Study On Model Predictive Control Methods For Constrained Nonlinear Systems

Model predictive control (MPC), which also called receding horizon control (RHC)and commonly abbreviated as predictive control, in essence is an advanced controlstrategy based on the system model and optimization techniques. In the field ofadvanced control of process industry, MPC is the synonym of multivariable constrainedcontrol. At present, the MPC methods for linear systems already have manycomparatively mature design thoughts, and the corresponding online computationaltime is short enough for application. However, since there are more or less nonlinearcharacteristics in practical systems, nonlinear system controlled by linear MPC mayobtain the worse performance, or even worse, lose its closed-loop stability. Hence, it isessential for constrained nonlinear systems to design the corresponding nonlinear MPCcontroller directly. Nonlinear MPC has a very wide range of applications, and so far ithas been applied to the practical systems, such as process industry system, electricalsystem, building energy-saving system and aircraft control system.The emphases of MPC methods research for constrained nonlinear systems areprediction model, stability, robustness and computational time and so on. Forconstrained nonlinear systems, the MPC methods are designed and the correspondingclosed-loop system properties are analyzed in this paper. The main contributions of thispaper are as follows.①A nonlinear sliding-mode MPC method based on contractive constraints ispresented, and the closed-loop stability is proved. By selecting an appropriate switchingfunction, and combining the state equations, the equivalent control is calculated. Inorder to guarantee the stability of closed-loop system, the switching function contractiveconstraints are added into the optimization problem. By solving the optimizationproblem, the switching function asymptotically converge to zero under the obtainedoptimal control inputs. Hence, the system states approach the sliding surface and thenconverge to the equilibrium along it. Due to the time interval for solving theoptimization problem and the parameter of contraction rate are variable, the nonlinearsliding-mode MPC methods, which respectively based on optimal contraction rate andoptimal time interval, are designed.②A distributed MPC method based on compatibility constraints is proposed, andthe exponential stability of the global closed-loop system is proved. Considering the case of constrained large-scale nonlinear systems with decoupled local dynamics, a newapproach for confirming the neighbors of each subsystem is proposed. Compared it withthe existing methods, the application of the proposed method results in that eachsubsystem just has one neighbor, so the communicational load is greatly reduced. Bydecentralized the optimization problem of centralized MPC, the optimization problemsof distributed MPC are confirmed, and the quasi-infinite MPC method is adopted ineach local controller. In order to guarantee the global closed-loop stability, the stabilitycondition for centralized MPC is decomposed, and then the compatibility constraints areobtained and added into each local optimization problem. In addition, the range oflooseness of optimality under distributed MPC is analyzed.③By virtue of the theorem of input-to-state stability, two robust MPC methodsbased on the suboptimal solution are presented. In order to achieve the input-to-statestability, an appropriate Lyapunov function and the state tighten constraints are adoptedin the optimization problem. Thus, the optimization problem of MPC is the generalnonlinear constrained optimization problem, and the computation will become large if itbe solved directly. Solving the nonlinear optimization problem by the feasible sequentialquadratic programming, the only feasible solution is obtained, so the onlinecomputation is greatly reduced.④By including the nonlinear model with the quasi linear parameter varying (LPV)model, and according to the existing interpolation MPC algorithms, two zero-horizoninterpolation MPC which respectly based on the ellipsoidal invariant set and thepolyhedral invariant set are designed. The interpolation-based algorithms can partlycompensate the decreasing of feasible region which caused by the linear differenceinclusion technique, thus increasing the attractivieness of solving the optimizationproblem in nonlinear MPC by convex programming. In order to get a larger feasibleregion, we further convert the LPV model into the disturbed LTI model and propose twofinite-horizon interpolation MPC methods which respectively based on the ellipsoidalinvariant set and the polyhedral invariant set. The simulations reveal that the feasibleregions of the proposed finite-horizon interpolation MPC methods are much larger thanthe zero-horizon methods.