Abstract: A new nonlinear time optimal model predictive control paradigm is proposed for a class of nonlinear system with constraints. Firstly, this method of nonlinear linearized based on Jacobian linearization is used to be derive a series of convex optimization problem, and the linearization error determines the upper boundary under Lipschitz conditions. Then it uses dual model strategy, in the case of offline condition step structures a series of ellipsoid sets to describe t step feasible region, balance point of each ellipsoid sets is based on an ellipsoid to choose, according to the ellipsoid sets suitable input, it makes the system stable by online computation. Using a step by step backwards computation method can ensure the feasibility and stability of the iteration, and reduce the computation burden greatly. Numerical examples prove the feasibility of the algorithm.

Key words: nonlinear model predictive control, time optimal, step by step backwards, Lipschitz condition

摘要： 针对一类带有约束的非线性系统，提出一种非线性时间最优模型预测控制算法。这种方法首先基于Jacobian线性化将非线性进行线性化，能够推导一系列凸优化问题，而且产生的线性化误差在Lipschitz条件下确定上边界范围。然后采用双重模式策略，在离线情况下构造一系列椭圆集来描述[t]步可行区域，每个椭圆集的平衡点根据上一个椭圆来选取，最后再根据在线计算合适的输入使系统稳定。采用逐步倒退计算的方法能够确保迭代的可行性和稳定性,大大减少了计算负担。数值例子证明了算法的有效性。

关键词: 非线性模型预测控制, 时间最优, 逐步倒退法, Lipschitz条件