Decentralized controller design with asymmetric input constraints for unknown unmatched interconnected systems

In this paper, the decentralized control problem is investigated based on adaptive dynamic programming for continuous-time nonlinear systems with unknown mismatched interconnections and asymmetric input constraints. First, the unknown interconnection term is approximated by the radial basis function neural network based on the local state of the isolated subsystem and the reference state of the coupled subsystem. As a result, common assumptions are eliminated that interconnections are matched and upper bounded. Then, by using the framework of adaptive critic networks, the stability problem of decentralized systems is transformed into the design of a series of local optimal controllers under asymmetric constraints, and it is also proved that asymmetric control strategies can stabilize large-scale systems. Then, a state observer is introduced to estimate the state of the interconnected subsystems and ensure that the observed errors are uniformly ultimately bounded. In addition, the optimal cost function can be approximated by the critic neural network, and then the Hamilton-Jacobi-Bellman equation can be approximatively solved, so as to obtain the optimal decentralized control strategy satisfying the asymmetric input constraints. At the same time, based on the weight updating rule of the critic neural network, it guarantees that the weight approximation errors are uniformly ultimately bounded. Finally, the effectiveness of the algorithm is verified by a simulation example, and the progressiveness of the developed method is reflected by comparing with the traditional method without improved cost function.