Abstract In this paper, a novel control scheme is proposed for model predictive control (MPC) of switched systems under arbitrarily generated undetectable switching signals. To this end, it is assigned that control scheme should simultaneously ensure reduction in optimization cost and maintain closed-loop stability. In other words, the control algorithm operates as single-mode in case corresponding conditions are satisfied, resulting in reduction of number of required calculations and ease of implementation. The proposed stabilization scheme is based on prediction of sliding hyperplane in various switched configurations, leading to reduced problem dimensions and ease of implementation of robustness analysis. To this end, an analytic gradient-descent expression of the optimization solution is obtained, shown to be robustly input-to-state stable (ISS) given the existence of a common Lyapunov function (CLF) corresponding to sliding mode controller (SMC). Furthermore, effects of dynamical variations over the prediction horizon are investigated, noting important effects on the stability criteria, which have been ignored in previous analytical studies. In case sufficient conditions are satisfied, the control scheme results in closed-loop stability and gradual convergence of sliding functions to origin in all potential modes of switched dynamics regardless of active switching state. However, the necessary conditions corresponding to sampling rate pertaining to this objective are potentially over-strict. To overcome this issue, it is proposed that control objectives and stability conditions can be relaxed such that boundedness of sliding functions in all switched modes is maintained according to the cost-reducing input update law rather than their strict convergence to the origin. The effects of state and input constraint violations are then incorporated as soft constraints. Experimental and numerical evaluations demonstrate the effectiveness of control method.

中文翻译：

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包含动态变化的任意切换非线性系统的解析单模滑动预测控制

摘要 本文提出了一种新的控制方案，用于在任意产生的不可检测的开关信号下对开关系统进行模型预测控制（MPC）。为此，指定控制方案应同时确保降低优化成本和保持闭环稳定性。换句话说，在满足相应条件的情况下，控制算法以单模式运行，从而减少了所需的计算次数并易于实现。所提出的稳定方案基于对各种切换配置中的滑动超平面的预测，从而减少了问题维度并易于实现稳健性分析。为此，得到优化解的解析梯度下降表达式，考虑到与滑模控制器 (SMC) 相对应的公共李雅普诺夫函数 (CLF) 的存在，显示为稳健输入到状态稳定 (ISS)。此外，还研究了预测范围内动态变化的影响，并指出了对稳定性标准的重要影响，而这些影响在以前的分析研究中已被忽略。在满足充分条件的情况下，控制方案会导致闭环稳定性和滑动函数逐渐收敛到所有潜在的切换动态模式，而不管主动切换状态如何。然而，与该目标相关的采样率对应的必要条件可能过于严格。为了克服这个问题，建议可以放宽控制目标和稳定性条件，使得所有切换模式中的滑动函数的有界性根据降低成本的输入更新定律而不是它们严格收敛到原点来保持。然后将违反状态和输入约束的影响合并为软约束。实验和数值评估证明了控制方法的有效性。