This study aims to investigate an optimal design problem for vibration control of vehicle suspension models for reducing dynamic responses of the systems. The controller is constructed and optimized based on the approach of the hedge-algebras theory. Optimized parameters include fuzziness measures and reference ranges of state and control variables. Objective functions are considered to minimize the car body vibration and other essential objectives. Initial and optimized controllers have validated their stability through a newly proposed method using rule surfaces of the hedge-algebras–based controller. The controllers based on hedge-algebras theory have higher performance than controllers in previous publications and ensure the system stability and robustness to changes in the car body and wheel masses. The optimal approach in the present work allows determining values of design variables that are appropriate for the controlled models instead of using a trial–error method to evaluate these variables. In addition, the proposed approach to test the system stability allows simplifying this task for controllers using hedge-algebras theory.

Hedge–algebras (HA) theory provides a useful mathematical tool for modeling the linguistic values of a linguistic variable. These values are quantified by real numbers between 0 and 1. Therefore, the HA-based controller (HAC) has many advantages over the traditional fuzzy set theory-based controller (FC) in setup steps, control efficiency, computation time, and optimization. This study aims to control the avoidance of obstacles in the workspace and move to the destination of an autonomous robot using HAC, in which the HAC is optimized using the balancing composite motion optimization (BCMO) to return the optimal path. In which the investigated model is inherited from a reference. The HAC is established and optimized to minimize the traveling distance of the mobile robot and help it to avoid obstacles simultaneously. Simulations include one and two obstacle environments. Design variables, when optimizing, include the fuzzy parameters of linguistic variables and the reference range of state variables. This work is the first study in motion control of mobile robots based on the HA theory. The simulation data show that the proposed control rule base suits the mobile robot models. Therefore, the control efficiency of HAC is higher than that of a FC both in terms of the traveling distance of the robot and computation time (CPU time). Also, the establishment steps of the HAC controller show that HAC is more explicit, easier to optimize, and simpler to operate than FC. Research results in the present work also indicate that HAC can be developed and applied in motion control problems for different robot models with the advantages of a smaller traveling distance and faster computation time.