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Design and Real Time implementation of fmincon, MOGA tuned IO-PID and FO-PIλDμ controllers for Stabilization of TRMS 3

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Design and Real Time implementation of fmincon, MOGA tuned I...

3rd International Conference on Computing and Network Communications, CoCoNet 2019

作者： Valluru, Sudarshan K. Kumar, Rajul Kumar, Rahul Center for Control of Dynamical Systems and Computation Dept. of Electrical Engineering Delhi Technological University Delhi110042 India

The insistence of this paper is to design Fractional order-proportional Integral Derivative (FO-PID) and Integral order -Proportional Integral Derivative (IO-PID) controllers for trajectory tracking control of Twin rotor Multiple Input Multiple Output (MIMO) system (TRMS). The aim of these designed controllers is to move the main and tail actuator at the desired angles accurately to fulfill the demanding attributes so that TRMS should stabilize while hovering. The controller parameters of both the controllers are optimized using fmincon function as well as Multiobjective genetic algorithm. Both the controller are tested in real time and their performance are compared for control of yaw and pitch angles of TRMS. Manual disturbances are given at after 40 seconds of first given disturbance, and the designed controllers are highly capable in diminishing quickly the effect of manual perturbations given to the main and tail rotor of TRMS. From experiment it is observed from comparative performance that FO-PID controller tuned using multiobjective genetic algorithm give best performance in term of time taken to stabilization after the given disturbance. © 2020 The Authors. Published by Elsevier B.V.

关键词： Three term control systems

Non-Euclidean Contraction Theory for Monotone and Positive systems

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arXiv 2021年

作者： Jafarpour, Saber Davydov, Alexander Bullo, Francesco The Center for Control Dynamical Systems and Computation University of California Santa Barbara93106-5070 United States

In this note we study contractivity of monotone systems and exponential convergence of positive systems using non-Euclidean norms. We first introduce the notion of conic matrix measure as a framework to study stability of monotone and positive systems. We study properties of the conic matrix measures and investigate their connection with weak pairings and standard matrix measures. Using conic matrix measures and weak pairings, we characterize contractivity and incremental stability of monotone systems with respect to non-Euclidean norms. Moreover, we use conic matrix measures to provide sufficient conditions for exponential convergence of positive systems to their equilibria. We show that our framework leads to novel results on (i) the contractivity of excitatory Hopfield neural networks, and (ii) the stability of interconnected systems using non-monotone positive comparison systems. Copyright © 2021, The Authors. All rights reserved.

关键词： Hopfield neural networks

From contraction theory to fixed point algorithms on Riemannian and non-Euclidean spaces

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arXiv 2021年

作者： Bullo, Francesco Cisneros-Velarde, Pedro Davydov, Alexander Jafarpour, Saber Center of Control Dynamical Systems and Computation University of California Santa Barbara93106-5070 United States

The design of fixed point algorithms is at the heart of monotone operator theory, convex analysis, and of many modern optimization problems arising in machine learning and control. This tutorial reviews recent advances in understanding the relationship between Demidovich conditions, one-sided Lipschitz conditions, and contractivity theorems. We review the standard contraction theory on Euclidean spaces as well as little-known results for Riemannian manifolds. Special emphasis is placed on the setting of non-Euclidean norms and the recently introduced weak pairings for the 1 and ∞ norms. We highlight recent results on explicit and implicit fixed point schemes for non-Euclidean contracting systems. Copyright © 2021, The Authors. All rights reserved.

关键词： Machine learning

Convex Optimization of the Basic Reproduction Number

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arXiv 2021年

作者： Smith, Kevin D. Bullo, Francesco The Center for Control Dynamical Systems and Computation UC Santa Barbara CA93106-5070 United States

The basic reproduction number R0 is a fundamental quantity in epidemiological modeling, reflecting the typical number of secondary infections that arise from a single infected individual. While R0is widely known to scientists, policymakers, and the general public, it has received comparatively little attention in the controls community. This note provides two novel characterizations of R0: a stability characterization and a geometric program characterization. The geometric program characterization allows us to write R0-constrained and budget-constrained optimal resource allocation problems as geometric programs, which are easily transformed into convex optimization problems. We apply these programs to allocating vaccines and antidotes in numerical examples, finding that targeting R0 instead of the spectral abscissa of the Jacobian matrix (a common target in the controls literature) leads to qualitatively different solutions. Copyright © 2021, The Authors. All rights reserved.

关键词： Convex optimization

Locating fast-varying line disturbances with the frequency mismatch

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IFAC-PapersOnLine 2022年第13期55卷 270-275页

作者： Robin Delabays Laurent Pagnier Melvyn Tyloo Center for Control Dynamical Systems and Computation UCSB Santa Barbara CA 93106 USA Department of Mathematics University of Arizona Tucson AZ 85721 USA Theoretical Division Los Alamos National Laboratory Los Alamos NM 87545 USA

In an attempt to provide an efficient method for line disturbance identification in complex networks of diffusively coupled agents, we recently proposed to leverage the frequency mismatch . The frequency mismatch filters out the intricate combination of interactions induced by the network structure and quantifies to what extent the trajectory of each agent is affected by the disturbance. In this previous work, we provided some analytical evidence of its efficiency when the perturbation is assumed to be slow . In the present work, we claim that the frequency mismatch performs actually well for most disturbance regimes. This is shown through a series of simulations and is backed up by an analytical argument. Therefore, we argue that the frequency mismatch is an efficient and elegant tool for line disturbance location in complex networks of diffusively coupled agents.

