This paper presents stability analysis of fuzzy model-based nonlinear control systems, and the design of nonlinear gains and feedback gains of the nonlinear controller using a genetic algorithm (GA) with arithmetic crossover and nonuniform mutation. A stability condition is derived based on Lyapunov's stability theory with a smaller number of Lyapunov conditions. A solution of the stability con...

We extend the method of controlled Lagrangians to include potential shaping for complete state-space stabilization of mechanical systems. The method of controlled Lagrangians deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the symmetry variables. Potential shaping complement...

Presents a recurrent neural network for solving the Sylvester equation with time-varying coefficient matrices. The recurrent neural network with implicit dynamics is deliberately developed in the way that its trajectory is guaranteed to converge exponentially to the time-varying solution of a given Sylvester equation. Theoretical results of convergence and sensitivity analysis are presented to ...

The problem of tracking control of nonlinear systems whose the zero dynamics are unstable is addressed in this paper. It is shown that, using a novel cascade structure where the backstepping approach is given to stabilise the internal dynamics and the standard input output linearization to stabilise the external dynamics. Assuming high-gain feedback for the external dynamics, a stability analys...

Backstepping control technique is a Lyapunov based nonlinear robust technique which is applicable to only strict feedback system. Backstepping technique has been applied on linear inverted pendulum which is under actuated system. Inverted pendulum is swung from its pendant position and stabilized at its upright position. Swing up is achieved by nonlinear backstepping controller but the linear i...

_ Inverted pendulum control is one of the fundamental and interesting problems in the field of control theory. This paper describes the steps to design various controllers for a rotary motion inverted pendulum which is operated by a rotary servo plant, SRV 02 Series. Nonlinear model of the rotary inverted pendulum and linear model (Upright) in the neighborhood of an equilibrium state are descri...

In order to explore the essence of structural controllability, structural controllability of inverted pendulum is analyzed in this presented study and a sufficient controllability condition of a class of perturbed linear system is obtained, which is essential to prove the structural controllability for the perturbed inverted pendulum. Two different structured models of inverted pendulum are con...

The purpose of this paper is to present the design of a complete control strategy for the classical and rotary single inverted pendulum system. The design, which involves swing-up and stabilization of both systems, is based on function blocks and GUI tools from the Inverted Pendula Modeling and Control, a Simulink block library developed by the author of the paper. Keywords—classical single inv...

The inverted pendulum is a canonical problem in both Nonlinear Dynamics and Control Theory. In this article, the phenomenon of dynamic stabilization of the vertically driven inverted pendulum is investigated experimentally and numerically. We resolve the first stabilizing boundary in driving parameter space, as well as investigate the effects of frictional damping on the dynamics of the pendulu...

This paper proposes an approach for the minimum time swing upof a rotary inverted pendulum. Our rotary inverted pendulum is supported bya pivot arm. The pivot arm rotates in a horizontal plane by means of a servomotor. The opposite end of the arm is instrumented with a joint whose axisis along the radial direction of the motor. A pendulum is suspended at thejoint. The task is to design a contro...