Continuous-time Single Network Adaptive Critic for Regulator Design of Nonlinear Control Affine Systems

An optimal control law for a general nonlinear system can be obtained by solving Hamilton-Jacobi-Bellman equation. However, it is difficult to obtain an analytical solution of this equation even for a moderately complex system. In this paper, we propose a continuoustime single network adaptive critic scheme for nonlinear control affine systems where the optimal cost-to-go function is approximated using a parametric positive semi-definite function. Unlike earlier approaches, a continuous-time weight update law is derived from the HJB equation. The stability of the system is analysed during the evolution of weights using Lyapunov theory. The effectiveness of the scheme is demonstrated through simulation examples.

Community-based Natural Resource Management: Issues and Cases from South Asia

Community-based natural resource management (CBNRM) is the joint management of natural resources by a community based on a community strategy, through a participatory mechanism involving all legitimate stakeholders. The approach is community-based in that the communities managing the resources have the legal rights, the local institutions and the economic incentives to take substantial responsibility for sustained use of these resources. This implies that the community plays an active role in the management of natural resources, not because it asserts sole ownership over them, but because it can claim participation in their management and benefits for practical and technical reasons1–4. This approach emerged as the dominant conservation concept in the late 1970s and early 1980s, of the disillusionment with the developmental state. Governments across South and South East Asia, Africa and Latin America have adopted and implemented CBNRM in various ways, viz. through sectoral programmes such as forestry, irrigation or wildlife management, multisectoral programmes such as watershed development and efforts towards political devolution. In India, the principle of decentralization through ‘gram swaraj’ was introduced by Mahatma Gandhi. The 73rd and 74th constitution amendments in 1992 gave impetus to the decentralized planning at panchayat levels through the creation of a statutory three-level local self-government structure5,6. The strength of this book is that it includes chapters by CBNRM advocates based on six seemingly innovative initiatives being implemented by nongovernmental organizations (NGOs) in ecologically vulnerable regions of South Asia: two in the Himalayas (watershed development programme in Lingmutechhu, Bhuthan and Thalisain tehsil, Paudi Grahwal District, Uttarakhand), three in semi-arid parts of western India (watershed development in Hivre Bazar, Maharashtra and Nathugadh village, Gujarat and water-harvesting structures in Gopalapura, Rajasthan) and one in the flood-plains of the Brahmaputra–Jamuna (Char land, Galibanda and Jamalpur districts, Bangladesh). Watersheds in semi-arid regions fall in the low-rainfall region (500–700 mm) and suffer the vagaries of drought 2–3 years in every five-year cycle. In all these locations, the major occupation is agriculture, most of which is rainfed or dry. The other two cases (in Uttarakhand) fall in the Himalayan region (temperate/sub-temperate climate), which has witnessed extensive deforestation in the last century and is now considered as one of the most vulnerable locations in South Asia. Terraced agriculture is being practised in these locations for a long time. The last case (Gono Chetona) falls in the Brahmaputra–Jamuna charlands which are the most ecologically vulnerable regions in the sub-continent with constantly changing landscape. Agriculture and livestock rearing are the main occupations, and there is substantial seasonal emigration for wage labour by the adult males. River erosion and floods force the people to adopt a semi-migratory lifestyle. The book attempts to analyse the potential as well as limitations of NGOdriven CBNRM endeavours across agroclimatic regions of South Asia with emphasis on four intrinsically linked normative concerns, namely sustainability, livelihood enhancement, equity and demographic decentralization in chapters 2–7. Comparative analysis of these case studies done in chapter 8, highlights the issues that require further research while portraying the strengths and limits of NGO-driven CBNRM. In Hivre Bazar, the post-watershed intervention scenario is such that farmers often grow three crops in a year – kharif bajra, rabi jowar and summer vegetable crops. Productivity has increased in the dry lands due to improvement in soil moisture levels. The revival of johads in Gopalpura has led to the proliferation of wheat and increased productivity. In Lingmuteychhu, productivity gains have also arisen, but more due to the introduction of both local and high-yielding, new varieties as opposed to increased water availability. In the case of Gono Chetona, improvements have come due to diversification of agriculture; for example, the promotion of vegetable gardens. CBNRM interventions in most cases have also led to new avenues of employment and income generation. The synthesis shows that CBNRM efforts have made significant contributions to livelihood enhancement and only limited gains in terms of collective action for sustainable and equitable access to benefits and continuing resource use, and in terms of democratic decentralization, contrary to the objectives of the programme. Livelihood benefits include improvements in availability of livelihood support resources (fuelwood, fodder, drinking water), increased productivity (including diversification of cropping pattern) in agriculture and allied activities, and new sources of livelihood. However, NGO-driven CBNRM has not met its goal of providing ‘alternative’ forms of ‘development’ due to impediments of state policy, short-sighted vision of implementers and confrontation with the socio-ecological reality of the region, which almost always are that of fragmented communities (or communities in flux) with unequal dependence and access to land and other natural resources along with great gender imbalances. Appalling, however, is the general absence of recognition of the importance of and the will to explore practical ways to bring about equitable resource transfer or benefit-sharing and the consequent innovations in this respect that are evident in the pioneering community initiatives such as pani panchayat, etc. Pertaining to the gains on the ecological sustainability front, Hivre Bazar and Thalisain initiatives through active participation of villagers have made significant regeneration of the water table within the village, and mechanisms such as ban on number of bore wells, the regulation of cropping pattern, restrictions on felling of trees and free grazing to ensure that in the future, the groundwater is neither over-exploited nor its recharge capability impaired. Nevertheless, the longterm sustainability of the interventions in the case of Ghoga and Gopalpura initiatives as the focus has been mostly on regeneration of resources, and less on regulating the use of regenerated resources. Further, in Lingmuteychhu and Gono Chetona, the interventions are mainly household-based and the focus has been less explicit on ecological components. The studies demonstrate the livelihood benefits to all of the interventions and significant variation in achievements with reference to sustainability, equity and democratic decentralization depending on the level and extent of community participation apart from the vision of implementers, strategy (or nature of intervention shaped by the question of community formation), the centrality of community formation and also the State policy. Case studies show that the influence of State policy is multi-faceted and often contradictory in nature. This necessitates NGOs to engage with the State in a much more purposeful way than in an ‘autonomous space’. Thus the role of NGOs in CBNRM is complementary, wherein they provide innovative experiments that the State can learn. This helps in achieving the goals of CBNRM through democratic decentralization. The book addresses the vital issues related to natural resource management and interests of the community. Key topics discussed throughout the book are still at the centre of the current debate. This compilation consists of well-written chapters based on rigorous synthesis of CBNRM case studies, which will serve as good references for students, researchers and practitioners in the years to come.

