Game theoretical approach to vehicle dynamic control

Pooyafar, Payam (2022) Game theoretical approach to vehicle dynamic control. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

There are multiple objectives that a controller designer pursues in vehicle dynamics, such as safety, tracking, comfort, and efficiency. These objectives are present in different dimensions of longitudinal, lateral, vertical, yaw, roll, and pitch for each vehicle and can be controlled or manipulated by all types of actuators. These actuators can affect the steering, braking, torques at each tire, suspension system, etc. The majority of studies in vehicle dynamics control address either one control objective or control action, and even the ones that address an integrated control structure (including more control objectives and actuators) neglect the counter effects of the controllers/actuators on each other’ objectives. So there exists the question of what can be the most efficient strategy in an integrated structure that provides the optimal solution for any set of objectives and control actions by taking into account the effects of each actuator in a way that no actuator can achieve a better optimal result by deviating from that strategy. Game theory is a field that addresses these types of questions, and its application in vehicle dynamics is called the theory of differential games. This dissertation explores differential game theory in two-player and three-player optimal games in vehicle dynamics. It presents a solution for an integrated optimal problem, where two/three actuators (players) are trying to achieve their own sets of optimal goals by taking into account other actuators' (players) actions. The control problems are categorized into two classes of Linear Quadratic Regulators (LQR) and Control Coupled Output Regulation (CCOR) due to coupling between the output objectives and control actions. The solution for the single-player game exists in the literature for both LQR and CCOR for infinite horizon linear continuous systems. This thesis extends this solution to the two-player and three-player games for continuous systems. After presenting the solution, in theory, the control feedback gains are calculated for the following case studies using linear control models:  The two-player game between active steering and corrective yaw moment  The two-player game between active steering and corrective roll moment  Three-player game between active steering, corrective yaw moment, and corrective roll moment  The two-player player game between active suspension and corrective roll moment The designed feedback gains are used in a closed-loop feedback system on a nonlinear vehicle model with both linear tire and nonlinear tire models. The simulation results for the two/three-player game theory approach are compared with the one player and the two/three payer decentralized approach (normal optimal approach without considering the counter effects of control actions on each others’ cost function). It is shown that the game theory approach provides better performance in terms of control action cost and objective cost in some scenarios.

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