Polynomial Chaos-Based Controller Design for Uncertain Linear Systems With State and Control Constraints
Polynomial Chaos-Based Controller Design for Uncertain Linear Systems With State and Control Constraints
复制标题
DOI：
10.1115/1.4038800
复制
发表时间：
2018-07
影响因子：
1.7
通讯作者：
S. Nandi;V. Migeon;T. Singh;P. Singla
中科院分区：
文献类型：
--
作者：
S. Nandi;V. Migeon;T. Singh;P. Singla
对于具有不确定参数的线性动态系统，在状态约束的约束下，如何设计控制器使系统在过渡过程中从初始状态进入期望的最终状态是一个非常重要的问题。本文提出了一种对时不变不确定变量具有鲁棒性的状态约束控制器的设计方法。多项式混沌展开是一种谱展开，它被用来对不确定变量进行参数化，允许将不确定状态的演化写成不确定变量的多项式函数。截断的PC展开的系数是使用Galerkin投影确定的，从而得到一组确定性方程。PC多项式空间到Bernstein多项式空间的变换允许确定感兴趣的演化状态的界。然后将线性规划(LP)用于具有状态边界约束的确定性方程组，以确定控制器。数值算例表明，该方法可用于设计具有变形约束且对基准弹簧-质量-阻尼器系统的刚度系数不确定具有鲁棒性的静止-静止控制器。
For linear dynamic systems with uncertain parameters, design of controllers which drive a system from an initial condition to a desired final state, limited by state constraints during the transition is a nontrivial problem. This paper presents a methodology to design a state constrained controller, which is robust to time invariant uncertain variables. Polynomial chaos (PC) expansion, a spectral expansion, is used to parameterize the uncertain variables permitting the evolution of the uncertain states to be written as a polynomial function of the uncertain variables. The coefficients of the truncated PC expansion are determined using the Galerkin projection resulting in a set of deterministic equations. A transformation of PC polynomial space to the Bernstein polynomial space permits determination of bounds on the evolving states of interest. Linear programming (LP) is then used on the deterministic set of equations with constraints on the bounds of the states to determine the controller. Numerical examples are used to illustrate the benefit of the proposed technique for the design of a rest-to-rest controller subject to deformation constraints and which are robust to uncertainties in the stiffness coefficient for the benchmark spring-mass-damper system.