H ∞ state feedback control of discrete-time Markov jump linear systems through linear matrix inequalities

This paper addresses the H ∞ state-feedback control design problem of discretetime Markov jump linear systems. First, under the assumption that the Markov parameter is measured, the main contribution is on the LMI characterization of all linear feedback controllers such that the closed loop output remains bounded by a given norm level. This results allows the robust controller design to deal with convex bounded parameter uncertainty, probability uncertainty and cluster availability of the Markov mode. For partly unknown transition probabilities, the proposed design problem is proved to be less conservative than one available in the current literature. An example is solved for illustration and comparisons. © 2011 IFAC.

Alocação de pólos com realimentação da derivada dos estados usando LMIs

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Método de estimativa de torque da articulação do joelho baseada em EMG

Este trabalho apresenta um método de estimativa de torque do joelho baseado em sinais eletromiográficos (EMG) durante terapia de reabilitação robótica. Os EMGs, adquiridos de cinco músculos envolvidos no movimento de flexão e extensão do joelho, são processados para encontrar as ativações musculares. Em seguida, mediante um modelo simples de contração muscular, são calculadas as forças e, usando a geometria da articulação, o torque do joelho. As funções de ativação e contração musculares possuem parâmetros limitados que devem ser calibrados para cada usuário, sendo o ajuste feito mediante a minimização do erro entre o torque estimado e o torque medido na articulação usando a dinâmica inversa. São comparados dois métodos iterativos para funções não-lineares como técnicas de otimização restrita para a calibração dos parâmetros: Gradiente Descendente e Quasi-Newton. O processamento de sinais, calibração de parâmetros e cálculo de torque estimado foram desenvolvidos no software MATLAB®; o cálculo de torque medido foi feito no software OpenSim com sua ferramenta de dinâmica inversa.

Flow of a micropolar fluid bounded by a stretching sheet

We consider boundary layer flow of a micropolar fluid driven by a porous stretching sheet. A similarity solution is defined, and numerical solutions using Runge-Kutta and quasilinearisation schemes are obtained. A perturbation analysis is also used to derive analytic solutions to first order in the perturbing parameter. The resulting closed form solutions involve relatively complex expressions, and the analysis is made more tractable by a combination of offline and online work using a computational algebra system (CAS). For this combined numerical and analytic approach, the perturbation analysis yields a number of benefits with regard to the numerical work. The existence of a closed form solution helps to discriminate between acceptable and spurious numerical solutions. Also, the expressions obtained from the perturbation work can provide an accurate description of the solution for ranges of parameters where the numerical approaches considered here prove computationally more difficult.

Bounded parameter Markov Decision Processes with average reward criterion

Bounded parameter Markov Decision Processes (BMDPs) address the issue of dealing with uncertainty in the parameters of a Markov Decision Process (MDP). Unlike the case of an MDP, the notion of an optimal policy for a BMDP is not entirely straightforward. We consider two notions of optimality based on optimistic and pessimistic criteria. These have been analyzed for discounted BMDPs. Here we provide results for average reward BMDPs. We establish a fundamental relationship between the discounted and the average reward problems, prove the existence of Blackwell optimal policies and, for both notions of optimality, derive algorithms that converge to the optimal value function.

Experimental and numerical investigation of jet injection in a wall bounded supersonic flow

Numerical and experimental studies of a supersonic jet (Helium) inclined at 45 degrees to a oncoming Mach 2 flow have been carried out. The numerical study has been used to arrive at a geometry that could reduce an oncoming Mach 5.75 flow to Mach 2 flow and in determining the jet parameters. Experiments are carried out in the IISc. hypersonic shock tunnel HST2 at similar conditions obtained from numerical studies. Flow visualization studies carried out using Schlieren technique clearly show the presence of the bow shock in front of the jet exposed to supersonic cross flow. The jet Mach number is experimentally found to be approximate to 3. Visual observations show that the jet has penetrated up to 60% of the total height of the chamber.

Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel

Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier-Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.

Energy efficient scheduling for cluster-tree wireless sensor networks with time-bounded data flows: application to IEEE 802.15.4/ZigBee

Cluster scheduling and collision avoidance are crucial issues in large-scale cluster-tree Wireless Sensor Networks (WSNs). The paper presents a methodology that provides a Time Division Cluster Scheduling (TDCS) mechanism based on the cyclic extension of RCPS/TC (Resource Constrained Project Scheduling with Temporal Constraints) problem for a cluster-tree WSN, assuming bounded communication errors. The objective is to meet all end-to-end deadlines of a predefined set of time-bounded data flows while minimizing the energy consumption of the nodes by setting the TDCS period as long as possible. Sinceeach cluster is active only once during the period, the end-to-end delay of a given flow may span over several periods when there are the flows with opposite direction. The scheduling tool enables system designers to efficiently configure all required parameters of the IEEE 802.15.4/ZigBee beaconenabled cluster-tree WSNs in the network design time. The performance evaluation of thescheduling tool shows that the problems with dozens of nodes can be solved while using optimal solvers.

Simulation study of energy efficient scheduling for IEEE 802.15.4/ZigBee cluster-treeWireless Sensor Networks with time-bounded data flows

The simulation analysis is important approach to developing and evaluating the systems in terms of development time and cost. This paper demonstrates the application of Time Division Cluster Scheduling (TDCS) tool for the configuration of IEEE 802.15.4/ZigBee beaconenabled cluster-tree WSNs using the simulation analysis, as an illustrative example that confirms the practical applicability of the tool. The simulation study analyses how the number of retransmissions impacts the reliability of data transmission, the energy consumption of the nodes and the end-to-end communication delay, based on the simulation model that was implemented in the Opnet Modeler. The configuration parameters of the network are obtained directly from the TDCS tool. The simulation results show that the number of retransmissions impacts the reliability, the energy consumption and the end-to-end delay, in a way that improving the one may degrade the others.

