scholarly journals Global Stabilization of a Reaction Wheel Pendulum: A Discrete-Inverse Optimal Formulation Approach via A Control Lyapunov Function

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1771
Author(s):  
Oscar Danilo Montoya ◽  
Walter Gil-González ◽  
Juan A. Dominguez-Jimenez ◽  
Alexander Molina-Cabrera ◽  
Diego A. Giral-Ramírez
Keyword(s):  
Optimal Control ◽  
Lyapunov Function ◽  
Time Domain ◽  
Discrete Control ◽  
Global Stabilization ◽  
Inverse Optimal Control ◽  
Reaction Wheel ◽  
Control Lyapunov Function ◽  
Control Approach ◽  
Optimal Control Approach

This paper deals with the global stabilization of the reaction wheel pendulum (RWP) in the discrete-time domain. The discrete-inverse optimal control approach via a control Lyapunov function (CLF) is employed to make the stabilization task. The main advantages of using this control methodology can be summarized as follows: (i) it guarantees exponential stability in closed-loop operation, and (ii) the inverse control law is optimal since it minimizes the cost functional of the system. Numerical simulations demonstrate that the RWP is stabilized with the discrete-inverse optimal control approach via a CLF with different settling times as a function of the control gains. Furthermore, parametric uncertainties and comparisons with nonlinear controllers such as passivity-based and Lyapunov-based approaches developed in the continuous-time domain have demonstrated the superiority of the proposed discrete control approach. All of these simulations have been implemented in the MATLAB software.

scholarly journals Discrete-time inverse optimal control for a reaction wheel pendulum: a passivity-based control approach

2020 ◽  
Vol 19 (4) ◽  
pp. 123-132 ◽  
Author(s):  
Oscar Danilo Montoya ◽  
Walter Gil-González ◽  
Federico Martin Serra
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Point Of View ◽  
Control Analysis ◽  
Inverse Optimal Control ◽  
Reaction Wheel ◽  
Control Approach ◽  
Control Functions ◽  
Passivity Based Control ◽  
The Time Domain

In this paper it is presented the design of a controller for a reaction wheel pendulum using a discrete-time representation via optimal control from the point of view of passivity-based control analysis. The main advantage of the proposed approach is that it allows to guarantee asymptotic stability convergence using a quadratic candidate Lyapunovfunction. Numerical simulations show that the proposed inverse optimal control design permits to reach superiornumerical performance reported by continuous approaches such as Lyapunov control functions and interconnection,and damping assignment passivity-based controllers. An additional advantageof the proposed inverse optimal controlmethod is its easy implementation since it does not employ additional states. It is only required a basic discretizationof the time-domain dynamical model based on the backward representation. All the simulations are carried out inMATLAB/OCTAVE software using a codification on the script environment.

scholarly journals USING DYNAMIC NEURAL NETWORKS TO GENERATE CHAOS: AN INVERSE OPTIMAL CONTROL APPROACH

2001 ◽  
Vol 11 (03) ◽  
pp. 857-863 ◽  
Author(s):  
EDGAR N. SANCHEZ ◽  
JOSE P. PEREZ ◽  
GUANRONG CHEN
Keyword(s):  
Neural Networks ◽  
Optimal Control ◽  
Chaotic Attractors ◽  
Control Law ◽  
Inverse Optimal Control ◽  
Dynamic Neural Network ◽  
Dynamic Neural Networks ◽  
New Approach ◽  
Control Approach ◽  
Optimal Control Approach

This Letter suggests a new approach to generating chaos via dynamic neural networks. This approach is based on a recently introduced methodology of inverse optimal control for nonlinear systems. Both Chen's chaotic system and Chua's circuit are used as examples for demonstration. The control law is derived to force a dynamic neural network to reproduce the intended chaotic attractors. Computer simulations are included for illustration and verification.

CHAOTIFYING FUZZY HYPERBOLIC MODEL USING ADAPTIVE INVERSE OPTIMAL CONTROL APPROACH

2004 ◽  
Vol 14 (10) ◽  
pp. 3505-3517 ◽  
Author(s):  
HUAGUANG ZHANG ◽  
ZHILIANG WANG ◽  
DERONG LIU
Keyword(s):  
Optimal Control ◽  
Chaotic System ◽  
Parameter Tuning ◽  
Hyperbolic Model ◽  
Inverse Optimal Control ◽  
Control Approach ◽  
Adaptive Parameter ◽  
System A ◽  
Tuning Methods ◽  
Optimal Control Approach

In this paper, the problem of chaotifying the continuous-time fuzzy hyperbolic model (FHM) is studied. By tracking the dynamics of a chaotic system, a controller based on inverse optimal control and adaptive parameter tuning methods is designed to chaotify the FHM. Simulation results show that for any initial value the FHM can track a chaotic system asymptotically.

From human to humanoid locomotion—an inverse optimal control approach

2009 ◽  
Vol 28 (3) ◽  
pp. 369-383 ◽  
Author(s):  
Katja Mombaur ◽  
Anh Truong ◽  
Jean-Paul Laumond
Keyword(s):  
Optimal Control ◽  
Inverse Optimal Control ◽  
Control Approach ◽  
Optimal Control Approach

scholarly journals Global Optimal Stabilization of MT-HVDC Systems: Inverse Optimal Control Approach

Electronics ◽  
2021 ◽  
Vol 10 (22) ◽  
pp. 2819
Author(s):  
Oscar Danilo Montoya ◽  
Walter Gil-González ◽  
Federico Martin Serra ◽  
Cristian Hernan De Angelo ◽  
Jesus C. Hernández
Keyword(s):  
Optimal Control ◽  
Control Method ◽  
Short Circuit ◽  
Hierarchical Control ◽  
Primary Control ◽  
Inverse Optimal Control ◽  
Control Lyapunov Function ◽  
Control Approach ◽  
Hvdc System ◽  
Control Stage

The stabilization problem of multi-terminal high-voltage direct current (MT-HVDC) systems feeding constant power loads is addressed in this paper using an inverse optimal control (IOC). A hierarchical control structure using a convex optimization model in the secondary control stage and the IOC in the primary control stage is proposed to determine the set of references that allows the stabilization of the network under load variations. The main advantage of the IOC is that this control method ensures the closed-loop stability of the whole MT-HVDC system using a control Lyapunov function to determine the optimal control law. Numerical results in a reduced version of the CIGRE MT-HVDC system show the effectiveness of the IOC to stabilize the system under large disturbance scenarios, such as short-circuit events and topology changes. All the simulations are carried out in the MATLAB/Simulink environment.

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