Control of nonlinear systems with partial state constraints using a barrier Lyapunov function
Control of nonlinear systems with partial state constraints using a barrier Lyapunov function
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DOI：
10.1080/00207179.2011.631192
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发表时间：
2011-11
影响因子：
2.1
通讯作者：
K. P. Tee;S. Ge
中科院分区：
文献类型：
--
作者：
K. P. Tee;S. Ge
本文讨论了状态有约束的严格反馈系统的控制设计问题。为了防止违反约束的状态，我们采用了一个障碍李雅普诺夫函数（BLF），增长到无穷大时，其参数接近一些有限的限制。基于BLF的反推，我们证明了渐近输出跟踪实现不违反任何约束，提供的初始状态和控制参数是可行的。我们还建立了充分的条件，以确保可行性，这可以检查离线没有精确的知识的初始状态。与完全状态约束问题相比，在处理部分状态约束问题时放宽了可行性条件。在存在参数不确定性的情况下，基于BLF的自适应反推可以有效地防止在线参数自适应过程中的瞬态状态超越约束区域。为了放宽可行性条件，考虑了非对称误差界，并使用非对称障碍函数进行控制设计。基于BLF的控制的性能示出了两个模拟的例子。
This article addresses the problem of control design for strict-feedback systems with constraints on the states. To prevent the states from violating the constraints, we employ a barrier Lyapunov function (BLF), which grows to infinity whenever its arguments approaches some finite limits. Based on BLF-based backstepping, we show that asymptotic output tracking is achieved without violation of any constraint, provided that the initial states and control parameters are feasible. We also establish sufficient conditions to ensure feasibility, which can be checked offline without precise knowledge of the initial states. The feasibility conditions are relaxed when handling the partial state constraint problem as compared to the full state constraint problem. In the presence of parametric uncertainties, BLF-based adaptive backstepping is useful in preventing the states from transgressing the constrained region during the transient stages of online parameter adaptation. To relax the feasibility conditions, asymmetric error bounds are considered and asymmetric barrier functions are used for control design. The performance of the BLF-based control is illustrated with two simulated examples.