On Adaptive Dynamics Surface Control Of MIMO Nonlinear Systems With Output Constraints

The control of nonlinear systems has been one of the hot spots in the control theory research.For the nonlinear systems existing in reality,they can be divided into single-input-single-output(SISO)nonlinear systems and multiple-input-multiple-output(MIMO)nonlinear systems.In recent years,the research results of SISO nonlinear systems have become more and more perfect,but the control of MIMO nonlinear systems needs to be further improved.Backstepping design and dynamic surface control technique are still two important methods to deal with MIMO nonlinear systems.At the same time,because the controlled objects in modern industrial process are often very complex,in addition to the nonlinear characteristics,there are many uncertain factors in the system,such as unmodeled dynamics,constraints on the system output,and so on.All of these will degrade the dynamic performance of the system and even make the system unstable.Therefore,it is of great significance to study the control problem of MIMO nonlinear systems with unmodeled dynamics and output constraints.In this paper,for several classes of MIMO nonlinear systems with unmodeled dynamics and output constraints,we use radial basis function neural networks to estimate the unknown continuous function vectors in the controller design process.Based on the barrier Lyapunov function,nonlinear mapping,three adaptive dynamic surface control schemes are proposed.The main contents of this paper are as follows:Firstly,for a class of MIMO strict feedback nonlinear systems with output constraints,the minimum adjusting parameters adaptive robust control scheme is designed.The modified dynamic surface control technique is firstly extended to MIMO nonlinear systems.A available dynamic signal is introduced to overcome the unmodeled dynamics influence in the system,and the minimum adjusting parameters of the adaptive law are constructed by using Young's inequality.Based on the symmetry barrier Lyapunov function,an adaptive controller is designed to realize the constraint on the output European norm.The stability analysis shows that the adaptive control method can ensure the closed-loop system to be semi-globally uniformly ultimately bounded.The simulation results verify the effectiveness of the proposed scheme.Secondly,the problem of adaptive dynamic surface control is discussed for a class of MIMO block-structure strict feedback nonlinear systems with unmodeled dynamics and output constraints.Based on the assumption that the unmodeled dynamics is exponentially input-state-practically stable(exp-ISpS),an auxiliary dynamic signal is constructed to deal with the unmodeled dynamics.The unknown continuous function vectors produced in the process of controller design are approximated by the radial basis function neural networks.By introducing a symmetric barrier Lyapunov function for each component of the output,the constraints on the output components of the system are realized.In order to overcome the difficulty in the design of control law for the system with unknown function control gain matrix,the input uncertain term is introduced.According to the proof characteristics of dynamic surface control,the introduced input uncertain term is proved to be bounded on the compact set defined in theoretical analysis.The stability analysis proves that all signals in the closed-loop system are semi-globally uniformly ultimately bounded,and the validity of the design scheme is verified by the two-link flexible manipulator system.Thirdly,for a class of MIMO block-structure pure-feedback nonlinear systems with unmodeled dynamics and output constraints,the adaptive neural network control strategy is investigated.The design of auxiliary signals effectively suppresses the dynamic uncertainties caused by unmodeled dynamics in the system.The unknown continuous black-box functions generated in the controller design process are estimated by the radial basis function neural networks.Based on a one-to-one nonlinear mapping,the MIMO nonaffine nonlinear system with output constraints is transformed into a novel block-structure MIMO nonaffine nonlinear system without output constraints.Making use of the modified dynamic surface control technology,the virtual control law and control law are designed on the basis of the transformed system,which simplifies the design of system controller.Using mean value theorem,the nonaffine nonlinear function of the states and input is denoted in the form of a linear function of the input signal and full states with bounded gain matrix.Furthermore,by introducing the input uncertain term,a simple controller is constructed based on modified dynamic surface control in the final step,and the assumption of the nonsingular control gain is eliminated.Finally,by means of the Lyapunov method,the closed-loop system is stable and the output of the system can satisfy the constraints while the tracking error converges to the small neighborhood of the origin.The numerical simulation and the two-link rigid manipulator system simulation are used to verify the effectiveness of the proposed scheme.