A Combined Stochastic and Greedy Hybrid Estimation Capability for Concurrent Hybrid Models with Autonomous Mode Transitions

Robotic and embedded systems have become increasingly pervasive in applicationsranging from space probes and life support systems to robot assistants. In order to act robustly in the physical world, robotic systems must be able to detect changes in operational mode, such as faults, whose symptoms manifest themselves only in the continuous state. In such systems, the state is observed indirectly, and must therefore be estimated in a robust, memory-efficient manner from noisy observations.Probabilistic hybrid discrete/continuous models, such as Concurrent Probabilistic Hybrid Automata (CPHA) are convenient modeling tools for such systems. In CPHA, the hidden state is represented with discrete and continuous state variables that evolve probabilistically. In this paper, we present a novel method for estimating the hybrid state of CPHA that achieves robustness by balancing greedy and stochastic search. The key insight is that stochastic and greedy search methods, taken together, are often particularly effective in practice.To accomplish this, we first develop an efficient stochastic sampling approach for CPHA based on Rao-Blackwellised Particle Filtering. We then propose a strategy for mixing stochastic and greedy search. The resulting method is able to handle three particularly challenging aspects of real-world systems, namely that they 1) exhibit autonomous mode transitions, 2) consist of a large collection of concurrently operating components, and 3) are non-linear. Autonomous mode transitions, that is, discrete transitions that depend on thecontinuous state, are particularly challenging to address, since they couple the discrete and continuous state evolution tightly. In this paper we extend the class of autonomous mode transitions that can be handled to arbitrary piecewise polynomial transition distributions.We perform an empirical comparison of the greedy and stochastic approaches to hybrid estimation, and then demonstrate the robustness of the mixed method incorporated with our HME (Hybrid Mode Estimation) capability. We show that this robustness comes at only a small performance penalty

Model predictive control techniques for hybrid systems

This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.Ministerio de Eduación y Ciencia DPI2007-66718-C04-01Ministerio de Eduación y Ciencia DPI2008-0581

Stochastic reaction networks with input processes: Analysis and applications to reporter gene systems

Stochastic reaction network models are widely utilized in biology and chemistry to describe the probabilistic dynamics of biochemical systems in general, and gene interaction networks in particular. Most often, statistical analysis and inference of these systems is addressed by parametric approaches, where the laws governing exogenous input processes, if present, are themselves fixed in advance. Motivated by reporter gene systems, widely utilized in biology to monitor gene activation at the individual cell level, we address the analysis of reaction networks with state-affine reaction rates and arbitrary input processes. We derive a generalization of the so-called moment equations where the dynamics of the network statistics are expressed as a function of the input process statistics. In stationary conditions, we provide a spectral analysis of the system and elaborate on connections with linear filtering. We then apply the theoretical results to develop a method for the reconstruction of input process statistics, namely the gene activation autocovariance function, from reporter gene population snapshot data, and demonstrate its performance on a simulated case study

Hybrid Pathwise Sensitivity Methods for Discrete Stochastic Models of Chemical Reaction Systems

Stochastic models are often used to help understand the behavior of intracellular biochemical processes. The most common such models are continuous time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of expectations of model output quantities with respect to model parameters, are useful in this setting for a variety of applications. In this paper, we introduce a class of hybrid pathwise differentiation methods for the numerical estimation of parametric sensitivities. The new hybrid methods combine elements from the three main classes of procedures for sensitivity estimation, and have a number of desirable qualities. First, the new methods are unbiased for a broad class of problems. Second, the methods are applicable to nearly any physically relevant biochemical CTMC model. Third, and as we demonstrate on several numerical examples, the new methods are quite efficient, particularly if one wishes to estimate the full gradient of parametric sensitivities. The methods are rather intuitive and utilize the multilevel Monte Carlo philosophy of splitting an expectation into separate parts and handling each in an efficient manner.Comment: 30 pages. The numerical example section has been extensively rewritte

Short and long-term wind turbine power output prediction

In the wind energy industry, it is of great importance to develop models that accurately forecast the power output of a wind turbine, as such predictions are used for wind farm location assessment or power pricing and bidding, monitoring, and preventive maintenance. As a first step, and following the guidelines of the existing literature, we use the supervisory control and data acquisition (SCADA) data to model the wind turbine power curve (WTPC). We explore various parametric and non-parametric approaches for the modeling of the WTPC, such as parametric logistic functions, and non-parametric piecewise linear, polynomial, or cubic spline interpolation functions. We demonstrate that all aforementioned classes of models are rich enough (with respect to their relative complexity) to accurately model the WTPC, as their mean squared error (MSE) is close to the MSE lower bound calculated from the historical data. We further enhance the accuracy of our proposed model, by incorporating additional environmental factors that affect the power output, such as the ambient temperature, and the wind direction. However, all aforementioned models, when it comes to forecasting, seem to have an intrinsic limitation, due to their inability to capture the inherent auto-correlation of the data. To avoid this conundrum, we show that adding a properly scaled ARMA modeling layer increases short-term prediction performance, while keeping the long-term prediction capability of the model