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Technical Brief

Many-Objective Optimal Design of Sliding Mode Controls

[+] Author and Article Information
Yousef Sardahi

Mem. ASME
School of Engineering,
University of California at Merced,
Merced, CA 95343
e-mail: ysardahi@ucmerced.edu

Jian-Qiao Sun

Fellow ASME
School of Engineering,
University of California at Merced,
Merced, CA 95343
e-mail: jqsun@ucmerced.edu

1Corresponding author. Honorary Professor, Tianjin University, Nankai District, Tianjin 300072, Tianjin China.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 9, 2016; final manuscript received August 2, 2016; published online September 26, 2016. Assoc. Editor: Hashem Ashrafiuon.

J. Dyn. Sys., Meas., Control 139(1), 014501 (Sep 26, 2016) (4 pages) Paper No: DS-16-1132; doi: 10.1115/1.4034421 History: Received March 09, 2016; Revised August 02, 2016

This paper presents a many-objective optimal (MOO) control design of an adaptive and robust sliding mode control (SMC). A second-order system is used as an example to demonstrate the design method. The robustness of the closed-loop system in terms of stability and disturbance rejection are explicitly considered in the optimal design, in addition to the typical time-domain performance specifications such as the rise time, tracking error, and control effort. The genetic algorithm is used to solve for the many-objective optimization problem (MOOP). The optimal solutions known as the Pareto set and the corresponding objective functions known as the Pareto front are presented. To assist the decision-maker to choose from the solution set, we present a post-processing algorithm that operates on the Pareto front. Numerical simulations show that the proposed many-objective optimal control design and the post-processing algorithm are promising.

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Figures

Grahic Jump Location
Fig. 1

Different projections of the Pareto front: (a) Eu versus tr, (b) Eu versus the JIAE, (c) Eu versus ‖S(jω)‖∞, and (d) tr versus ‖S(jω)‖∞ (see color figures online)

Grahic Jump Location
Fig. 2

The Pareto set: (a) η versus c, (b) γ versus c, and (c) ϕ versus c

Grahic Jump Location
Fig. 3

The top 20% of the Pareto front in Fig. 1

Grahic Jump Location
Fig. 4

System responses before (red solid line) and after (black dashed-dotted line) adding both an external disturbance and 20% uncertainty in the model parameters under four randomly chosen controls from the Pareto set in Fig. 3. Here, JIAEdu is the system tracking error after applying the uncertainty and disturbance (see color figures online).

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