Multi-Objective Optimal Feedback Controls for Under-Actuated Dynamical System

doi:10.1007/s12204-020-2211-2

Abstract

Abstract: This paper presents a study of optimal control design for a single-inverted pendulum (SIP) system with
the multi-objective particle swarm optimization (MOPSO) algorithm. The proportional derivative (PD) control
algorithm is utilized to control the system. Since the SIP system is nonlinear and the output (the pendulum angle)
cannot be directly controlled (it is under-actuated), the PD control gains are not tuned with classical approaches.
In this work, the MOPSO method is used to obtain the best PD gains. The use of multi-objective optimization
algorithm allows the control design of the system without the need of linearization, which is not provided by
using classical methods. The multi-objective optimal control design of the nonlinear system involves four design
parameters (PD gains) and six objective functions (time-domain performance indices). The Hausdorff distances of
consecutive Pareto sets, obtained in the MOPSO iterations, are computed to check the convergence of the MOPSO
algorithm. The MOPSO algorithm finds the Pareto set and the Pareto front efficiently. Numerical simulations
and experiments of the rotary inverted pendulum system are done to verify this design technique. Numerical and
experimental results show that the multi-objective optimal controls offer a wide range of choices including the
ones that have comparable performance to the linear quadratic regulator (LQR) control.

Key words: multi-objective optimal control| under-actuated system| particle swarm optimization (PSO)| rotary
inverted pendulum

摘要： This paper presents a study of optimal control design for a single-inverted pendulum (SIP) system with
the multi-objective particle swarm optimization (MOPSO) algorithm. The proportional derivative (PD) control
algorithm is utilized to control the system. Since the SIP system is nonlinear and the output (the pendulum angle)
cannot be directly controlled (it is under-actuated), the PD control gains are not tuned with classical approaches.
In this work, the MOPSO method is used to obtain the best PD gains. The use of multi-objective optimization
algorithm allows the control design of the system without the need of linearization, which is not provided by
using classical methods. The multi-objective optimal control design of the nonlinear system involves four design
parameters (PD gains) and six objective functions (time-domain performance indices). The Hausdorff distances of
consecutive Pareto sets, obtained in the MOPSO iterations, are computed to check the convergence of the MOPSO
algorithm. The MOPSO algorithm finds the Pareto set and the Pareto front efficiently. Numerical simulations
and experiments of the rotary inverted pendulum system are done to verify this design technique. Numerical and
experimental results show that the multi-objective optimal controls offer a wide range of choices including the
ones that have comparable performance to the linear quadratic regulator (LQR) control.

关键词: multi-objective optimal control| under-actuated system| particle swarm optimization (PSO)| rotary
inverted pendulum

CLC Number:

O 232
TP 183

QIN Zhichang, XIN Ying, SUN Jianqiao . Multi-Objective Optimal Feedback Controls for Under-Actuated Dynamical System[J]. Journal of Shanghai Jiao Tong University(Science), 2020, 25(5): 545-552.

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