论文标题
受约束非线性系统的系统，基于Lyapunov的，安全和稳定的控制器合成
Systematic, Lyapunov-Based, Safe and Stabilizing Controller Synthesis for Constrained Nonlinear Systems
论文作者
论文摘要
提出了一种针对状态和输入约束的非线性系统的控制器合成方法，该方法同时寻求连续的分段仿射（CPA）类似Lyapunov的功能和控制器。非凸优化问题是在可允许状态的三角剖分子集上提出的，这些子集可以完善，以达到诸如稳定性和安全性的主要控制目标，以及次要绩效目标。还给出了多阶段的设计，可以顺序扩大吸引力区域（ROA），同时允许每个阶段的独家性能。闭环系统ROA不变子集的明确边界是从最终的Lipschitz Lyapunov函数中获得的。对于控制疗法的非线性系统，非凸面问题被提出为一系列保守但良好的半明确程序。这些会迭代降低成本功能，直到达到设计目标为止。由于所得的CPA Lyapunov样函数也是Lipschitz控制（或屏障）Lyapunov功能，因此它们可用于在线二次编程中以查找最小值控制输入。提供了数值示例以证明该方法的有效性。
A controller synthesis method for state- and input-constrained nonlinear systems is presented that seeks continuous piecewise affine (CPA) Lyapunov-like functions and controllers simultaneously. Non-convex optimization problems are formulated on triangulated subsets of the admissible states that can be refined to meet primary control objectives, such as stability and safety, alongside secondary performance objectives. A multi-stage design is also given that enlarges the region of attraction (ROA) sequentially while allowing exclusive performance for each stage. A clear boundary for an invariant subset of closed-loop system's ROA is obtained from the resulting Lipschitz Lyapunov function. For control-affine nonlinear systems, the non-convex problem is formulated as a series of conservative, but well-posed, semi-definite programs. These decrease the cost function iteratively until the design objectives are met. Since the resulting CPA Lyapunov-like functions are also Lipschitz control (or barrier) Lyapunov functions, they can be used in online quadratic programming to find minimum-norm control inputs. Numerical examples are provided to demonstrate the effectiveness of the method.
