## Pareto design of decoupled sliding-mode controllers for nonlinear systems based on a multiobjective genetic algorithm.(English)Zbl 1254.90214

Summary: We present a Pareto design of decoupled sliding-mode controllers based on a multiobjective genetic algorithm for several fourth-order coupled nonlinear systems. In order to achieve an optimum controller, at first, the decoupled sliding mode controller is applied to stablize the fourth-order coupled nonlinear systems at the equilibrium point. Then, the multiobjective genetic algorithm is applied to search the optimal coefficients of the decoupled sliding-mode control to improve the performance of the control system. Considered objective functions are the angle and distance errors. Finally, the simulation results implemented in the MATLAB software environment are presented for the inverted pendulum, ball and beam, and seesaw systems to assure the effectiveness of this technique.

### MSC:

 90C29 Multi-objective and goal programming 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory

Matlab
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### References:

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