Control of nonlinear systems via state feedback state-dependent Riccati equation techniques
Control of nonlinear systems via state feedback state-dependent Riccati equation techniques
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发表时间：
1997-06
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通讯作者：
K. Hammett
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作者：
K. Hammett
摘要：研究了基于状态依赖黎卡提方程的非线性调节和非线性H_无穷控制问题。研究了SDRE与Hamilton-Jacobi/Bellman不等式/方程之间的关系，得到了具有非线性可镇定性的解存在的必要条件。给出了SDRE方法获得最优控制或保证诱导L2增益性质的一个额外的必要条件。对于次优SDRE调节器的标准数值实现的适定性，分解的点态可镇定性和可检测性分别被证明是必要的和充分的，但如果允许解析解，则证明这两个条件都不是必要的。对于标量解析系统或具有满秩常数控制输入矩阵的系统，由于非线性可控性与因式分解可控性的等价性，状态加权矩阵函数的可镇定性和非奇性分别导致局部和全局渐近稳定。文中还给出了采样数据解析SDRE控制器渐近稳定性的证明，但限制性假设使这些结果在选择适当的系统分解时起到了指导作用。给出了系统指数稳定的条件。所有结果都可推广到具有附加假设的SDRE非线性H_无穷控制。通过将SDRE理论应用于双自旋卫星的动量控制，并与现有方法进行了比较，说明了SDRE理论的有效性。
Abstract : Nonlinear regulation and nonlinear H-infinity control via state-dependent Riccati equation (SDRE) techniques are considered. Relationships between SDREs and Hamilton-Jacobi/Bellman inequalities/equations are examined, and a necessary condition for existence of solutions involving nonlinear stabilizability is derived. A single additional necessary criterion is given for the SDRE methods to yield the optimal control or guaranteed induced L2 gain properties. Pointwise stabilizability and detectability of factorizations prove necessary and sufficient, respectively, for well-posedness of standard numerical implementations of suboptimal SDRE regulators, but neither proves necessary if analytical solutions are allowed. For scalar analytic systems or those with full rank constant control input matrices, stabilizability and nonsingularity of the state weighting matrix function result in local and global asymptotic stability, respectively, due to equivalence between nonlinear and factored controllability in these cases. A proof of asymptotic stability for sampled data analytic SDRE controllers is also given, but restrictive assumptions make the main utility of these results guidance in choosing appropriate system factorizations. Conditions for exponential stability are also derived. All results are extendable to SDRE nonlinear H-infinity control with additional assumptions. The SDRE theory is illustrated by application to momentum control of a dual-spin satellite and comparison with other current methods.