Inverse Open-Loop Noncooperative Differential Games and Inverse Optimal Control

Abstract

We consider the problem of computing parameters of player cost functionals such that given state and control trajectories constitute an open-loop Nash equilibrium for a noncooperative differential game. We propose two methods for solving this inverse differential game problem and novel conditions under which our methods compute unique cost-functional parameters. Our conditions are analogous to persistence of excitation conditions in adaptive control and parameter estimation. The efficacy of our methods is illustrated in simulations. Index Terms-Game theory, inverse differential games, inverse optimal control, optimal control.

Online inverse reinforcement learning for nonlinear systems with adversarial attacks

“…Molloy and Zhang 29,30 computed performance objective weights given optimal state and control input behavior trajectories. Rothfuss and Molloy 31,32 further studied the theory in noncooperative differential games. Stability is rigorously studied in these references 27‐32 …”

“…Rothfuss and Molloy 31,32 further studied the theory in noncooperative differential games. Stability is rigorously studied in these references 27‐32 …”

“…Compared with the probabilistic inverse RL algorithms, 1‐7 the proposed algorithm applies for the deterministic nonlinear continuous‐time systems described by differential equations. The algorithm does not need the knowledge of the expert's drift dynamics, while Molloy 29,32 needs the dynamic model. It has two learning stages: an optimal control learning stage and a second learning stage based on inverse optimal control.…”

“…It has two learning stages: an optimal control learning stage and a second learning stage based on inverse optimal control. Our approach clarifies the relations between inverse RL and inverse optimal control. This article further develops an online tuning inverse RL method to learn the expert's performance objective and mimic the expert behaviors using learner's real‐time trajectories and the observation of expert's behavior trajectories, compared with offline methods 1‐6,29,32 . Different from online inverse RL algorithm, 8 the proposed online algorithm is based on integral RL and does not need to use or identify the system drift dynamics.…”

Continuous-Time Perfect Control Algorithm—A State Feedback Approach

“…Systems with multiple input and output variables often deliver challenges and opportunities that are not available in the Single-Input Single-Output (SISO) plants. For example, in the Multi-Input Multi-Output (MIMO) approach, the Inverse Model Control (IMC) extends the potential of nonunique solutions for a given problem [1][2][3][4][5][6][7].…”