This article proposes a systematic approach for optimal reset law design of a class of nonlinear systems. By using the guaranteed cost control method, sufficient conditions for the design of optimal reset law are derived in terms of linear matrix inequalities. In an offline design procedure, the reset law is computed that minimizes the upper bound of a quadratic cost function. The proposed method can be implemented for real-time applications even with small sampling time. The simulation results verify the efficacy and effectiveness of the proposed theoretical results.
In this study, the control problem of trajectory tracking of mobile robots considering the difference between the center of mass and the geometric center is presented. In vehicles, sometimes the mass and geometric centers are not the same, which may be due to a load. In this case, the tracking error model is obtained for the first time. Then, this model is linearized around the reference trajectory. The control law consists of feedforward and feedback actions. The feedforward part is calculated from the reference trajectory, which leads to solving a complex differential equation. On the other hand, based on the linearized tracking error model, a model predictive controller is utilized to compute the feedback control part. Finally, the simulation results illustrate the modeling accuracy and efficiency of the proposed method.
In this study, the problem of optimal guaranteed cost control (OGCC) for nonlinear systems under input saturation is investigated. The purpose is to design a dynamic output feedback controller such that the closed-loop system is asymptotically stable and the upper bound of the cost function is minimized. Moreover, the designed controller ensures that the control signals do not exceed their permissible values. This leads to an optimization problem with bilinear matrix inequality (BMI) constraints. The BMI conditions are converted into the linear matrix inequality conditions by using some technical lemmas for straightforward computation of the controller matrices. The simulation results show the effectiveness and advantages of the proposed theoretical results.
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