Robust, Distributed, and Optimal Control via Dissipativity-Augmentation

Dissipativity has been an influential tool for stability analysis of networked systems for several decades. In particular, the Network Dissipativity Theorem provides robust stability guarantees for interconnections based on open-loop input-output properties of subsystems. While this theorem has been applied with great success to analysis and controller design for stability, its application in optimal control has been limited. This is due in large part to two factors. First, overly conservative dissipativity characterizations -- especially for network effects like time-varying delays and for data-based estimations -- greatly restrict the controller design space, resulting in poor performance. Second, a framework for combining optimal control problems with the Network Dissipativity Theorem has yet to be put forward in its full generality. In this dissertation addresses these two limitations. First, stochastic dissipativity is defined and used to tightly characterize input-output properties of systems with probabilistically time-varying delays. This includes a KYP-type lemma for nonlinear systems, and a linear matrix inequality condition for linear systems. It is shown that this method yields tighter dissipativity characterizations than its deterministic counterpart, which results in improved controller performance. Second, dissipativity-augmented multiobjective control is proposed as a means of generating network controllers that attain high performance (in terms of H2, colored-H2, H-infinity, pole placement, and learned objectives) with robust stability guarantees using centralized, decentralized, and distributed control structures. While the problem is NP-hard, in each case a feasible point is constructed, and an algorithm for locally optimizing performance is proposed based on the convex-concave procedure. Numerical experiments demonstrate broad applicability, guaranteed stability, and improved performance over existing methods where applicable. In addition, a proof of the optimal convex-concave decomposition for bilinear matrix inequalities is derived, the Network Dissipativity Theorem is extended to subsets of inputs and outputs, some improvements are made to existing model-free data-based dissipativity estimation, and critical limitations of data-based dissipativity estimation are illustrated through a case study.