Mixed H2/ H ∞ optimal hierarchical tracking control for partially unknown dynamics

The mixed H-2/H-infinity dual-performance tracking control optimization problem for continuous-time systems with unknown internal dynamics is solved in the framework of Stackelberg games with hierarchical control. Compared with the traditional Nash games, the mixed H-2/H-infinity tracking optimization problem is solved by finding the solution to a two-stage constrained optimal tracking control problem. The hierarchical tracking control problem is first changed into an optimization regulation problem by augmenting the state vector. The control input and the unknown external disturbances are deemed as the leader and the follower, which is obtained by solving the coupled hierarchical leader-follower Hamiltonian-Jacobi (HJ) tracking equations with constrained conditions. An improved hierarchical online integral reinforcement learning (IRL) tracking control algorithm is proposed to obtain the Stackelberg equilibrium and the optimal cost functions iteratively based on the Lyapunov-like equations. The single NN structure is applied for each player to approximate the unknown cost function. In addition, the sufficient and necessary condition is discussed about the uniqueness and existence of Stackelberg equilibrium. The universality and the practicability of the learning algorithm are shown by two simulation results.