Publications

Abstract: Min–max optimization arise in many domains such as game theory, adversarial machine learning, robust optimization, control, and signal processing. In convex–concave min-max optimization, gradient-based methods are well understood and enjoy strong guarantees. However, in absence of convexity or concavity, existing approaches study convergence to an approximate saddle point or first-order stationary points, which may be arbitrarily far from global optima. In this work, we present an algorithmic apparatus for computing globally optimal solutions in convex–non-concave and non-convex–concave min-max optimization. For convex–non-concave min-max problems, we employ a reformulation that transforms it into a non-concave–convex max-min optimization problem with suitably defined feasible sets and objective function; the new form can be viewed as a generalization of Sion’s minimax theorem to convex–non-concave min-max optimization. Next, we introduce EXOTIC — an Exact, Optimistic, Tree-based algorithm for solving the reformulated max–min problem. EXOTIC employs an iterative convex optimization solver to (approximately) solve the inner minimization and a hierarchical tree search for the outer maximization to optimistically select promising regions to search based on the approximate solution returned by convex optimization solver. We establish an upper bound on its optimality gap as a function of the number of calls to the inner solver, the solver’s convergence rate, and additional problem-dependent parameters. Both our algorithmic apparatus along with its accompanying theoretical analysis can also be applied for non-convex–concave min-max optimization. In addition, we propose a class of benchmark convex–non-concave min–max problems along with their analytical global solutions, providing a testbed for evaluating algorithms for min-max optimization. Empirically, EXOTIC outperforms gradient-based methods on this benchmark as well as on existing numerical benchmark problems from the literature. Finally, we demonstrate the utility of EXOTIC by computing security strategies in multi-player games with three or more players–a computationally challenging task that, to our knowledge, no prior method solves exactly. 

Abstract: This article presents a numerically tractable technique for synthesizing feedbacks to ensure robust positive invariance of given compact sets for nonlinear control systems. In broad strokes, the search for suitable feedback is turned into a linear approximation problem in a functional analytic sense, and the verification of the so-called 'tangent conditions' for robust positive invariance are employed for the ensuing approximation. This verification turns out to be equivalent to solving a compact family of convex inequalities on a compact domain, and an algorithmic procedure based on the recent work DACC22 is deployed and charged with this task. The technique applies to noisy continuous nonlinear control-affine systems without special algebraic structure and does not even require the analytical expressions of the various vector fields as long as they can be evaluated at will. Several numerical examples are presented to illustrate our results.

Abstract: In a lot of scientific problems, there is the need to generate data through the running of an extensive number of experiments. Further, some tasks require constant human intervention. We consider the problem of crack detection in steel plates. The way in which this generally happens is through humans looking at an image of the thermogram generated by heating the plate and classifying whether it is cracked or not. There has been a rise in the use of Artificial Intelligence (AI) based methods which try to remove the requirement of a human from this loop by using algorithms such as Convolutional Neural Netowrks (CNN)s as a proxy for the detection process. The issue is that CNNs and other vision models are generally very data-hungry and require huge amounts of data before they can start performing well. This data generation process is not very easy and requires innovation in terms of mechanical and electronic design of the experimental setup. It further requires massive amount of time and energy, which is difficult in resource-constrained scenarios. We try to solve exactly this problem, by creating a synthetic data generation pipeline based on Finite Element Simulations. We employ data augmentation techniques on this data to further increase the volume and diversity of data generated. The working of this concept is shown via performing inference on fine-tuned vision models and we have also validated the results by checking if our approach translates to realistic experimental data. We show the conditions where this translation is successful and how we can go about achieving that.

Abstract:  Unmanned Aerial Vehicle (UAV) surveillance has emerged as a transformative tool in disaster management and response. In disaster scenarios, maximizing UAV network coverage is essential for extracting maximum environmental information. A majority of the planar coverage maximization solutions are primarily inapplicable to non-convex and dis connected regions. This paper presents a novel framework that processes input images, extracts boundaries, and reduces their dimensionality using the Ramer-Douglas-Peucker algorithm to generate a union of polygons, which may exhibit non-convexity, disconnectedness, or both. It then implements a genetic algorithm to produce a high-quality sensor configuration. Our approach innovatively integrates Monte Carlo sampling and directly encodes sensor positions into the chromosome, optimizing the use of problem geometry. 

Abstract: A star tracker is a highly accurate attitude determination system for satellites. Star tracker’s algorithms rely on certain system-specific parameters to obtain precise quaternions. Tuning these parameters is challenging and time-intensive owing to the wide range of potential parameter values and the need for precise adjustments. This paper proposes the use of a novel approach employing Genetic Algorithm (GA) to identify the optimal parameters for a star tracker’s image processing algorithms. The star tracker algorithm consists of a feature extraction block that determines the centroids of stars in the image, a star matching block that employs a k-vector based technique to match stars with the stars in the guide star catalogue available on-board, and an estimation block that calculates the quaternion using inertial and body frame vectors of the matched stars. The parameters targeted by the GA include: a measure that characterises localization uncertainty which is crucial for effectively exploring the search space and utilising the k-vector search technique in star matching, three validation parameters to authenticate the matched stars, and an error metric for assessing the feasibility of the obtained quaternion. The GA encompasses a fitness function formulated in terms of error between estimated and ideal quaternions in Euler form. The algorithm then uses this fitness function to iterate over the population of parameters, which undergo multiple rounds of crossover, mutation, and selection to reach the optimal values of these parameters. The parameters having comparatively large search intervals were dealt with using logarithmic scaling. Preliminary testing on simulated night sky images has shown promising results, with 80% of the images having errors less than 10 arc seconds. This provides a strong foundation for the algorithm’s performance. Ongoing testing with real night sky images will further validate its practical applicability and robustness in real-world scenarios.

Abstract- 

This paper aims to discuss an innovative way to simulate orbital conditions in software such as Ansys Workbench,

which lacks direct orbital modelling. It aims to explore the modelling of the thermal subsystem of a small satellite in

the launch and in-orbit conditions through the performance of transient thermal simulations. These simulations

quantify the requirement of thermal control for maintaining the optimal functionality of electronic components

within the satellite. Passive thermal control methods such as multi-layer insulation and surface coatings have been

modelled and simulated in this paper. The paper attempts to study the effect of parameters such as the number of

layers and layer thickness on the effectiveness of multi-layer insulation. It studies the variation of temperature on

absorption and emission properties of surface coatings. It further looks at the optimisation of these techniques by

improving the meshing, which can significantly decrease computation time and reduce convergence issues. The

paper also proposes a method of performing thermo-structural simulations, which can provide an analysis of the

thermal stresses produced in satellites because of the temperature gradients. The role played by joint and contact

definitions in thermal simulations has also been highlighted.