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  1. The objective of this paper is to develop an open loop insulin input profile over a span of 24 hours which makes the glucose trajectory of a Type 1 diabetic person track a target glucose trajectory. The Bergman minimal model is chosen to represent the glucose-insulin dynamics which is shown to be differentially flat. An optimal control problem is posed by parameterizing the differentially flat output of the Bergman model using Fourier series, to result in an input profile that can be repeatedly administered every day. The solution to the optimization problem is then shown to present acceptable performance in terms of tracking and adhering to imposed constraints. 
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  2. In this paper, a novel way to compute derivativebased global sensitivity measures is presented. Conjugate Unscented Transform (CUT) is used to evaluate the multidimensional definite integrals which lead to the sensitivity measures. The method is compared with Monte Carlo estimates as well as the screening method of Morris. It is shown that using CUT provides a much more accurate estimate of sensitivity measures as compared to Monte Carlo (with far lesser computational cost) as well as the Morris method (with similar computational cost). Illustrations on three test functions are presented as evidence. 
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  3. Unmanned aerial vehicles (UAVs) are making increasingly long flights today with significantly longer mission times. This requires the UAVs to have long endurance as well as have long range capabilities. Motivated by locomotory patterns in birds and marine animals which demonstrate a powered-coasting-powered periodic locomotory behavior, an optimal control problem is formulated to study UAV trajectory planning. The concept of differential flatness is used to reformulate the optimal control problem as a nonlinear programing problem where the flat outputs are parameterized using Fourier series. The Π test is also used to verify the existence of a periodic solution which outperforms the steady-state motion. An example of an Aerosonde UAV is used to illustrate the improvement in endurance and range costs of the periodic control solutions relative to the equilibrium flight. 
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  4. The focus of this paper is on the global sensitivity analysis (GSA) of linear systems with time-invariant model parameter uncertainties and driven by stochastic inputs. The Sobol' indices of the evolving mean and variance estimates of states are used to assess the impact of the time-invariant uncertain model parameters and the statistics of the stochastic input on the uncertainty of the output. Numerical results on two benchmark problems help illustrate that it is conceivable that parameters, which are not so significant in contributing to the uncertainty of the mean, can be extremely significant in contributing to the uncertainty of the variances. The paper uses a polynomial chaos (PC) approach to synthesize a surrogate probabilistic model of the stochastic system after using Lagrange interpolation polynomials (LIPs) as PC bases. The Sobol' indices are then directly evaluated from the PC coefficients. Although this concept is not new, a novel interpretation of stochastic collocation-based PC and intrusive PC is presented where they are shown to represent identical probabilistic models when the system under consideration is linear. This result now permits treating linear models as black boxes to develop intrusive PC surrogates. 
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  5. The focus of this paper is on the development of a chance constrained controller for type 1 diabetic patients in the presence of model, meal and initial condition uncertainty. Since the chance constraints require the mean and variance of the evolving uncertain blood-glucose, a conjugate unscented transform based approach is used to estimate the blood-glucose statistics. The proposed approach is demonstrated on the classic Bergman model augmented with a gut dynamics model. 
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  6. The focus of this paper is on the development of an open loop controller for type 1 diabetic patients which is robust to meal and initial condition uncertainties in the presence of hypoand hyperglycemic constraints. Bernstein polynomials are used to parametrize the evolving uncertain blood-glucose. The unique bounding properties of these polynomials are then used to enforce the desired glycemic constraints. A convex optimization problem is posed in the perturbation space of the model and is solved repeatedly to sequentially converge on a sub-optimal solution. The proposed approach is demonstrated on the classic Bergman model for Type 1 diabetic patients. 
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  7. An adjoint sensitivity-based approach to determine the gradient and Hessian of cost functions for system identification of dynamical systems is presented. The motivation is the development of a computationally efficient approach relative to the direct differentiation (DD) technique and which overcomes the challenges of the step-size selection in finite difference (FD) approaches. An optimization framework is used to determine the parameters of a dynamical system which minimizes a summation of a scalar cost function evaluated at the discrete measurement instants. The discrete time measurements result in discontinuities in the Lagrange multipliers. Two approaches labeled as the Adjoint and the Hybrid are developed for the calculation of the gradient and Hessian for gradient-based optimization algorithms. The proposed approach is illustrated on the Lorenz 63 model where part of the initial conditions and model parameters are estimated using synthetic data. Examples of identifying model parameters of light curves of type 1a supernovae and a two-tank dynamic model using publicly available data are also included. 
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  8. For linear dynamic systems with uncertain parameters, design of controllers which drive a system from an initial condition to a desired final state, limited by state constraints during the transition is a nontrivial problem. This paper presents a methodology to design a state constrained controller, which is robust to time invariant uncertain variables. Polynomial chaos (PC) expansion, a spectral expansion, is used to parameterize the uncertain variables permitting the evolution of the uncertain states to be written as a polynomial function of the uncertain variables. The coefficients of the truncated PC expansion are determined using the Galerkin projection resulting in a set of deterministic equations. A transformation of PC polynomial space to the Bernstein polynomial space permits determination of bounds on the evolving states of interest. Linear programming (LP) is then used on the deterministic set of equations with constraints on the bounds of the states to determine the controller. Numerical examples are used to illustrate the benefit of the proposed technique for the design of a rest-to-rest controller subject to deformation constraints and which are robust to uncertainties in the stiffness coefficient for the benchmark spring-mass-damper system. 
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