چكيده به لاتين
Abstract
This thesis developed the explicit Model Predictive Control (eMPC) for uncertain linear systems with disturbances and noises. On-line model predictive control approaches require the online solution of an optimization problem. In contrast, the explicit model predictive control moves major part of computation offline. Therefore, eMPC enables one to implement a MPC in real time for wide range of fast systems. The eMPC approach requires the exact system model and results a piecewise affine control law defined on a polyhedral partition in the state space. As an important limitation, disturbances may reduce performance of the explicit model predictive control. First, this thesis presents efficient approach for handling the problem of using eMPC for constrained systems with disturbances. It proposes an approach to improve performance of the closed loop system by designing a suitable state and disturbance estimator. Second, a two-stage approach is proposed where the observer design procedure is completely decoupled from the MPC problem, known as the separation principle. We focus on the decupling principal and it is shown that the observer can be designed independently via a norm minimization problem to reduce effects of disturbances and model mismatch. On the other hand, the MPC law is obtained using the multi-parametric quadratic programming approach where the parameters are the components of the state vector. Then, the robust explicit model predictive control scheme is developed for linear systems with input and output constraint in the presence of disturbances and noises. It is shown that the solution includes a set of regions with piecewise affine (PWA) functions of state and reference vectors and a set of regions with optimal observers. In the proposed method, two sets of partitions are required, i.e. control law and observers. Therefore, the online computation includes finding the active regions of both observer and control law partitions in which the current state is located. Finally, an approximate multiparametric convex programming approach is developed with its application to control constrained linear parameter-varying systems. In this method, the feasible space of the time varying parameters is divided into simplexes in which approximate solutions are calculated provided that the approximation error is kept limited by solving sequences of linear programs. The approximate optimal solution within each simplex is obtained by linear interpolation of the optimal solutions in the simplex vertices and then multiparametric programming tool is utilized to compute an explicit state-feedback solution of linear quadratic optimal control problem for simplex vertices subject to state and input constraints.
Keywords: Explicit Model Predictive Control, Multi-parametric programming, Feasibility, Linear Parameter Varying system, Polyhedral.
