Parameter estimation-based coupling control for generalized cascade systems with guaranteed cost

This paper proposes a parameter estimation-based coupling control for the generalized cascade systems with uncertain parameters, where the single driven system is actuated by the multi-driving subsystems, resulting in the complicated coupling problem of output tracking and subsystems synchronization. To address this issue, a prescribed performance function (PPF) is firstly incorporated with the filtered representation of the driven system dynamics to design the adaptive parameter law, which maintains the finite-time parameter estimation with the prescribed performances. Then, the desired position of each driving subsystem is proposed to attain the driven system tracking with the sub-guaranteed cost, which is employed for the generalized coupling error (GCE) design to convert the complicated coupling issue into the GCE convergence, such that the complexity of controller design is extremely simplified. By applying the Chebyshev neural network (CNN), a novel integral sliding mode controller is presented to successfully eliminate the reaching phase and guarantee the finite-time GCE convergence with the suboptimal time. For the nonlinearity compensation, the novel learning law is derived to lessen the computational cost, where only a scalar weight needs to be updated online for each output of CNN. Finally, the comparative experiments illustrate the benefits of the proposed algorithms.