Search results for "Lyapunov stability"
showing 10 items of 20 documents
Flow Control of Fluid in Pipelines Using PID Controller
2019
In this paper, a PID controller is utilized in order to control the flow rate of the heavy oil in pipelines by controlling the vibration in a motor pump. A torsional actuator is placed on the motor pump in order to control the vibration on a motor and consequently controlling the flow rates in pipelines. The necessary conditions for the asymptotic stability of the proposed controller are validated by implementing the Lyapunov stability theorem. The theoretical concepts are validated utilizing numerical simulations and analysis, which proves the effectiveness of the PID controller in the control of flow rates in pipelines.
An Ecology and Economy Coupling Model. A global stationary state model for a sustainable economy in the Hamiltonian formalism
2020
Abstract The severity of the two deeply correlated crises, the environmental and the economic ones, needs to be faced also in theoretical terms; thus, the authors propose a model yielding a global “stationary state”, following the idea of a “steady-state economics” by Georgescu-Rogen and Herman Daly, by constructing only one dynamical system of ecological and economic coupled variables. This is possible resorting to the generalized Volterra model, that, translated in the Hamiltonian formalism and its Hamilton equations, makes possible to “conjugate” every pair of variables, one economic, the other one ecological, in describing the behavior in time of a unique dynamical system. Applying the …
Dynamics of the Shapovalov mid-size firm model
2020
Forecasting and analyses of the dynamics of financial and economic processes such as deviations of macroeconomic aggregates (GDP, unemployment, and inflation) from their long-term trends, asset markets volatility, etc., are challenging because of the complexity of these processes. Important related research questions include, first, how to determine the qualitative properties of the dynamics of these processes, namely, whether the process is stable, unstable, chaotic (deterministic), or stochastic; and second, how best to estimate its quantitative indicators including dimension, entropy, and correlation characteristics. These questions can be studied both empirically and theoretically. In t…
Stability analysis for stochastic hybrid systems: A survey
2014
This survey addresses stability analysis for stochastic hybrid systems (SHS), which are dynamical systems that combine continuous change and instantaneous change and that also include random effects. We re-emphasize the common features found in most of the models that have appeared in the literature, which include stochastic switched systems, Markov jump systems, impulsive stochastic systems, switching diffusions, stochastic impulsive systems driven by renewal processes, diffusions driven by Lévy processes, piecewise-deterministic Markov processes, general stochastic hybrid systems, and stochastic hybrid inclusions. Then we review many of the stability concepts that have been studied, inclu…
Control of Flow Rate in Pipeline Using PID Controller
2019
In this paper a PID controller is utilized in order to control the flow rate of the heavy-oil in pipelines by controlling the vibration in motor-pump. A torsional actuator is placed on the motor-pump in order to control the vibration on motor and consequently controlling the flow rates in pipelines. The necessary conditions for asymptotic stability of the proposed controller is validated by implementing the Lyapunov stability theorem. The theoretical concepts are validated utilizing numerical simulations and analysis, which proves the effectiveness of the PID controller in the control of flow rates in pipelines.
Adaptive output feedback neural network control of uncertain non-affine systems with unknown control direction
2014
Abstract This paper deals with the problem of adaptive output feedback neural network controller design for a SISO non-affine nonlinear system. Since in practice all system states are not available in output measurement, an observer is designed to estimate these states. In comparison with the existing approaches, the current method does not require any information about the sign of control gain. In order to handle the unknown sign of the control direction, the Nussbaum-type function is utilized. In order to approximate the unknown nonlinear function, neural network is firstly exploited, and then to compensate the approximation error and external disturbance a robustifying term is employed. …
The chaotic Dadras–Momeni system: control and hyperchaotification
2015
In this paper a novel three-dimensional autonomous chaotic system, the so called Dadras-Momeni system, is considered and two different control techniques are employed to realize chaos control and chaos synchronization. Firstly, the optimal control of the chaotic system is discussed and an open loop feedback controller is proposed to stabilize the system states to one of the system equilibria, minimizing the cost function by virtue of the Pontryagin’s minimum principle. Then, an adaptive control law and an update rule for uncertain parameters, based on Lyapunov stability theory, are designed both to drive the system trajectories to an equilibrium or to realize a complete synchronization of t…
Trajectory Decentralized Fuzzy Control of Multiple UAVs.
2008
This paper considers a complete position and heading rate control system for multiple unmanned aerial vehicles (UAVs) with constant altitude. A decentralized trajectory planning algorithm is proposed, where the UAVs will avoid collisions while moving. In order to stabilize the UAVs in the reference planned trajectories and ensure the boundedness of the control velocities, a fuzzy control law is proposed with Lyapunov's stability proof. Simulation experiments developed in Matlab environment confirm the effectiveness and the robustness of the proposed control algorithm with respect to possible turbulence disturbances perturbing the nominal motion of the UAVs.
Chaos synchronization for a class of chaotic systems via H<inf>&#x221E;</inf> control technique
2013
In this paper, the robust synchronization control for a class of chaotic systems is studied. Based on linear matrix inequality techniques and Lyapunov stability theory, a novel H∝ robust synchronization controller is designed for the possible application in real engineering. Finally, some numerical simulations are included to demonstrate the effectiveness of the proposed techniques.
Adaptive neural state-feedback stabilizing controller for nonlinear systems with mismatched uncertainty
2014
In this paper, an adaptive neural network (NN) state-feedback controller for a class of nonlinear systems with mismatched uncertainties is presented. By using a radial basis (RBF) neural network, a bound of unknown nonlinear functions is approximated so that no information about the upper bound of mismatched uncertainties is required. The state-feedback is based on Lyapunov stability theory, and it is shown that the asymptotic convergence of the closed-loop system to zero is achieved while maintaining bounded states at the same time. The presented methods are more general than the previous approaches, handling systems with no restriction on the dimension of the system and the number of inpu…