Polytopic Approximation Of Explicit Model Predictive Control And Its Applications

The explicit model predictive control (EMPC) is an advanced control algorithm that combines multi-parametric quadratic programming (mp-QP) with model predictive control (MPC). The state space of the optimal control problem can be divided into small convex partitions by mp-QP, and the corresponding optimal control sequences can be precomputed, so that what the controller needs to do is to get the control laws by a look-up table without repeated online optimization. However, the complexity can grow exponentially with problem size in solving a MPC problem, which makes it harder to deal with problems and further limits the ranges of application. Therefore, how to reduce the complexity of control problems is a challenge for the field of predictive control.In this paper, polytopic approximate explicit model predictive control is proposed to solve linear time invariant problems by setting a certain error, so that to reduce the complexity, and the effectiveness and real-time performance of the proposed algorithm is verified by simulation. In this paper, the main work and achievements are as follows:(1)The research status and developments of EMPC and approximate EMPC and the control methods of three-dof helicopter are summarized. The basic principle of EMPC and the double-description algorithm are proposed, as well as the definition and solution of barycentric function, all of which provide the theoretical basis for the following study.(2)Based on the shortages of EMPC, the polytopic approximation of EMPC algorithm is proposed by the combination of double-description method and barycentric function. The approximate explicit control laws are computed, besides, the stability of the control law and the closed-loop system is analyzed, and the influences of parameters on the simulation results are discussed.(3)Mathematical model of linear inverted pendulum system is built, and then the polytopic approximation of EMPC is used in this model. The result shows that in terms of computation time, the control effect of polytopic approximate algorithm is better than EMPC:also the feasibility and effectiveness of the proposed algorithm is verified. (4)Based on the semi-physical simulation platform of three-DOF helicopter system, the mathematical model is built. Considering the practical feasibility, the model of helicopter is divided into two sub-models, and then the polytopic approximation of EMPC is applied to this model. The result proves the theoretical feasibility of polytopic approximate EMPC in helicopter system.(5)Summary of this paper is given, and the future research direction is discussed.