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A Control Lyapunov Approach to Predictive Control of Hybrid Systems

机译:混合系统预测控制的控制Lyapunov方法

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In this paper we consider the stabilization of hybrid systems with both continuous and discrete dynamics via predictive control. To deal with the presence of discrete dynamics we adopt a "hybrid" control Lyapunov function approach, which consists of using two different functions. A Lyapunov-like function is designed to ensure finite-time convergence of the discrete state to a target value, while asymptotic stability of the continuous state is guaranteed via a classical local control Lyapunov function. We show that by combining these two functions in a proper manner it is no longer necessary that the control Lyapunov function for the continuous dynamics decreases at each time step. This leads to a significant reduction of conservativeness in contrast with classical Lyapunov based predictive control. Furthermore, the proposed approach also leads to a reduction of the horizon length needed for recursive feasibility with respect to standard predictive control approaches.
机译:在本文中,我们通过预测控制考虑具有连续和离散动力学的混合系统的稳定性。为了处理离散动力学的存在,我们采用“混合”控制Lyapunov函数方法,该方法包括使用两个不同的函数。设计一个类似于Lyapunov的函数,以确保离散状态到目标值的有限时间收敛,而通过经典的局部控制Lyapunov函数,可以保证连续状态的渐近稳定性。我们证明,通过以适当的方式组合这两个函数,不再需要在每个时间步长减小用于连续动力学的控制Lyapunov函数。与经典的基于Lyapunov的预测控制相比,这导致保守性的显着降低。此外,相对于标准预测控制方法,所提出的方法还导致递归可行性所需的视域长度的减少。

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