具有未知控制方向的MIMO系统的模块化符号补偿：一种精确的标称恢复方法
Modular Sign Compensation for MIMO Systems with Unknown Control Direction: An Exact Nominal Recovery Approach
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中文总结 AI 辅助
研究具有不确定时变对角输入方向的MIMO系统稳定化，提出模块化切换符号补偿层，利用基于标称李雅普诺夫量的自适应变量和调度器搜索未知符号配置，恢复标称稳定性，通过多个实例说明该方法。
中文摘要 AI 辅助
本文研究具有不确定时变对角输入方向的MIMO系统的稳定化问题。我们提出了一种模块化切换符号补偿层，作为标称控制器周围的外层。该方法与努斯鲍姆型增益、监测函数或二进制自适应机制不同，仅使用有界符号变化，保持标称控制量及其性质。补偿层利用基于标称李雅普诺夫量构建的自适应变量，通过调度器搜索未知输入符号配置。开发了两种调度器：向量调度器，每个输入通道探索自身符号补偿并允许在线捕获证书；标量模式调度器，一个变量访问所有对角符号矩阵并在足够长的恒定符号间隔上给出设计时恢复保证。一旦设置正确的符号配置，实际闭环与标称闭环一致，恢复原始标称稳定性。该方法在飞行滚转反转问题、视觉伺服基准和地下水库控制示例中得到说明。
英文摘要
This paper addresses stabilization of MIMO systems with uncertain time-varying diagonal input direction. We propose a modular switching sign-compensation layer acting as an outer wrapper around a nominal controller. Unlike Nussbaum-type gains, monitoring functions, or binary adaptive mechanisms, the method uses only bounded sign changes that preserve the nominal control magnitude and its properties. The compensation layer uses adaptive variables built from nominal Lyapunov quantities to search for the unknown input-sign configuration based on schedulers. Two schedulers are developed: a vector scheduler, where each input channel explores its own sign compensation and admits an online trapping certificate, and a scalar pattern scheduler, where one variable visits all diagonal sign matrices and gives a design-time recovery guarantee on sufficiently long constant-sign intervals. Once the correct sign configuration is set, the actual closed loop coincides with the nominal closed loop and the original nominal stability property is recovered. The approach is illustrated on a flight roll-reversal problem, a visual-servoing benchmark, and an underground-reservoir control example motivated by human induced-seismicity mitigation.
