This study is concerned with the computationally efficient robust model predictive control (MPC) for discrete-time stochastic switching systems. Aiming at achieving optimal control synthesis under the requirement of bumpless transfer control (BTC), the min–max MPC formulation is extended to the transition-dependent paradigm, such that the abrupt variation of mode-dependent gains can be mitigated via BTC performance optimization. To address the high computational complexity caused by the transition-dependent variables and constraints, the MPC algorithm is developed with an offline-to-online synthesis strategy, achieving comparable online computation cost to non-switching MPC. Meanwhile, a class of more general stochastic switching signals is considered, where the sojourn time may follow any form of distribution, and the recursive feasibility and mean-square stability are theoretically guaranteed. Compared with existing studies on switching MPC and the ones on BTC, this work avoids the assumption of the Markov property on mode switching and reduces conservatism by exploiting the statistical information of sojourn time. An illustrative example is provided to show the potential of the obtained results.

中文翻译：

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随机切换系统的高效、平稳的鲁棒模型预测控制

本研究涉及离散时间随机切换系统的计算高效的鲁棒模型预测控制（MPC）。为了在无扰动传递控制（BTC）的要求下实现最优控制综合，将最小-最大MPC公式扩展到依赖于转换的范式，从而可以通过BTC性能优化来缓解依赖于模式的增益的突然变化。为了解决由转换相关变量和约束引起的高计算复杂度，MPC 算法采用离线到在线综合策略来开发，实现了与非切换 MPC 相当的在线计算成本。同时，考虑了一类更一般的随机开关信号，其中停留时间可以服从任何形式的分布，并且理论上保证了递归可行性和均方稳定性。与现有的切换 MPC 和 BTC 的研究相比，本工作避免了模式切换的马尔可夫性质的假设，并通过利用停留时间的统计信息来减少保守性。提供了一个说明性示例来显示所获得结果的潜力。