Direct Data-Driven Computation of Polytopic Robust Control Invariant Sets and State-Feedback Controllers

This paper presents a direct data-driven approach for computing robust control invariant (RCI) sets and their associated state-feedback control laws. The proposed method utilizes a single state-input trajectory generated from the system, to compute a polytopic RCI set with a desired complexity and an invariance-inducing feedback controller, without the need to identify a model of the system. The problem is formulated in terms of a set of sufficient LMI conditions that are then combined in a semi-definite program to maximize the volume of the RCI set while respecting the state and input constraints. We demonstrate through a numerical case study that the proposed data-driven approach can generate RCI sets that are of comparable size to those obtained by a model-based method in which exact knowledge of the system matrices is assumed. Under the assumption of persistency of excitation of the data, the proposed algorithm guarantees robust invariance even with a small number of data samples. Overall, the direct data-driven approach presented in this paper offers a reliable and efficient counterpart to the model-based methods for RCI set computation and state-feedback controller design.Comment: 9 pages, 4 figures, preprint submitted to 62nd IEEE Conference on Decision and Control 202

Data-Driven Computation of Robust Invariant Sets and Gain-Scheduled Controllers for Linear Parameter-Varying Systems

We present a direct data-driven approach to synthesize robust control invariant (RCI) sets and their associated gain-scheduled feedback control laws for linear parameter-varying (LPV) systems subjected to bounded disturbances. The proposed method utilizes a single state-input-scheduling trajectory to compute polytopic RCI sets, without requiring a model of the system. The problem is formulated in terms of a set of sufficient data-based LMI conditions that are then combined in a semi-definite program to maximize the volume of the RCI set, while respecting the state and input constraints. We demonstrate through a numerical example that the proposed approach can generate RCI sets with a relatively small number of data samples when the data satisfies certain excitation conditions.Comment: 7 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:2303.1815

Spectral Properties of Disordered Interacting Non-Hermitian Systems

Non-hermitian systems have gained a lot of interest in recent years. However, notions of chaos and localization in such systems have not reached the same level of maturity as in the Hermitian systems. Here, we consider non-hermitian interacting disordered Hamiltonians and attempt to analyze their chaotic behavior or lack of it through the lens of the recently introduced non-hermitian analog of the spectral form factor and the complex spacing ratio. We consider three widely relevant non-hermitian models which are unique in their ways and serve as excellent platforms for such investigations. Two of the models considered are short-ranged and have different symmetries. The third model is long-ranged, whose hermitian counterpart has itself become a subject of growing interest. All these models exhibit a deep connection with the non-hermitian Random Matrix Theory of corresponding symmetry classes at relatively weak disorder. At relatively strong disorder, the models show the absence of complex eigenvalue correlation, thereby, corresponding to Poisson statistics. Our thorough analysis is expected to play a crucial role in understanding disordered open quantum systems in general.Comment: 12 pages, 15 figures, 3 table

Computation of Parameter Dependent Robust Invariant Sets for LPV Models with Guaranteed Performance

This paper presents an iterative algorithm to compute a Robust Control Invariant (RCI) set, along with an invariance-inducing control law, for Linear Parameter-Varying (LPV) systems. As the real-time measurements of the scheduling parameters are typically available, in the presented formulation, we allow the RCI set description along with the invariance-inducing controller to be scheduling parameter dependent. The considered formulation thus leads to parameter-dependent conditions for the set invariance, which are replaced by sufficient Linear Matrix Inequality (LMI) conditions via Polya\u27s relaxation. These LMI conditions are then combined with a novel volume maximization approach in a Semidefinite Programming (SDP) problem, which aims at computing the desirably large RCI set. In addition to ensuring invariance, it is also possible to guarantee performance within the RCI set by imposing a chosen quadratic performance level as an additional constraint in the SDP problem. The reported numerical example shows that the presented iterative algorithm can generate invariant sets which are larger than the maximal RCI sets computed without exploiting scheduling parameter information

Computation of Parameter Dependent Robust Invariant Sets for LPV Models with Guaranteed Performance

This paper presents an iterative algorithm to compute a Robust Control Invariant (RCI) set, along with an invariance-inducing control law, for Linear Parameter-Varying (LPV) systems. As the real-time measurements of the scheduling parameters are typically available, in the presented formulation, we allow the RCI set description along with the invariance-inducing controller to be scheduling parameter dependent. The considered formulation thus leads to parameter-dependent conditions for the set invariance, which are replaced by sufficient Linear Matrix Inequality (LMI) conditions via Polya's relaxation. These LMI conditions are then combined with a novel volume maximization approach in a Semidefinite Programming (SDP) problem, which aims at computing the desirably large RCI set. In addition to ensuring invariance, it is also possible to guarantee performance within the RCI set by imposing a chosen quadratic performance level as an additional constraint in the SDP problem. The reported numerical example shows that the presented iterative algorithm can generate invariant sets which are larger than the maximal RCI sets computed without exploiting scheduling parameter information.Comment: 32 pages, 5 figure

