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首页> 外文期刊>Automatica >A randomized relaxation method to ensure feasibility in stochastic control of linear systems subject to state and input constraints
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A randomized relaxation method to ensure feasibility in stochastic control of linear systems subject to state and input constraints

机译：一种随机的弛豫方法，以确保线性系统随机控制的可行性和输入限制

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摘要

We consider a linear system affected by an additive stochastic disturbance and address the design of a finite horizon control policy that is optimal according to some cost criterion and accounts also for probabilistic constraints on both the input and state variables. The resulting policy can be implemented over a receding horizon according to the model predictive control strategy. Such a possibility, however, is hampered by the fact that a feasibility issue may arise when recomputing the policy. Infeasibility indeed can occur if the disturbance has unbounded support and the state is required to remain in a bounded set. In this paper, we propose a solution to this issue that is based on the introduction of a constraint relaxation that becomes effective only when the original problem turns out to be unfeasible. This is obtained via a cascade of two probabilistically-constrained optimization problems where, in the first one, performance is neglected and the policy is designed to fully recover feasibility or - if this is not possible - to determine the minimum level of relaxation which is needed to recover feasibility; in the second step, such a minimum relaxation level is imposed while optimally (re-)tuning the control policy parameters. Both problems are solved through a computationally tractable scenario-based scheme using a finite number of disturbance realizations and providing an approximate solution that satisfies with high confidence the original probabilistic constraints of the cascade. (C) 2020 Elsevier Ltd. All rights reserved.
机译：我们考虑一种受附加随机扰动的线性系统，并解决了根据一些成本标准和账户最佳的有限地平线控制策略的设计，也适用于输入和状态变量上的概率约束。根据模型预测控制策略，可以在后退地平线上实施所产生的策略。然而，这种可能性受到在重新计算政策时可能出现的可行性问题的阻碍。如果干扰具有无束缚的支撑，则确实可能发生不可发挥率，并且该状态需要保持在有界集中。在本文中，我们提出了解决这个问题的解决方案，这是基于引入约束放松，只有当原始问题结果不可行时才变得有效。这是通过级联的两个概率限制的优化问题获得，其中，在第一个，忽略了性能，并且策略旨在完全恢复可行性或 - 如果不可能 - 确定所需的最小放松水平恢复可行性;在第二步中，在最佳地（重新）调整控制策略参数的同时施加这样的最小松弛水平。通过使用有限数量的干扰实现，通过提供的基于技术的基于方案的方案来解决这两个问题，并提供了满足级联的原始概率约束的高度置信度的近似解。 （c）2020 elestvier有限公司保留所有权利。

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