Tuning a Discrete Linear Quadratic Regulator Controller using the Region of Attraction for The Simplest Walker Model

The work done within this thesis strives to expand the capabilities of a designed Discrete Linear Quadratic Regulator (DLQR) controller. The controller is implemented into The Simplest Walker Model, and after perturbing the initial state of the system the goal is to cause the system trajectory to converge back onto the limit cycle. Every initial state that converges to the limit cycle lies within the region of attraction, depicting the controller strength. An approach to visualizing the region of attraction is used to not only depict the robustness of the controller but also assist in tuning the input parameters of the DLQR controller. The region of attraction is measured by the percentage of successful initial states out of the total attempted initial states. The percentage produced using other input parameters is used to determine the effects they have on the system. This approach is used to tune the input parameters so that a larger percentage is produced by the region of attraction. The region of attraction is calculated for the uncontrolled Simplest Walker and for the walker controlled by a basic DLQR controller using the identity matrices as inputs. The approach using the region of attraction to tune the DLQR controller is then compared with the uncontrolled and the basic DLQR-controlled Simplest Walker. The comparison displays that the tuning approach is valid in expanding the region of attraction for the Simplest Walker.