Decentralized Control of Constrained Linear Systems via Assume-Guarantee Contracts
Decentralized Control of Constrained Linear Systems via Assume-Guarantee Contracts
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DOI：
10.23919/acc45564.2020.9147215
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
Weixuan Lin;E. Bitar
中科院分区：
文献类型：
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作者：
Weixuan Lin;E. Bitar
我们考虑了一个离散时间线性系统的分散控制，该系统受到外源干扰和状态和输入轨迹上的多面体约束。底层系统由动态耦合子系统的有限集合组成，其中每个子系统都假定有一个专用的本地控制器。信息的分散是根据每个本地控制器可以访问的状态测量的稀疏性约束来表示的。在这种情况下，我们研究了在其测量历史中仿射参数化的分散控制器的设计。对于部分嵌套信息结构的问题，这种策略空间的优化是凸的。然而，在更一般的（非经典的）信息结构下，凸性并不能得到保证，在这种信息结构中，一个本地控制器可用的信息可能会受到它无法访问或重构的控制动作的影响。为了缓解此类问题中出现的非凸性，我们提出了一种分散控制设计方法，该方法将信息耦合状态有效地视为干扰，其轨迹被约束为椭球契约集中的值，其位置、规模和方向与底层仿射分散控制策略共同优化。在允许契约空间上建立了一个自然的结构条件，便于通过半定规划对控制策略和契约集进行联合优化。
We consider the decentralized control of a discretetime, linear system subject to exogenous disturbances and polyhedral constraints on the state and input trajectories. The underlying system is composed of a finite collection of dynamically coupled subsystems, where each subsystem is assumed to have a dedicated local controller. The decentralization of information is expressed according to sparsity constraints on the state measurements that each local controller has access to. In this context, we investigate the design of decentralized controllers that are affinely parameterized in their measurement history. For problems with partially nested information structures, the optimization over such policy spaces is known to be convex. Convexity is not, however, guaranteed under more general (nonclassical) information structures in which the information available to one local controller can be affected by control actions that it cannot access or reconstruct. With the aim of alleviating the nonconvexity that arises in such problems, we propose an approach to decentralized control design where the information-coupling states are effectively treated as disturbances whose trajectories are constrained to take values in ellipsoidal contract sets whose location, scale, and orientation are jointly optimized with the underlying affine decentralized control policy. We establish a natural structural condition on the space of allowable contracts that facilitates the joint optimization over the control policy and the contract set via semidefinite programming.