Simplified robust adaptive control of a class of time‐varying chaotic systems

Abstract

Purpose-To develop a simplified robust control scheme for a class of nonlinear time-varying uncertain chaotic systems. Design/methodology/approach-By means of input-to-state stability theory, a new robust adaptive control scheme is designed, which is simpler than the one proposed by Li et al. and applicable to a larger class of nonlinear systems. Only one parameter is adjusted in the controller and the scheme assures that all the signals remain bounded. The behavior of the proposed control scheme is also analyzed through simulations on the Rössler system. Findings-By adjusting only one parameter in the controller and imposing only one mild assumption on the time-varying parameters, the proposed control algorithm assures that all the signal remain bounded and that the state of the original system will follow a desired trajectory defined either by the trajectory and its first time derivative, or given by a reference model. Research limitations/implications-The results are limited to a particular class of nonlinear systems where the dimension of the input vector is equal to the order of the system (dimension of the state vector). Practical implications-The main advantage of the proposed method is that the modification introduced leads to a substantially simpler adaptive robust controller whose practical implementation will be easier. Originality/value-The contribution of the proposed method is in the simplification of the control algorithm applied to a class of nonlinear time-varying uncertain chaotic systems. This will be useful for control engineers to control complex industrial plants.

Adaptive stabilization of linear and nonlinear plants in the presence of large and arbitrarily fast variations of the parameters

“…Later, in [21] a method is presented where the constraint of the second assumption is moved from the plant to the reference model. Recently, an attempt to generalize the results in [16,17,21] for the case of B known was made in [20], where it is considered only the assumption on the boundedness of the time-varying parameters and both cases when a model reference or a desired trajectory and its time derivative are known, were resolved. Table 1 Summary of stability results.…”

Robust synchronization of Rossler systems with mismatched time-varying parameters

“…Also, the aforementioned methods cannot handle time-varying parameters, which may exist in a chaotic system. Recently, new methods based on adaptive robust control strategy have been introduced in efforts to control chaotic and nonlinear systems with time-varying uncertainties [26][27][28]. However, these methods are designed based on the vector control input signal.…”

Adaptive robust stabilization of a class of uncertain non-linear systems with mismatched time-varying parameters

“…Robust control of uncertain non-linear systems is one of the most significant issues in both theoretical and practical aspects of control systems, having attracted a lot of attention during the last three decades. Consequently, different methods relevant to stabilization of non-linear dynamical systems with significant uncertainties have been presented [1][2][3][4].…”