Decentralized linear optimal control for cooperative networked teams via invariant subspace decomposition

Abstract

In this thesis, we consider decentralized cooperative control problems of linear systems. We propose the direct sum decomposition method of invariant subspaces, which enables us to model and investigate the decentralized control problems in a well-known control theory framework. The main advantage of this approach is that it provides insights and intuitions of the relative controllable and observable spaces of each subsystem and extends the Kalman decomposition technique into a graph representation. Based on this approach, we derive the separation condition for dynamic orthogonality through the Kalman filters based on the sequential separable principle of subsystems. We show that the certainty equivalence condition plays a vital role in decomposing the problem into several subproblems. Under the separable condition, we obtain the optimal decentralized control policy which, aggregates the solutions of decomposed independent centralized control policy of each subsystem. The optimal decentralized control policy is investigated to implicit and explicit output equations. This provides insight into applying decentralized control policy to various practical problems. The decentralized control policy is implemented by applying to cooperative guidance problems of the networked missile system. The decentralized optimal guidance laws are derived, and the performance and practical issues are investigated. We also proposed a practical way to utilize the decentralized guidance laws.