A Probabilistic Approach to Robust Optimal Experiment Design with Chance Constraints

Accurate estimation of parameters is paramount in developing high-fidelity models for complex dynamical systems. Model-based optimal experiment design (OED) approaches enable systematic design of dynamic experiments to generate input-output data sets with high information content for parameter estimation. Standard OED approaches however face two challenges: (i) experiment design under incomplete system information due to unknown true parameters, which usually requires many iterations of OED; (ii) incapability of systematically accounting for the inherent uncertainties of complex systems, which can lead to diminished effectiveness of the designed optimal excitation signal as well as violation of system constraints. This paper presents a robust OED approach for nonlinear systems with arbitrarily-shaped time-invariant probabilistic uncertainties. Polynomial chaos is used for efficient uncertainty propagation. The distinct feature of the robust OED approach is the inclusion of chance constraints to ensure constraint satisfaction in a stochastic setting. The presented approach is demonstrated by optimal experimental design for the JAK-STAT5 signaling pathway that regulates various cellular processes in a biological cell.Comment: Submitted to ADCHEM 201

On the convergence of stochastic MPC to terminal modes of operation

The stability of stochastic Model Predictive Control (MPC) subject to additive disturbances is often demonstrated in the literature by constructing Lyapunov-like inequalities that guarantee closed-loop performance bounds and boundedness of the state, but convergence to a terminal control law is typically not shown. In this work we use results on general state space Markov chains to find conditions that guarantee convergence of disturbed nonlinear systems to terminal modes of operation, so that they converge in probability to a priori known terminal linear feedback laws and achieve time-average performance equal to that of the terminal control law. We discuss implications for the convergence of control laws in stochastic MPC formulations, in particular we prove convergence for two formulations of stochastic MPC

Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints

This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost function in terms of expected values and higher moments of the states, and chance constraints that ensure probabilistic constraint satisfaction. The generalized polynomial chaos framework is used to propagate the time-invariant stochastic uncertainties through the nonlinear system dynamics, and to efficiently sample from the probability densities of the states to approximate the satisfaction probability of the chance constraints. To increase computational efficiency by avoiding excessive sampling, a statistical analysis is proposed to systematically determine a-priori the least conservative constraint tightening required at a given sample size to guarantee a desired feasibility probability of the sample-approximated chance constraint optimization problem. In addition, a method is presented for sample-based approximation of the analytic gradients of the chance constraints, which increases the optimization efficiency significantly. The proposed stochastic nonlinear model predictive control approach is applicable to a broad class of nonlinear systems with the sufficient condition that each term is analytic with respect to the states, and separable with respect to the inputs, states and parameters. The closed-loop performance of the proposed approach is evaluated using the Williams-Otto reactor with seven states, and ten uncertain parameters and initial conditions. The results demonstrate the efficiency of the approach for real-time stochastic model predictive control and its capability to systematically account for probabilistic uncertainties in contrast to a nonlinear model predictive control approaches.Comment: Submitted to Journal of Process Contro

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.Comment: American Control Conference (ACC) 201

Asymptotic theory for the Cox model with missing time-dependent covariate

The relationship between a time-dependent covariate and survival times is usually evaluated via the Cox model. Time-dependent covariates are generally available as longitudinal data collected regularly during the course of the study. A frequent problem, however, is the occurence of missing covariate data. A recent approach to estimation in the Cox model in this case jointly models survival and the longitudinal covariate. However, theoretical justification of this approach is still lacking. In this paper we prove existence and consistency of the maximum likelihood estimators in a joint model. The asymptotic distribution of the estimators is given along with a consistent estimator of the asymptotic variance.Comment: Published at http://dx.doi.org/10.1214/009053606000000038 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Range entropy: A bridge between signal complexity and self-similarity

Approximate entropy (ApEn) and sample entropy (SampEn) are widely used for temporal complexity analysis of real-world phenomena. However, their relationship with the Hurst exponent as a measure of self-similarity is not widely studied. Additionally, ApEn and SampEn are susceptible to signal amplitude changes. A common practice for addressing this issue is to correct their input signal amplitude by its standard deviation. In this study, we first show, using simulations, that ApEn and SampEn are related to the Hurst exponent in their tolerance r and embedding dimension m parameters. We then propose a modification to ApEn and SampEn called range entropy or RangeEn. We show that RangeEn is more robust to nonstationary signal changes, and it has a more linear relationship with the Hurst exponent, compared to ApEn and SampEn. RangeEn is bounded in the tolerance r-plane between 0 (maximum entropy) and 1 (minimum entropy) and it has no need for signal amplitude correction. Finally, we demonstrate the clinical usefulness of signal entropy measures for characterisation of epileptic EEG data as a real-world example.Comment: This is the revised and published version in Entrop

Spatial Dimensions of US Crop Selection: Recent Responses to Markets and Policy

We explicitly measure corn acreage response to the biofuels boom from 2006 to 2010. Specifically, we use newly available micro-scale planting data over time to test whether corn cultivation intensifies in proportion to the proximity of ethanol processors. We control for the endogeneity of plant location to corn acreage by using transportation network data for instruments. Our results show that reducing the distance between a farm and an ethanol plant by one percent increases acreage in corn by 0.64% and reveal a price elasticity of supply of 0.47%. To our knowledge, this is the first study that measures changes in location and intensity of corn planting in response to incentives posed by the recent biofuels boom. The results can serve as a springboard for researchers and policy-makers concerned with crop diversity, environmental sustainability, and greenhouse gas emissions.corn acreage, ethanol, panel data analysis, instrumental variables, Agricultural and Food Policy, Crop Production/Industries, Land Economics/Use, Q1, Q28, C33,

Software dynamic pricing by an optimization deterministic model with presence of piracy

This project presents an optimization model for pricing a monopolistic software application with presence of piracy. The purpose is raising revenue produced by product’s sale with adjusting prices in a price skimming strategy and minimizing amount of piracy. The model is a multifunctional price skimming optimization with simplex method which accompanied by deterministic and stochastic methods for calculating time intervals of each segment. Linear functions are used to describing demand of each segment. In addition a linear piracy function is proposed to making piracy a dynamic parameter. The model has the ability to apply penetration pricing and controlling market share. Windows 7 is chosen for case study. Optimizing case of Windows 7 is resulted in 8.2 percentage increase in revenue, while value of net market share is virtually constant. Therefore the developed model demonstrates its competence in optimizing revenue by modifying prices with presence of piracy. Results show that to face with piracy, range of price skimming must decreased in a way that highest price need to be intensely decreased and also lowest one must be slightly decreased. By using this strategy lowest loss in revenue due to piracy can be recurred. Effects of an escalation in piracy on proposed optimization model are: increase in number of sale, demand, selling portion, market share but decrease in price, price difference between segments, and revenue. Time intervals between successive prices, which are obtained for Windows 7, is obtained by deterministic and stochastic technics which are shown to be nearly equal due to large number of customers