Abstract In designing optimal servocontrollers for mobile robots, a quadratic cost function of states and control inputs is sometimes used [33, 53, 107]. In this design, two unknown symmetric weighting matrices — Q and R — are incorporated normally by designers. Their selection is only weakly connected to performance specifications, and certain trial and error is usually required with an interactive computer program before a satisfactory design results [53]. Regarding this, some guidelines exist in the literature. After selecting suitable weighting matrices, optimal gains are computed based on an algebraic Riccati equation solution that optimizes the fitness function — a rather complex and indirect process. It is also tedious to find stable-optimal gains to make the system stable and provide minimum servotracking error of a control system by off-line trial and error method [83, 127]. To demand stability and minimum trajectory error, one must find a trade-off between them. To alleviate this trade-off, it is possible to tune stable-optimal gains automatically by constructing an appropriate fitness function using evolutionary algorithms [61]. Consequently, it will provide the controller design process with an automatic notion.


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