A Study on the Transport and Distribution of Atmospheric Aerosols and its Influence on Regional Meteorological Parameters over the Indian Subcontinent

This doctoral thesis addresses the growing concern about the significant changes in the climatic and weather patterns due to the aerosol loading that have taken place in the Indo Gangetic Plain(IGP)which includes most of the Northern Indian region. The study region comprises of major industrial cities in India (New Delhi, Kanpur, Allahabad, Jamshedpur and Kolkata). Northern and central parts of India are one of the most thickly populated areas in the world and have the most intensely farmed areas. Rapid increase in population and urbanization has resulted in an abrupt increase in aerosol concentrations in recent years. The IGP has a major source of coal; therefore most of the industries including numerous thermal power plants that run on coal are located around this region. They inject copious amount of aerosols into the atmosphere. Moreover, the transport of dust aerosols from arid locations is prevalent during the dry months which increase the aerosol loading in theatmosphere. The topography of the place is also ideal for the congregation of aerosols. It is bounded by the Himalayas in the north, Thar Desert in the west, the Vindhyan range in the south and Brahmaputra ridge in the east. During the non‐monsoon months (October to May) the weather in the location is dry with very little rainfall. Surface winds are weak during most of the time in this dry season. The aerosols that reach the location by means of long distance transport and from regional sources get accumulated under these favourable conditions. The increase in aerosol concentration due to the complex combination of aerosol transport and anthropogenic factors mixed with the contribution from the natural sources alters the optical properties and the life time of clouds in the region. The associated perturbations in radiative balance have a significant impact on the meteorological parameters and this in turn determines the precipitation forming process. Therefore, any change in weather which disturbs the normal hydrological pattern is alarming in the socio‐economic point of view. Hence, the main focus of this work is to determine the variation in transport and distribution of aerosols in the region and to understand the interaction of these aerosols with meteorological parameters and cloud properties.

Sparse partition universal graphs for graphs of bounded degree

In 1983, Chvatal, Trotter and the two senior authors proved that for any Delta there exists a constant B such that, for any n, any 2-colouring of the edges of the complete graph K(N) with N >= Bn vertices yields a monochromatic copy of any graph H that has n vertices and maximum degree Delta. We prove that the complete graph may be replaced by a sparser graph G that has N vertices and O(N(2-1/Delta)log(1/Delta)N) edges, with N = [B`n] for some constant B` that depends only on Delta. Consequently, the so-called size-Ramsey number of any H with n vertices and maximum degree Delta is O(n(2-1/Delta)log(1/Delta)n) Our approach is based on random graphs; in fact, we show that the classical Erdos-Renyi random graph with the numerical parameters above satisfies a stronger partition property with high probability, namely, that any 2-colouring of its edges contains a monochromatic universal graph for the class of graphs on n vertices and maximum degree Delta. The main tool in our proof is the regularity method, adapted to a suitable sparse setting. The novel ingredient developed here is an embedding strategy that allows one to embed bounded degree graphs of linear order in certain pseudorandom graphs. Crucial to our proof is the fact that regularity is typically inherited at a scale that is much finer than the scale at which it is assumed. (C) 2011 Elsevier Inc. All rights reserved.

A neural network approach for robust nonlinear parameter estimation in presence of unknown-but-bounded errors

Systems based on artificial neural networks have high computational rates due to the use of a massive number of simple processing elements and the high degree of connectivity between these elements. This paper presents a novel approach to solve robust parameter estimation problem for nonlinear model with unknown-but-bounded errors and uncertainties. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the network convergence to the equilibrium points. A solution for the robust estimation problem with unknown-but-bounded error corresponds to an equilibrium point of the network. Simulation results are presented as an illustration of the proposed approach. Copyright (C) 2000 IFAC.

Spatio-temporal dynamics and transition from asymptotic equilibrium to bounded oscillations in Chrysomya albiceps (Diptera, Calliphoridae)

The sensitivity of parameters that govern the stability of population size in Chrysomya albiceps and describe its spatial dynamics was evaluated in this study. The dynamics was modeled using a density-dependent model of population growth. Our simulations show that variation in fecundity and mainly in survival has marked effect on the dynamics and indicates the possibility of transitions from one-point equilibrium to bounded oscillations. C. albiceps exhibits a two-point limit cycle, but the introduction of diffusive dispersal induces an evident qualitative shift from two-point limit cycle to a one fixed-point dynamics. Population dynamics of C. albiceps is here compared to dynamics of Cochliomyia macellaria, C. megacephala and C. putoria.

The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems

Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When the penalty parameter becomes very large, solving the subproblem becomes difficult; therefore, the effectiveness of this approach is associated with the boundedness of the penalty parameters. In this paper, it is proved that under more natural assumptions than the ones employed until now, penalty parameters are bounded. For proving the new boundedness result, the original algorithm has been slightly modified. Numerical consequences of the modifications are discussed and computational experiments are presented.

A new approach for modeling and control of nonlinear systems via norm-bounded linear differential inclusions

A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model, and this feature is also one important contribution of this paper. Once the NLDI representation of the nonlinear system is obtained, the paper proposes the application of a linear control design method to this representation. The design is based on quadratic Lyapunov functions and formulated as search problem over a set of bilinear matrix inequalities (BMIs), which is solved using a two-step separation procedure that maps the BMIs into a set of corresponding linear matrix inequalities. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.