Optimal control of uncertain nonlinear quadratic systems
Optimal control of uncertain nonlinear quadratic systems
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DOI：
10.1016/j.automatica.2017.05.012
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发表时间：
2017-01
期刊：
影响因子：
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通讯作者：
A. Merola;C. Cosentino;Domenico Colacino;F. Amato
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文献类型：
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作者：
A. Merola;C. Cosentino;Domenico Colacino;F. Amato
本文解决了受范数有界参数不确定性和扰动影响的非线性二次系统的鲁棒和最优控制问题。通过使用基于保证成本控制理论的方法，提出了一种设计状态反馈控制器的技术，确保闭环系统：（i）零平衡点的局部指数稳定性；（ii）将给定区域纳入平衡点的指数稳定性域；（iii）根据某些最优性指标的有界性满足保证性能水平。特别地，提供满足规定积分二次指数的状态反馈控制器存在的充分条件，随后提供满足给定L 2 增益扰动抑制约束的状态反馈控制器存在的充分条件。通过所提出的设计过程，这里处理的最优控制问题可以有效地解决为线性矩阵不等式（LMI）优化问题。
This paper addresses the problem of robust and optimal control for the class of nonlinear quadratic systems subject to norm-bounded parametric uncertainties and disturbances. By using an approach based on the guaranteed cost control theory, a technique is proposed to design a state feedback controller ensuring for the closed-loop system:(i) the local exponential stability of the zero equilibrium point;(ii) the inclusion of a given region into the domain of exponential stability of the equilibrium point;(iii) the satisfaction of a guaranteed level of performance, in terms of boundedness of some optimality indexes. In particular, a sufficient condition for the existence of a state feedback controller satisfying a prescribed integral–quadratic index is provided, followed by a sufficient condition for the existence of a state feedback controller satisfying a given L 2-gain disturbance rejection constraint. By the proposed design procedures, the optimal control problems dealt with here can be efficiently solved as Linear Matrix Inequality (LMI) optimization problems.