Data-Driven Convex Approach to Off-road Navigation via Linear Transfer Operators

We consider the problem of optimal navigation control design for navigation on off-road terrain. We use traversability measure to characterize the degree of difficulty of navigation on the off-road terrain. The traversability measure captures the property of terrain essential for navigation, such as elevation map, terrain roughness, slope, and terrain texture. The terrain with the presence or absence of obstacles becomes a particular case of the proposed traversability measure. We provide a convex formulation to the off-road navigation problem by lifting the problem to the density space using the linear Perron-Frobenius (P-F) operator. The convex formulation leads to an infinite-dimensional optimal navigation problem for control synthesis. The finite-dimensional approximation of the infinite-dimensional convex problem is constructed using data. We use a computational framework involving the Koopman operator and the duality between the Koopman and P-F operator for the data-driven approximation. This makes our proposed approach data-driven and can be applied in cases where an explicit system model is unavailable. Finally, we demonstrate the application of the developed framework for the navigation of vehicle dynamics with Dubin's car model

Data-driven optimal control under safety constraints using sparse Koopman approximation

In this work we approach the dual optimal reach-safe control problem using sparse approximations of Koopman operator. Matrix approximation of Koopman operator needs to solve a least-squares (LS) problem in the lifted function space, which is computationally intractable for fine discretizations and high dimensions. The state transitional physical meaning of the Koopman operator leads to a sparse LS problem in this space. Leveraging this sparsity, we propose an efficient method to solve the sparse LS problem where we reduce the problem dimension dramatically by formulating the problem using only the non-zero elements in the approximation matrix with known sparsity pattern. The obtained matrix approximation of the operators is then used in a dual optimal reach-safe problem formulation where a linear program with sparse linear constraints naturally appears. We validate our proposed method on various dynamical systems and show that the computation time for operator approximation is greatly reduced with high precision in the solutions

Vehicle-to-Grid Integration for Enhancement of Grid: A Distributed Resource Allocation Approach

In the future grids, to reduce greenhouse gas emissions Electric Vehicles (EVs) seems to be an important means of transportation. One of the major disadvantages of the future grid is the demand-supply mismatch which can be mitigated by incorporating the EVs into the grid. The paper introduces the concept of the Distributed Resource Allocation (DRA) approach for incorporating a large number of Plug-in EV (PEVs) with the power grid utilizing the concept of achieving output consensus. The charging/discharging time of all the participating PEVs are separated with respect to time slots and are considered as strategies. The major aim of the paper is to obtain a favorable charging strategy for each grid-connected PEVs in such a way that it satisfies both grid objectives in terms of load profile smoothening and minimizing of load shifting as well as economic and social interests of vehicle owners i.e. a fair share of the rate of charging for all connected PEVs. The three-fold contribution of the paper in smoothening of load profile, load shifting minimization, and fair charging rate is validated using a representative case study. The results confirm improvement in load profile and also highlight a fair deal in the charging rate for each PEV