This paper is devoted to discuss arbitrarily switching control problem for a class of nonlinearly parameterised nonlinear switched systems. Compared with the existing results, improvements are that a systematic procedure is given for an explicit construction of a common smooth adaptive controller independent of the switching signals. Meanwhile, the developed design method can be extended to the adaptive arbitrarily switching stabilisation problem for a class of cascade switched nonlinear systems. The theoretical analysis is presented for the Lyapunov stability of the resulting closed-loop switched system and the convergence of the original switched system states at the equilibrium under arbitrary switching. Moreover, the effectiveness and feasibility of the developed method are demonstrated by both a numerical example and a chemical system.