Constrained predictive control for consensus of nonlinear multi-agent systems by using game Q-learning

This paper develops constrained learning predictive control for achieving consensus in nonlinear multi-agent systems. First, a general predictive and learning framework is constructed for the optimization of control policies by employing an Identifier-Actor-Critic network. Specifically, the Identifier neural network is utilized to approximately characterize the dynamics of the nonlinear system and generate predictive data for available datasets. Each time point within the predictive horizon, regarded as a participant in a non-zero-sum game (NZSG), executes distributed policy and is fed into the Actor-Critic network. When the constrained control policies at all time points reach optimality via the policy gradient algorithm (PGA), the NZSG achieves Nash equilibrium. Subsequently, a gradient recentered self-concordant barrier function is employed to address the joint constraints on tracking error and control input. Moreover, by introducing incremental adjustments, the learning rate factors within the PGA are optimized to enhance the learning efficiency of the Actor-Critic network. Finally, simulation results demonstrate the effectiveness and the rapidity of achieving consensus of the learning predictive control approach compared to the general predictive control methodology.