Optimal performance of constrained control systems
Optimal performance of constrained control systems
复制标题
约束控制系统的最优性能
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
J. Scruggs
中科院分区：
文献类型：
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作者：
Philip S Harvey;H. Gavin;J. Scruggs
本文提出了一种方法来计算系统的最优开环轨迹的状态和控制不等式约束，其中的成本函数是二次和状态动态是线性的。对于不等式约束相对于控制是分散的情况，通过庞特里亚金最小值原理可以在任何时候找到执行不等式约束的最优拉格朗日乘子。在这样做时，微分代数欧拉-拉格朗日方程组转化为一个非线性两点边值问题的状态和costates的解决方案满足必要条件的最优性。不等式约束控制系统的最优性能是可计算的，允许与以前的次优解进行比较。该方法适用于控制的阻尼力的振动隔离系统受到的约束所施加的一个特定的可控阻尼器的物理实现。本研究的结果是给定特定目标、隔离系统和半主动阻尼器约束条件下可实现的最佳性能。
This paper presents a method to compute optimal open-loop trajectories for systems subject to state and control inequality constraints in which the cost function is quadratic and the state dynamics are linear. For the case in which inequality constraints are decentralized with respect to the controls, optimal Lagrange multipliers enforcing the inequality constraints may be found at any time through Pontryagin’s minimum principle. In so doing, the set of differential algebraic Euler–Lagrange equations is transformed into a nonlinear two-point boundary-value problem for states and costates whose solution meets the necessary conditions for optimality. The optimal performance of inequality constrained control systems is calculable, allowing for comparison to previous, sub-optimal solutions. The method is applied to the control of damping forces in a vibration isolation system subjected to constraints imposed by the physical implementation of a particular controllable damper. An outcome of this study is the best performance achievable given a particular objective, isolation system, and semi-active damper constraints.