arXiv subjects

A. Sanand Amita Dilip

Publications and source records attributed to A. Sanand Amita Dilip.

4 recordsLinked to original sources

arXiv2024

Structural Controllability of Bilinear Systems on $\mathbb{SE(n)}$

Structural controllability challenges arise from imprecise system modeling and system interconnections in large scale systems. In this paper, we study structural control of bilinear systems on the special Euclidean group. We employ graph theoretic methods to analyze the structural controllability problem for driftless bilinear systems and structural accessibility for bilinear systems with drift. This facilitates the identification of a sparsest pattern necessary for achieving structural controllability and discerning redundant connections. To obtain a graph theoretic characterization of structural controllability and accessibility on the special Euclidean group, we introduce a novel idea of solid and broken edges on graphs; subsequently, we use the notion of transitive closure of graphs.

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arXiv2020

Geometry and control of the nonholonomic integrator: An electrodynamics analogy

We consider some generalizations of the classical nonholonomic integrator and give a geometric approach to characterize controllability for these systems. We use Stokes' theorem and results from complex analysis to obtain necessary and sufficient conditions for controllability. Furthermore, we show that optimal trajectories of certain minimum energy optimal control problems defined on these systems can be identified with the trajectory of a charged particle in an electromagnetic field.

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arXiv2019

Probabilistic state transfer, estimation and measures for optimal actuator/sensor placement for linear systems with packet dropouts

We consider linear systems subject to packet dropouts and obtain necessary and sufficient conditions for an arbitrary state transfer and state estimation over a finite time instance $T$. The data loss signal is modeled using the Bernoulli random variable. We leverage properties of the Hadamard product in our approach and use the derived necessary and sufficient conditions to compute the probability that an arbitrary state transfer is possible at a specified time instant. Similarly, the probability of finding an exact state estimate is found using the observability counterparts of the results. Using the necessary and sufficient conditions obtained for the invertibility of the Gramian, we give new probabilistic measures for optimal actuator and sensor placement problems and obtain optimal/sub-optimal solutions. We demonstrate by an example how the probabilities of packet dropouts influence the choice of an optimal actuator. We also discuss how to implement feedback laws and the LQR problem for these models involving packet dropouts.

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arXiv2019

Yet another approach to the Algebraic Riccati Inequality

We give a rank characterization of the solution set of algebraic Riccati inequality (ARI) for both controllable and uncontrollable systems. Assuming an existence of a solution of the corresponding algebraic Riccati equation (ARE), we characterize the boundedness/unboundedness properties of solutions of ARI for controllable/uncontrollable systems without any assumption on sign controllability. As a consequence of our observations, we obtain Willems' result $K_{min}\leq K\leq K_{max}$ for an ARI in the case of controllable systems and explore some structure on the extremal solutions. We also consider the curious case of uncontrollable purely imaginary eigenvalues and the behavior of the solution set of ARI. In particular, we show that a system is controllable if and only if the set of solutions of an ARI is bounded. In addition, we study the effect of the position of eigenvalues of the system matrix in the complex plane on the behavior of the solution set of ARIs. Furthermore, we obtain a rank parametrization for solutions of ARI for controllable systems.

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