Julius, Agung
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Publication Metabolic Networks Analysis using Convex Optimization(2008-12-09) Julius, A. Agung; Imielinski, Marcin; Pappas, George JMetabolic networks map the biochemical reactions in a living cell to the flow of various chemical substances in the cell, which are called metabolites. A standard model of a metabolic network is given as a linear map from the reaction rates to the change in metabolites concentrations. We study two problems related to the analysis of metabolic networks, the minimal network problem and the minimal knockout problem.Publication Probabilistic Testing for Stochastic Hybrid Systems(2008-12-09) Julius, A. Agung; Pappas, George JIn this paper we propose a testing based method for safety/ reachability analysis of stochastic hybrid systems. Testing based methods are characterized by analysis based on the execution traces of the system or the simulation thereof. Testing based method is very appealing because of the simplicity of its execution, the possibility of having a partial verification, and its highly parallel structure. The key idea in this paper is the construction of a robust neighborhood consisting of states that have the same probabilistic safety/reachability properties. We construct the robust neighborhood using the level sets of a stochastic bisimulation function. We also show how to construct stochastic bisimulation functions for systems whose continuous dynamics is stable and linear. As a case example, we consider the problem of conflict detection of aircraft flight, and show that we can infer some robust probabilistic safety property by using the algorithm that we present in this paper.Publication Trajectory Based Verification Using Local Finite-Time Invariance(2009-04-30) Julius, A. Agung; Pappas, George JIn this paper we propose a trajectory based reachability analysis by using local finite-time invariance property. Trajectory based analysis are based on the execution traces of the system or the simulation thereof. This family of methods is very appealing because of the simplicity of its execution, the possibility of having a partial verification, and its highly parallel structure. The key idea in this paper is the construction of local barrier functions with growth bound in local domains of validity. By using this idea, we can generalize our previous method that is based on the availability of global bisimulation functions. We also propose a computational scheme for constructing the local barrier functions and their domains of validity, which is based on the S-procedure. We demonstrate that our method subsumes some other existing methods as special cases, and that for polynomial systems the computation can be implemented using sum-of-squares programming.Publication Bisimulation as Congruence in the Behavioral Setting(2005-12-01) Julius, A Agung; van der Schaft, A JWe cast the notion of bisimulation in the Willems' behavioral setting. We show that in this setting, bisimulation is also a congruence, as it is known in teh field of concurrent processes. Bisimulation is a congruence means if A and A' are bisimilar systems, then A II B and A' II B are also bisimilar. Here, the operator II denotes systems with composition, and B is any other system that is composed with A or A'.Publication Behavioral Control in the Presence of Disturbances(2005-01-01) Julius, A Agung; Belur, Madhu NThis paper deals with the issue of control with a constraint that in the controlled system certain variables remain free. By free, we mean that the variables are allowed to assume any trajectory. These variables can be interpreted as disturbances. The question of which controlled behaviors are a priori possible such that the controlled behaviors do not impose any constraints on the disturbance variables is addressed and solved. Certain generalities are imposed on the problem in the sense that a controller can act on only certain variables called control variables, while the performance specification is in terms of a different variable called the tobe- controlled variable. Another issue that we deal with is the notion of compatibility of such controllers. Further, the issue of controllability of the controller itself is dealt with, for the specific control problems of pole placement and stabilization. We use the behavioral approach to address these issues. In this setup control is considered as interconnection of two systems without distinguishing the variables of each system into inputs and outputs.Publication Identification of stable genetic networks using convex programming(2008-06-11) Zavlanos, Michael M; Julius, A. Agung; Pappas, George J; Boyd, Stephen PGene 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.Publication Stochastic Modeling and Control of Biological Systems: The Lactose Regulation System of Escherichia Coli(2009-01-01) Julius, Agung; Halász, Ádám; Sakar, M Selman; Rubin, Harvey; Kumar, Vijay; Pappas, George JIn 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.Publication Robust Test Generation and Coverage for Hybrid Systems(2007-04-01) Julius, Agung; Fainekos, Georgios E; Anand, Madhukar; Lee, Insup; Pappas, GeorgeTesting is an important tool for validation of the system design and its implementation. Model-based test generation allows to systematically ascertain whether the system meets its design requirements, particularly the safety and correctness requirements of the system. In this paper, we develop a framework for generating tests from hybrid systems’ models. The core idea of the framework is to develop a notion of robust test, where one nominal test can be guaranteed to yield the same qualitative behavior with any other test that is close to it. Our approach offers three distinct advantages: 1) It allows for computing and formally quantifying the robustness of some properties; 2) it establishes a method to quantify the test coverage for every test case; and 3) the procedure is parallelizable and therefore, very scalable. We demonstrate our framework by generating tests for a navigation benchmark application.Publication Harnessing bacterial power in microscale actuation(2009-05-12) Julius, A. Agung; Sakar, M. Selman; Kumar, Vijay; Steager, Edward; Pappas, George J; Cheang, U Kei; Kim, MinJunThis paper presents a systematic analysis of the motion of microscale structures actuated by flagellated bacteria. We perform the study both experimentally and theoretically. We use a blotting procedure to attach flagellated bacteria to a buoyancy-neutral plate called a microbarge. The motion of the plate depends on the distribution of the cells on the plate and the stimuli from the environment. We construct a stochastic mathematical model for the system, based on the assumption that the behavior of each bacterium is random and independent of that of its neighbors. The main finding of the paper is that the motion of the barge plus bacteria system is a function of a very small set of parameters. This reduced-dimensional model can be easily estimated using experimental data. We show that the simulation results obtained from the model show an excellent match with the experimentally-observed motion of the barge.