关键词： Networks inference fault attack detection

Design and experimental implementation of multi-loop LQR, PID, and LQG controllers for the trajectory tracking control of twin rotor MIMO system 3rd

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Design and experimental implementation of multi-loop LQR, PI...

3rd International Conference on Intelligent Communication, control and Devices, ICICCD 2018

作者： Valluru, Sudarshan K. Singh, Madhusudan Ayush Dharavath, Abhiraj Department of Electrical Engineering Incubation Center for Control Dynamical Systems and Computation Delhi Technological University New DelhiDelhi110042 India

ISBN: (纸本)9789811386176

One DOF (degree of freedom) Twin Rotor multi-input multi-output system (TRMS) is one of the benchmarked dynamical systems which has striking comparability with Helicopter. Design of controllers for such complex air vehicle is a daunting task as it has inherent nonlinearities and cross-coupling between its main and tail rotors. Therefore, it is an interesting laboratory benchmarked control problem, to test the performance of various controllers. The control techniques focused in this paper are the experimental implementation of multi-loop controllers such as Linear Quadratic Regulator (LQR), linear proportional integral derivative (L-PID), and Linear Quadratic Gaussian (LQG) controllers on TRMS system to verify the performance of these controllers. © Springer Nature Singapore Pte Ltd. 2020.

关键词： controllers

Dual Seminorms, Ergodic Coefficients and Semicontraction Theory

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arXiv 2022年

作者： De Pasquale, Giulia Smith, Kevin D. Bullo, Francesco Valcher, Maria Elena The Dipartimento di Ingegneria dell'Informazione Università di Padova Padova35131 Italy The Center for Control Dynamical Systems and Computation UC Santa Barbara Santa BarbaraCA93101 United States

dynamical systems that are contracting on a subspace are said to be semicontracting. Semicontraction theory is a useful tool in the study of consensus algorithms and dynamical flow systems such as Markov chains. To develop a comprehensive theory of semicontracting systems, we investigate seminorms on vector spaces and define two canonical notions: projection and distance seminorms. We show that the well-known p ergodic coefficients are induced matrix seminorms and play a central role in stability problems. In particular, we formulate a duality theorem that explains why the Markov-Dobrushin coefficient is the rate of contraction for both averaging and conservation flows in discrete time. Moreover, we obtain parallel results for induced matrix log seminorms. Finally, we propose comprehensive theorems for strong semicontractivity of linear and non-linear time-varying dynamical systems with invariance and conservation properties both in discrete and continuous time. © 2022, CC BY.

关键词： Matrix algebra

Newton and interior-point methods for (constrained) nonconvex-nonconcave minmax optimization with stability and instability guarantees

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arXiv 2022年

作者： Chinchilla, Raphael Yang, Guosong Hespanha, João P. Center for Control Dynamical Systems and Computation University of California Santa BarbaraCA93106 United States Department of Electrical and Computer Engineering Rutgers University New BrunswickNJ08854 United States

We address the problem of finding a local solution to a nonconvex-nonconcave minmax optimization using Newton type methods, including primal-dual interior-point ones. The first step in our approach is to analyze the local convergence properties of Newton’s method in nonconvex minimization. It is well established that Newton’s method iterations are attracted to any point with a zero gradient, irrespective of it being a local minimum. From a dynamical system standpoint, this occurs because every point for which the gradient is zero is a locally asymptotically stable equilibrium point. We show that by adding a multiple of the identity such that the Hessian matrix is always positive definite, we can ensure that every non-local-minimum equilibrium point becomes unstable (meaning that the iterations are no longer attracted to such points), while local minima remain locally asymptotically stable. Building on this foundation, we develop Newton-type algorithms for minmax optimization, conceptualized as a sequence of local quadratic approximations for the minmax problem. Using a local quadratic approximation serves as a surrogate for guiding the modified Newton’s method towards a solution. For these local quadratic approximations to be well-defined, it is necessary to modify the Hessian matrix by adding a diagonal matrix. We demonstrate that, for an appropriate choice of this diagonal matrix, we can guarantee the instability of every non-local-minmax equilibrium point while maintaining stability for local minmax points. Using numerical examples, we illustrate the importance of guaranteeing the instability property. While our results are about local convergence, the numerical examples also indicate that our algorithm enjoys good global convergence properties. © 2022, CC BY.

关键词： Stability

Experimental validation of fully informed particle swarm optimization tuned multi-loop L-PID controllers for stabilization of gantry crane system 3rd

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Experimental validation of fully informed particle swarm opt...

3rd International Conference on Intelligent Communication, control and Devices, ICICCD 2018

作者： Valluru, Sudarshan K. Singh, Madhusudan Dobhal, Daksh Kartikeya, Kumar Kaur, Manpreet Goel, Arnav Department of Electrical Engineering Incubation Center for Control Dynamical Systems and Computation Delhi Technological University New DelhiDelhi110042 India

ISBN: (纸本)9789811386176

Linear PID controllers are commonly used as an electrical component to decrease the error between anticipated set value and actual measured values for control of various benchmarked systems. The Multi-Loop Linear PID (ML-PID) controller, gives a robust and efficient performance in most of the situations. This paper presents the implementation of linear PID controller to stabilize and control the Gantry Crane System. Optimal performance is obtained for a few specific combinations of the proportional, integral, and derivative gains, which makes it essential to tune these values through Optimization techniques. The Fully Informed Particle Swarm Optimizer (FIPSO) is used to tune the gain values of the ML-PID controlled Gantry Crane System. These values are validated experimentally, and obtained results prove that the FIPSO tuned multi-loop linear PID controller quickly stabilizes the system subjected to external disturbances. © Springer Nature Singapore Pte Ltd. 2020.

关键词： controllers