In this paper, the construction of CLFs for nonlinear systems and a new inverse optimal control law are presented. The construction of a CLF for an affine nonlinear system is reduced to the construction of a CLF for a simpler system, and a new LgV type control law with respect to a CLF is provided. This control law is a generalization of Sontag's formula and contains a design parameter. Tuning this parameter gives many suboptimal solutions for the optimization problem. Also, the gain margin and sector margin of the control law are calculated. Examples are provided to illustrate the main theoretical results of the paper.
This paper describes the design of robust control of PI/Backstepping for the snake robot to control the joints motion. First, the stability of the method is proved and, by applying this controller to the robot, its motion pattern is controlled in a way that it can move and follow by mimicking the motion of real snakes on the predefined trajectories. Then, the control parameters are optimized using the Genetic Algorithm (GA). Comparing obtained results with sliding mode revealed that, the former has significantly reduced the tracking error and control energy; in addition there is no chattering phenomenon.
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