Abstract
The stabilization problem is investigated in this paper for a class of nonlinear systems with disturbances. The disturbances are supposed to be classified into two types. One type in the input channel is generated by an exogenous system, which can represent the constant or harmonic signals with unknown phase and magnitude. The other type is stochastic disturbance. Two kinds of nonlinear dynamics in the plants are considered, respectively, which correspond to the known and unknown functions. By integrating the disturbance observers with conventional control method, the first type of disturbances can be estimated and rejected. Simultaneously, the desired dynamic performances can be guaranteed. An example is given to show the effectiveness of the proposed scheme.
Highlights
Though the stochastic stabilization theory emerged in the 1960s [1], the progress has been slow
The stabilization of nonlinear stochastic systems was considered in the work of Florchinger [4,5,6,7], who, among other things, extended the concept of control Lyapunov functions and Sontag’s stabilization formula to stochastic setting
Only stability of the nominal system in the absence of deterministic disturbances was the concern in this approach, which means that the stability cannot be guaranteed in the presence of both deterministic and stochastic disturbances
Summary
Though the stochastic stabilization theory emerged in the 1960s [1], the progress has been slow. Pan and Baser [8] solved the stabilization problem for a class of strict-feedback systems representative of stabilization results for deterministic systems. The adaptive neural tracking control problem was the concern in [12] for a class of strict-feedback stochastic nonlinear systems with unknown dead zone. Most of these results were focused on systems that only have one kind of disturbance-stochastic disturbance. [23] designed output feedback controller for a class of Markovian jump repeated scalar nonlinear systems and [24] investigated the problem of composite DOBC and H∞ control for Markovian jump systems with nonlinearity and multiple disturbances. Simulations on an A4D aircraft model show the effectiveness of the proposed approaches
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