Nonlinear control synthesis for asymptotic stabilization of the swing equation using a controllable series capacitor via Immersion and Invariance

2008 ◽  
Author(s):  
N. S. Manjarekar ◽  
R. N. Banavar ◽  
R. Ortega
Keyword(s):  
Nonlinear Control ◽  
Control Synthesis ◽  
Asymptotic Stabilization ◽  
Immersion And Invariance ◽  
Nonlinear Control Synthesis ◽  
Series Capacitor ◽  
Swing Equation

A homotopy approach for nonlinear control synthesis

1998 ◽  
Vol 43 (9) ◽  
pp. 1311-1318 ◽  
Author(s):  
K. Reif ◽  
K. Weinzierl ◽  
A. Zell ◽  
R. Unbehauen
Keyword(s):  
Nonlinear Control ◽  
Control Synthesis ◽  
Nonlinear Control Synthesis

Nonlinear Control Synthesis

1997 ◽  
Vol 30 (21) ◽  
pp. 115-120
Author(s):  
Antonín Víteček ◽  
Miluše Vítečková
Keyword(s):  
Nonlinear Control ◽  
Control Synthesis ◽  
Nonlinear Control Synthesis

scholarly journals A Convex Data-Driven Approach for Nonlinear Control Synthesis

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2445
Author(s):  
Hyungjin Choi ◽  
Umesh Vaidya ◽  
Yongxin Chen
Keyword(s):  
Nonlinear Control ◽  
Dynamic Systems ◽  
Data Driven ◽  
Control Synthesis ◽  
Density Functions ◽  
Convex Problem ◽  
Data Driven Approach ◽  
The Stability ◽  
Nonlinear Control Synthesis ◽  
Convex Formulation

We consider a class of nonlinear control synthesis problems where the underlying mathematical models are not explicitly known. We propose a data-driven approach to stabilize the systems when only sample trajectories of the dynamics are accessible. Our method is built on the density-function-based stability certificate that is the dual to the Lyapunov function for dynamic systems. Unlike Lyapunov-based methods, density functions lead to a convex formulation for a joint search of the control strategy and the stability certificate. This type of convex problem can be solved efficiently using the machinery of the sum of squares (SOS). For the data-driven part, we exploit the fact that the duality results in the stability theory can be understood through the lens of Perron–Frobenius and Koopman operators. This allows us to use data-driven methods to approximate these operators and combine them with the SOS techniques to establish a convex formulation of control synthesis. The efficacy of the proposed approach is demonstrated through several examples.

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