show that in the absence of internal disturbances, we can pose the construction of quadratic stochastic bisimulation functions as a tractable linear matrix inequality problem

Identification of stable genetic networks using convex programming

Gene regulatory networks capture interactions between genes and other cell substances, resulting in various models for the fundamental biological process of transcription and translation. The expression levels of the genes are typically measured in mRNA concentrations in micro-array experiments. In a so called genetic perturbation experiment, small perturbations are applied to equilibrium states and the resulting changes in expression activity are measured. This paper develops a novel algorithm that identifies a sparse stable genetic network that explains noisy genetic perturbation experiments obtained at equilibrium. Our identification algorithm can also incorporate a variety of possible prior knowledge of the network structure, which can be either qualitative, specifying positive, negative or no interactions between genes, or quantitative, specifying a range of interaction strength. Our method is based on a convex programming relaxation for handling the sparsity constraint, and therefore is applicable to the identification of genome-scale genetic networks.

Approximate abstraction of stochastic hybrid automata

This paper discusses a notion of approximate abstraction for linear stochastic hybrid automata (LSHA). The idea is based on the construction of the so called stochastic bisimulation function. Such function can be used to quantify the distance between a system and its approximate abstraction. The work in this paper generalizes our earlier work for jump linear stochastic systems (JLSS). In this paper we demonstrate that linear stochastic hybrid automata can be cast as a modified JLSS and modify the procedure for constructing the stochastic bisimulation function accordingly. The construction of quadratic stochastic bisimulation functions is essentially a linear matrix inequality problem. In this paper, we also discuss possible extensions of the framework to handle nonlinear dynamics and variable rate Poisson processes. As an example, we apply the framework to a chain-like stochastic hybrid automaton.

Multiple-robot drug delivery strategy through coordinated teams of microswimmers

Untethered robotic microswimmers are very promising to significantly improve various types of minimally invasive surgeries by offering high accuracy at extremely small scales. A prime example is drug delivery, for which a large number of microswimmers is required to deliver sufficient dosages to target sites. For this reason, the controllability of groups of microswimmers is essential. In this paper, we demonstrate simultaneous control of multiple geometrically similar but magnetically different microswimmers using a single global rotating magnetic field. By exploiting the differences in their magnetic properties, we triggered different swimming behaviors from the microswimmers by controlling the frequency and the strength of the global field, for example, one swim and the other does not while exposed to the same control input. Our results show that the balance between the applied magnetic torque and the hydrodynamic torque can be exploited for simultaneous control of two microswimmers to swim in opposite directions, with different velocities, and with similar velocities. This work will serve to establish important concepts for future developments of control systems to manipulate multiple magnetically actuated microswimmers and a step towards using swarms of microswimmers as viable workforces for complex operations.