Fractional-Order Echo State Network Backstepping Control of Fractional-Order Nonlinear Systems

Classical backstepping control of fractional-order nonlinear systems (FONSs) needs to calculate fractional derivatives of virtual control inputs recursively, which usually results in the “explosion of complexity” problem. This article proposes a command-filtering adaptive control scheme based on fractional-order echo state networks (FOESNs) for strict-feedback uncertain FONSs. Finite-time command filters are introduced to estimate instead of calculating the complicated fractional-order derivatives of virtual control inputs, which not only has the advantages of the conventional command-filters, but also guarantees the finite-time convergent property. An FOESN with stronger approximation ability is presented to approach uncertainties. Compared with conventional adaptive neural network or fuzzy control, the proposed method with similar computational complexity has more design freedom and better approximation effect. The effectiveness of the proposed control framework is verified by two simulation examples.