2596761
Variance-constrained control for uncertain stochastic systems with missing measurements
In this paper, we are concerned with a new control problem for uncertain discrete-time stochastic systems with missing measurements. The parameter uncertainties are allowed to be norm-bounded and enter into the state matrix. The system measurements may be unavailable (i.e., missing data) at any sample time, and the probability of the occurrence of missing data is assumed to be known. The purpose of this problem is to design an output feedback controller such that, for all admissible parameter uncertainties and all possible incomplete observations, the system state of the closed-loop system is mean square bounded, and the steady-state variance of each state is not more than the individual prescribed upper bound. We show that the addressed problem can be solved by means of algebraic matrix inequalities. The explicit expression of the desired robust controllers is derived in terms of some free parameters, which may be exploited to achieve further performance requirements. An illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach.
44693659
Global exponential stability of generalized recurrent neural networks with discrete and distributed delays
This paper is concerned with analysis problem for the global exponential stability of a class of recurrent neural networks (RNNs) with mixed discrete and distributed delays. We first prove the existence and uniqueness of the equilibrium point under mild conditions, assuming neither differentiability nor strict monotonicity for the activation function. Then, by employing a new Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the RNNs to be globally exponentially stable. Therefore, the global exponential stability of the delayed RNNs can be easily checked by utilizing the numerically efficient Matlab LMI toolbox, and no tuning of parameters is required. A simulation example is exploited to show the usefulness of the derived LMI-based stability conditions.
1087779
A note on the robust stability of uncertain stochastic fuzzy systems with time-delays
Takagi-Sugeno (T-S) fuzzy models are now often used to describe complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear submodels. In this note, the T-S fuzzy model approach is exploited to establish stability criteria for a class of nonlinear stochastic systems with time delay. Sufficient conditions are derived in the format of linear matrix inequalities (LMIs), such that for all admissible parameter uncertainties, the overall fuzzy system is stochastically exponentially stable in the mean square, independent of the time delay. Therefore, with the numerically attractive Matlab LMI toolbox, the robust stability of the uncertain stochastic fuzzy systems with time delays can be easily checked.
11194956
Fuzzy guaranteed cost control for nonlinear systems with time-varying delay
This paper focuses on the problem of guaranteed cost control for Takagi-Sugeno (T-S) fuzzy systems with time-varying delayed state. A linear quadratic cost function is considered as a performance index of the closed-loop fuzzy system. Then, the guaranteed cost control of the closed-loop fuzzy system is discussed, and the sufficient conditions are provided for the construction of a guaranteed cost controller via state feedback and observer-based output feedback. When these conditions, which are given in terms of the feasibility of linear matrix inequalities (LMIs), are satisfied, the designed state feedback controller and observer-based controller gain matrices can be obtained via a convex optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the approaches proposed in this paper.
36513177
A Bayesian network approach to explaining time series with changing structure
Many examples exist of multivariate time series where dependencies between variables change over time. If these changing dependencies are not taken into account, any model that is learnt from the data will average over the different dependency structures. Paradigms that try to explain underlying processes and observed events in multivariate time series must explicitly model these changes in order to allow non-experts to analyse and understand such data. In this paper we have developed a method for generating explanations in multivariate time series that takes into account changing dependency structure. We make use of a dynamic Bayesian network model with hidden nodes. We introduce a representation and search technique for learning such models from data and test it on synthetic time series and real-world data from an oil refinery, both of which contain changing underlying structure. We compare our method to an existing EM-based method for learning structure. Results are very promising for our method and we include sample explanations, generated from models learnt from the refinery dataset.
12770105
A tractable probabilistic model for Affymetrix probe-level analysis across multiple chips
MOTIVATION
Affymetrix GeneChip arrays are currently the most widely used microarray technology. Many summarization methods have been developed to provide gene expression levels from Affymetrix probe-level data. Most of the currently popular methods do not provide a measure of uncertainty for the expression level of each gene. The use of probabilistic models can overcome this limitation. A full hierarchical Bayesian approach requires the use of computationally intensive MCMC methods that are impractical for large datasets. An alternative computationally efficient probabilistic model, mgMOS, uses Gamma distributions to model specific and non-specific binding with a latent variable to capture variations in probe affinity. Although promising, the main limitations of this model are that it does not use information from multiple chips and does not account for specific binding to the mismatch (MM) probes.


RESULTS
We extend mgMOS to model the binding affinity of probe-pairs across multiple chips and to capture the effect of specific binding to MM probes. The new model, multi-mgMOS, provides improved accuracy, as demonstrated on some bench-mark datasets and a real time-course dataset, and is much more computationally efficient than a competing hierarchical Bayesian approach that requires MCMC sampling. We demonstrate how the probabilistic model can be used to estimate credibility intervals for expression levels and their log-ratios between conditions.


AVAILABILITY
Both mgMOS and the new model multi-mgMOS have been implemented in an R package, which is available at http://www.bioinf.man.ac.uk/resources/puma.
5760140
Reliable control design of fuzzy dynamic systems with time-varying delay
This paper focuses on the reliable fuzzy control design problem for fuzzy control systems with time delay. Based on linear matrix inequality (LMI) approach, a method for designing a reliable fuzzy controller is presented. The resulting fuzzy control systems are reliable in the sense that asymptotic stability is achieved not only when all control components are operating well, but also in the presence of some component failures. A reliable fuzzy control design scheme via state feedback is proposed in terms of LMIs. The result is extended to the case of observer-based reliable fuzzy control. Two illustrative examples are given to illustrate the validity of the proposed design procedures.
2229369
Recognizing Berge Graphs
A graph is Berge if no induced subgraph of G is an odd cycle of length at least five or the complement of one. In this paper we give an algorithm to test if a graph G is Berge, with running time O(|V (G)|9). This is independent of the recent proof of the strong perfect graph conjecture.