Adaptive PI Control For Nonlinear Uncertain Systems

In recent years,the tracking control problem for a class of complex and uncertain nonlinear dynamic systems have received a great deal of attention.It may be suffer great losses when the uncertainties are not considered in the control design for nonlinear systems.These uncertain factors include unknown parameters and external disturbance,measurement error,etc.In this work,we explore a low-cost proportional-integral(PI)tracking control solution for MIMO nonlinear systems,which are simplicity and intuitiveness in both structure and concept.For a class of MIMO nonaffine nonlinear systems,neural adaptive PI control with self-tuning gains is proposed.Because of the nonaffine and uncertain nature,the control input enters into and impacts on the behavior of nonaffine system through a completely uncertain and implicit way,making it nontrivial to design a reliable and cost-effective control scheme for such system.First,converting the original nonaffine system into an affine one by using the mean value theory.Second,using the neural network(NN)to approximate the resultant lumped nonlinearities and uncertainties in the system and introducing the concept of virtual parameter.Third,blending the virtual parameter estimation error into the skillfully chosen Lyapunov function to guide the derivation of the tracking control algorithms.It is shown that the proposed neuro-adaptive PI control ensures the uniformly ultimately boundedness of all the signals of the closed-loop system.The benefits and feasibility of the developed control are also confirmed by simulations.For a class of multi-input multi-output subject to unknown actuation characteristics and external disturbances.,neural adaptive PI control with self-tuning gains is proposed.First,to facilitate the controller construction,a smooth function is used to approximate the saturation function.Second,using the neural network(NN)to approximate the resultant lumped nonlinearities and uncertainties in the system and introducing the concept of virtual parameter.Third,blending the virtual parameter estimation error into the skillfully chosen Lyapunov function to guide the derivation of the tracking control algorithms.It is shown that the proposed neuro-adaptive PI control ensures the uniformly ultimately boundedness of all the signals of the closed-loop system.The proposed PI control has better stability and transient performance.For a class of multi-input multi-output subject to unknown actuation characteristics and external disturbances.,Motivated by the established PI control scheme with well explained analytical tuning algorithms.Now present a modified version to ensure the full functionality of the method.Note that to use NN for function approximation,the selected training input vector must remain in a compact set.To this end,we make use of the unique feature of barrier Lyapunov function(BLF)to develop strategies for confining/constraining the NN input.Stability analysis and simulation studies are performed to illustrate and verify the benefits and feasibility of the proposed method.