Research On Model Predictive Control For Nonlinear Systems With Persistent Bounded Disturbance

Linear model predictive control has been developed for more than decades,so its theoretical research is getting more perfect day by day and its industrial applications is more extensive.Because of the complexity and diversity of nonlinear systems,the establishment of prediction model,the explicit representation of constrained conditions and stable conditions,the design of controller,the stability analysis,the enlargement of terminal region and to reduce online computation burden have become the focus and difficulties of nonlinear model predictive control scheme.Based on affine control input,multi-step control set,polytopic invariant set and output feedback,the nonlinear model predictive control schemes are designed for several nonlinear systems with persistent bounded disturbance.The closed-loop system is stable.The main work of this dissertation is given as follows.(1)The min-max nonlinear model predictive control scheme with input-to-state stability is investigated for the affine nonlinear system with persistent bounded disturbance.The nonlinear system is linearized at the equilibrium point to establish the prediction model.The affine state feedback control input with perturbations is designed.The affine state feedback control gain matrix and the polytopic terminal region can be calculated offline by the stable condition based on the infinity norm and the perturbations of control input are optimized online,which improve the design freedom of the controller and reduce the conservation of the controller.(2)Base on the notion of multi-step control set,the single Lyapunov function and parameter-dependent Lyapunov functions model predictive control schemes are investigated for constrained nonlinear system.The prediction model is built by the linear polytopic description including initial system.The state and input constraint conditions and the stable conditions are converted into a few of linear matrix inequalities.The proposed algorithms computes two series of multi-step control sets offline and the convex combination of them online respectively by solving convex optimization problems described by those linear matrix inequalities.At the end,a sub-optimal nonlinear model predictive model scheme is designed based on the offline look-up table.The proposed algorithms are all input-to-state practical stable through the theoretical derivation and simulation.(3)Considering the nonlinear system included by linear parameter varying polytopic description,the two-step offline design of the polytopic invariant set is presented based on norm interpolant.When the system states does not converge to the polytopic invariant set,the min-max optimization problem based on a sequence of vertex control actions is solved online to get the control action of current moment.When the system states are steered to the polytopic invariant set,the norm interpolant nonlinear feedback control action is calculated online.The dual-mode control method can ensure that the closed system is input-to-state stable.(4)Based on two polytopic description sets of prediction model and mode transition probability matrix,the mode-dependent output feedback nonlinear model predictive control scheme is investigated for the nonlinear Markov jump system.The mode-dependent estimation gain can be handled offline.The online optimization problem contains the control input constraints,stochastic mode and stable conditions based on the quadratic boundedness theory.The closed-loop system is stochastically stale.Finally,an offline look-up table model predictive control method is designed.While reducing the online computing burden,it can also ensure that the system has certain control performance.