Almost disturbance decoupling of MIMO nonlinear systems and application to chemical processes

Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping approach

“…All f ij and g s ij functions vanish at the origin. In the case of all constants b ij and functions f ij , g s ij and h ij being known, the almost disturbance decoupling of system (1) is defined as in [5]: given a nonlinear system of form (1), find, for every choice of a positive real number , feedback controllers u i = u i (x 1 , . .…”

“…In [9], the geometric conditions were proposed under which a system can be put into a lower triangular form, and the backstepping technique was used to the almost disturbance decoupling problem for MIMO nonlinear systems. In recent years, the backstepping technique was successfully applied to the adaptive control and the almost disturbance decoupling problems for a class of MIMO nonlinear systems with the nested lower triangular structure, which is much weaker than lower triangular form [4,5]. However, all the existing results on decoupling problems were obtained based on the assumption that the uncertain nonlinear functions are parameter uncertainties or their norm superboundedness is known.…”

Fuzzy almost disturbance decoupling for MIMO nonlinear uncertain systems based on high-gainobserver

“…Consider a two continuous stirred tank reactor process, which is described by the following differential equations [12][13][14]: …”

“…In recent years, fuzzy logical system (FLS) [1][2][3] or neural networks (NNs), as the universal approximators, have been employed for adaptive system control design by combing with backstepping technique [4], and many important adaptive control approaches have been developed, see for example . Among them, works in [5][6][7][8][9] are for single-input-single-output (SISO) nonlinear systems, [10][11][12][13][14][15][16] for multiple-input-multiple-output (MIMO) nonlinear systems, while [17][18][19][20][21][22] for SISO/MIMO nonlinear systems with immeasurable states, respectively. The main features of these adaptive control approaches are that they can handle the nonlinear systems without the requirement of the matching condition, and that there is no need to linearly parameterize the unknown nonlinear uncertainties, but the fuzzy logic systems or NNs are employed to the unknown nonlinear uncertainties.…”

Adaptive Fuzzy Output Tracking Control of MIMO Nonlinear Uncertain Systems

“…1) Example 1: Consider a two continuous stirred tank reactor process, which is described by the following differential equations [11]: The reference signals are assumed to be The control objective is to design adaptive fuzzy controllers such that the outputs follows for , under the condition that in the system (45) the parameters and the functions ( ; ) are completely unknown. In the simulation, eleven fuzzy sets are defined over interval for all , , , , , , and by choosing the partitioning points as , , , , the fuzzy membership functions are given as follows:…”