时间：2023年2月17日10:00-12:00

地点：电院群楼2-410会议室    

Lattice piecewise affine approximation of explicit linear/nonlinear model predictive control

许鋆 副教授  

哈尔滨工业大学(深圳)

Abstract:

To alleviate the online computational complexity of MPC, explicit MPC has been proposed, in which the optimal solution is derived offline and the online computation reduces to function evaluation. It has been proved that the solution of explicit linear MPC is a continuous piecewise affine (PWA) function of the state, and deriving it offline is time-consuming for complex linear system or nonlinear system. Besides, online evaluation of the continuous PWA function is not easy. In the recent years, we have made efforts to solve problems existed both offline and online in explicit MPC. First, we have proposed disjunctive and conjunctive lattice PWA approximations of explicit linear model predictive control. The training data are generated on trajectories of the linear MPC, consisting of the state samples and corresponding affine control laws, based on which the lattice PWA approximations are constructed. If all the distinct affine functions have been sampled, the disjunctive lattice PWA approximation constitutes a lower bound while the conjunctive lattice PWA approximation formulates an upper bound of the original optimal control law. The equivalence of the two lattice PWA approximations then guarantees that the approximations are error-free in the domain of interest, which is tested through a statistical guarantee. Then, the lattice PWA approximation method has been used to approximate both the nonlinear system and control law of explicit nonlinear MPC, i.e., the kinematic model of a nonlinear system, say the mobile robot is successively linearized along the trajectory to obtain a linear time-varying description of the system, and then the nonlinear MPC problem can be transformed into a series of linear MPC problems, which are then solved using lattice PWA approximation. Simulations results show the efficacy of the proposed strategy.

Biography:

许鋆，女，工学博士，哈尔滨工业大学(深圳)副教授。2005年在哈尔滨工业大学获工学学士学位(英才学院，控制科学与工程专业)，同年进入清华大学自动化系，2010年获工学博士学位(控制科学与工程专业)。2013年至2014年，在荷兰TU Delft从事博士后研究。报告人在权威国际学术期刊IEEE Transactions on Automatic Control, Automatica以一作身份发表了4篇学术论文(其中2篇长文)。报告人还共同翻译出版了S. Boyd教授和L. Vandenberghe教授的经典教材《凸优化》。报告人及其课题组长期致力于数据驱动的分片线性建模和控制。