Convex computation of the region of attraction of polynomial control systems

We address the long-standing problem of computing the region of attraction (ROA) of a target set (e.g., a neighborhood of an equilibrium point) of a controlled nonlinear system with polynomial dynamics and semialgebraic state and input constraints. We show that the ROA can be computed by solving an infinite-dimensional convex linear programming (LP) problem over the space of measures. In turn, this problem can be solved approximately via a classical converging hierarchy of convex finite-dimensional linear matrix inequalities (LMIs). Our approach is genuinely primal in the sense that convexity of the problem of computing the ROA is an outcome of optimizing directly over system trajectories. The dual infinite-dimensional LP on nonnegative continuous functions (approximated by polynomial sum-of-squares) allows us to generate a hierarchy of semialgebraic outer approximations of the ROA at the price of solving a sequence of LMI problems with asymptotically vanishing conservatism. This sharply contrasts with the existing literature which follows an exclusively dual Lyapunov approach yielding either nonconvex bilinear matrix inequalities or conservative LMI conditions. The approach is simple and readily applicable as the outer approximations are the outcome of a single semidefinite program with no additional data required besides the problem description

Evolving model-free scattering matrix via evolutionary algorithm: 16^{16}O-16^{16}O elastic scattering at 350 MeV

We present a new procedure which enables to extract a scattering matrix $S(l)$ as a complex function of angular momentum directly from the scattering data, without any a priori model assumptions implied. The key ingredient of the procedure is the evolutionary algorithm with diffused mutation which evolves the population of the scattering matrices, via their smooth deformations, from the primary arbitrary analytical $S(l)$ shapes to the final ones giving high quality fits to the data. Due to the automatic monitoring of the scattering matrix derivatives, the final $S(l)$ shapes are monotonic and do not have any distortions. For the $^{16}$O-$^{16}$O elastic scattering data at 350 MeV, we show the independence of the final results of the primary $S(l)$ shapes. Contrary to the other approaches, our procedure provides an excellent fit by the $S(l)$ shapes which support the ``rainbow'' interpretation of the data under analysis.Comment: 7 pages, 7 figures, to be published in Phys. Rev. C (2005

Stability and Performance Verification of Optimization-based Controllers

This paper presents a method to verify closed-loop properties of optimization-based controllers for deterministic and stochastic constrained polynomial discrete-time dynamical systems. The closed-loop properties amenable to the proposed technique include global and local stability, performance with respect to a given cost function (both in a deterministic and stochastic setting) and the $\mathcal{L}_2$ gain. The method applies to a wide range of practical control problems: For instance, a dynamical controller (e.g., a PID) plus input saturation, model predictive control with state estimation, inexact model and soft constraints, or a general optimization-based controller where the underlying problem is solved with a fixed number of iterations of a first-order method are all amenable to the proposed approach. The approach is based on the observation that the control input generated by an optimization-based controller satisfies the associated Karush-Kuhn-Tucker (KKT) conditions which, provided all data is polynomial, are a system of polynomial equalities and inequalities. The closed-loop properties can then be analyzed using sum-of-squares (SOS) programming

Impact Investing and Inclusive Business Development in Africa: A research agenda

Impact investing aims to create sustainable social and environmental impacts for investee enterprises and communities as well as adequate financial returns. As an attractive emerging market investment strategy, it involves development finance institutions and philanthropic foundations partnering with mainstream private venture capital to create impact funds with the goal of catalysing inclusive market-based enterprise development in low income countries. In this paper, we present findings from a scoping study discussing the nature and operations of impact funds in African economies and the associated research opportunities on this topic. To facilitate the assessment, we reviewed the existing literature on impact investing, considering this along three interrelated perspectives, namely 1) impact investing as development finance policy for economic development, 2) impact investing as a development in socially responsible investing, and 3) impact investing as capacity-building for inclusive business development in African economies. The interplay of these perspectives shapes the constitution and operational strategies of specific impact funds and provide a conceptual context for understanding impact investing at country level. Drawing on interviews, email exchanges and roundtable discussions with representative global and country-specific (Sierra Leone, Cameroon and Kenya) stakeholders our analysis makes three contributions to the impact investing debate. First we explore a model for understanding the ways in which impact funds are being channeled into inclusive businesses in Africa and the associated catalytic effects on poverty alleviation, social and economic development. Second we identified and tested access to, a range of impact funds and associated sector-specific inclusive businesses for future case writing – hopefully ‘failures’ as well as ‘successes’. Finally, we reflect on some of the unanswered managerial and policy-related questions that require a more rigorous inquiry-led appraisal to better understand and enhance the contribution of impact funds to inclusive business development in Africa

Development, Validity and Reliability of Perceived Service Quality in Retail Banking and its Relationship With Perceived Value and Customer Satisfaction

Microfinance is often hailed both as a tool for fighting poverty and as a tool for post-conflict reconciliation. This paper explores the use of microfinance in post-civil war Bosnia and Herzegovina, assessing its results in terms of both goals. As it combined high unemployment with a highly educated population in an institutionally open context, Bosnia and Herzegovina provides a crucial test of the effect of microfinance. If unambiguous signs of success cannot be found in a case with such favorable conditions, this would raise serious questions about the potential benefits of microfinance. The paper draws together evidence from a series of independent reviews of microfinance in Bosnia and Herzegovina, to assess its impact in terms of economic performance, the economic system, social welfare and post-conflict integration. Based on this case study, microfinance appears a better tool for dealing with poverty than with social integration or institution building.perceived quality, perceived value, satisfaction, retail banking services