Push-out bond strength of different endodontic obturation material at three different sites : in-vitro study

The key to success of any root canal therapy is adequate obturation of the prepared root canal space. Root canal sealers are not dimensionally stable and might dissolve partially over a period of time. The objective of this in vitro study is to evaluate the push-out bond strength to intraradicular dentin of two endodontic obturation materials. Forty extracted single rooted permanent teeth were used. Canals orifice was explored, teeth were instrumented. The samples were divided into two groups each containing twenty specimens obturated with different obturation material (Group1 Epiphany/Resilon and Group 2 Gutta Percha/AH Plus).The obturation systems used in this study was Element Obturation unit (Sybron Endo). Each tooth root was horizontally sectioned in approximately 2-mm thick slices from the coronal 1/3rd, middle 1/3rd and apical 1/3rd. The push-out bond strength of each specimen was calculated using Universal Testing Machine. The statistical analysis was done using two way analysis of variance (ANOVA) and tukey?s test. There was significant difference between push out bond strength of Resilon/Epiphany and AH Plus/Gutta Percha. Gutta percha group was superior with push out bond strength of 2.22 (± 0.16) Mpa in comparison to Resilon/Epiphany group with 1.61 (±0.14) Mpa (p<0.001). The interfacial bond strength achieved with Resilon/Epiphany self-etch (SE) to intraradicular dentine was not superior to that of AH Plus/Gutta Percha

Hamiltonian learning from time dynamics using variational algorithms

The Hamiltonian of a quantum system governs the dynamics of the system via the Schrodinger equation. In this paper, the Hamiltonian is reconstructed in the Pauli basis using measurables on random states forming a time series dataset. The time propagation is implemented through Trotterization and optimized variationally with gradients computed on the quantum circuit. We validate our output by reproducing the dynamics of unseen observables on a randomly chosen state not used for the optimization. Unlike the existing techniques that try and exploit the structure/properties of the Hamiltonian, our scheme is general and provides freedom with regard to what observables or initial states can be used while still remaining efficient with regard to implementation. We extend our protocol to doing quantum state learning where we solve the reverse problem of doing state learning given time series data of observables generated against several Hamiltonian dynamics. We show results on Hamiltonians involving XX, ZZ couplings along with transverse field Ising Hamiltonians and propose an analytical method for the learning of Hamiltonians consisting of generators of the SU(3) group. This paper is likely to pave the way toward using Hamiltonian learning for time series prediction within the context of quantum machine learning algorithms.Comment: 33 pages, 18 figure

Coin Based Solar Mobile Charger

Energy plays a very important role for powering the system to work well either in Humans or in any artificial system. Communication is fundamental need for humans and a mobile system provides the power to communicate with the world so easily. Mobile phone is like a part of our day to day life. Without it, one feels incomplete and unsecure because most of the work is done with the help of it. Smartphone is the most common gadget in cities and also in the small towns now. But a big backlog of this phone is high battery consumption due to several features. Thus, most of the time the smart phones users runs out of battery, suppose on a Railway station a person is waiting for train by enjoying music on phone or surfing internet for any important information and suddenly run out of battery. That time if the charging facility is available somewhere then it is like boon. So, this necessity is being conceptualized in this paper. A Coin Insertion based mobile charger can be useful in today’s scenario. It can be used on bus stations, railway compartments, railway stations, etc

Congestion Managed Multicast Routing in Wireless Mesh Network

To provide broad band connectivity to the mobile users and to build a self-structured network, where it is not possible to have wired network, “Wireless Mesh Networks” are the most vital suitable technology. Routing in Wireless Mesh Networks is a multi-objective nonlinear optimization problem with some constraints. We explore multicast routing for least-cost, delay-sensitive and congestion-sensitive in optimizing the routing in Wireless mesh networks (WMNs). In this work different parameters are associated like edge cost, edge delay and edge congestion. The aim is to create a tree traversing which the set of target nodes are spanned, so as to make the cost and congestion to be minimum with a bounded delay over the path between every pair of source and destination. Since searching optimal routing satisfying multi constraints concurrently is an NP complete problem, we have presented a competent estimated algorithm certified with experimental results, which shows that the performance of presented algorithm is nearly optimum