Spin State Selective Excitation of Single Quantum Transitions Using Multiple Quantum Spectroscopy- an Aid to Analyse Complex Proton NMR spectra of Oriented Molecules

NMR spectra of molecules oriented in liquid-crystalline matrix provide information on the structure and orientation of the molecules. Thermotropic liquid crystals used as an orienting media result in the spectra of spins that are generally strongly coupled. The number of allowed transitions increases rapidly with the increase in the number of interacting spins. Furthermore, the number of single quantum transitions required for analysis is highly redundant. In the present study, we have demonstrated that it is possible to separate the subspectra of a homonuclear dipolar coupled spin system on the basis of the spin states of the coupled heteronuclei by multiple quantum (MQ)−single quantum (SQ) correlation experiments. This significantly reduces the number of redundant transitions, thereby simplifying the analysis of the complex spectrum. The methodology has been demonstrated on the doubly 13C labeled acetonitrile aligned in the liquid-crystal matrix and has been applied to analyze the complex spectrum of an oriented six spin system.

Relationship Between Physical Structure and Tribology of Single Soot Particles Generated by Burning Ethylene

Ethylene gas is burnt and the soot generated is sampled thermophoretically at different heights along the flame axis starting from a region close to the root of the flame. The morphology and crystallinity of the particle are recorded using high resolution transmission electron microscopes. The hardness of a single particle is measured using a nanoindenter. The frictional resistance and material removal of a particle are measured using an atomic force microscope. The particles present in the mid-flame region are found to have a crystalline shell. The ones at the flame root are found to be highly disordered and the ones at the flame tip and above have randomly distributed pockets of short range order. The physical state of a particle is found to relate, but not very strongly, with the mechanical and tribological properties of the particles.

Jointly Optimal Power Control and Hop Length for a Single Cell, Dense, Ad hoc Wireless Network

We consider a dense, ad hoc wireless network confined to a small region, such that direct communication is possible between any pair of nodes. The physical communication model is that a receiver decodes the signal from a single transmitter, while treating all other signals as interference. Data packets are sent between source-destination pairs by multihop relaying. We assume that nodes self-organise into a multihop network such that all hops are of length d meters, where d is a design parameter. There is a contention based multiaccess scheme, and it is assumed that every node always has data to send, either originated from it or a transit packet (saturation assumption). In this scenario, we seek to maximize a measure of the transport capacity of the network (measured in bit-meters per second) over power controls (in a fading environment) and over the hop distance d, subject to an average power constraint. We first argue that for a dense collection of nodes confined to a small region, single cell operation is efficient for single user decoding transceivers. Then, operating the dense ad hoc network (described above) as a single cell, we study the optimal hop length and power control that maximizes the transport capacity for a given network power constraint. More specifically, for a fading channel and for a fixed transmission time strategy (akin to the IEEE 802.11 TXOP), we find that there exists an intrinsic aggregate bit rate (Thetaopt bits per second, depending on the contention mechanism and the channel fading characteristics) carried by the network, when operating at the optimal hop length and power control. The optimal transport capacity is of the form dopt(Pmacrt) x Thetaopt with dopt scaling as Pmacrt 1 /eta, where Pmacrt is the available time average transmit power and eta is the path loss exponent. Under certain conditions on the fading distribution, we then pro- - vide a simple characterisation of the optimal operating point.

Multi-agent Search using Voronoi partitions

This paper addresses the problem of multiagent search in an unknown environment. The agents are autonomous in nature and are equipped with necessary sensors to carry out the search operation. The uncertainty, or lack of information about the search area is known a priori as a probability density function. The agents are deployed in an optimal way so as to maximize the one step uncertainty reduction. The agents continue to deploy themselves and reduce uncertainty till the uncertainty density is reduced over the search space below a minimum acceptable level. It has been shown, using LaSalle’s invariance principle, that a distributed control law which moves each of the agents towards the centroid of its Voronoi partition, modified by the sensor range leads to single step optimal deployment. This principle is now used to devise search trajectories for the agents. The simulations were carried out in 2D space with saturation on speeds of the agents. The results show that the control strategy per step indeed moves the agents to the respective centroid and the algorithm reduces the uncertainty distribution to the required level within a few steps.

The single ring theorem

We study the empirical measure LA of the eigenvalues of nonnormal square matrices of the form A(n) = U(n)T(n)V(n), with U(n), V(n) independent Haar distributed on the unitary group and T(n) diagonal. We show that when the empirical measure of the eigenyalues of T(n) converges, and T(n) satisfies some technical conditions, L(An) converges towards a rotationally invariant measure mu on the complex plane whose support is a single ring. In particular, we provide a complete proof of the Feinberg-Zee single ring theorem [6]. We also consider the case where U(n), V(n) are independently Haar distributed on the orthogonal group.