2,939 research outputs found
Design of Optimal Sparse Feedback Gains via the Alternating Direction Method of Multipliers
We design sparse and block sparse feedback gains that minimize the variance
amplification (i.e., the norm) of distributed systems. Our approach
consists of two steps. First, we identify sparsity patterns of feedback gains
by incorporating sparsity-promoting penalty functions into the optimal control
problem, where the added terms penalize the number of communication links in
the distributed controller. Second, we optimize feedback gains subject to
structural constraints determined by the identified sparsity patterns. In the
first step, the sparsity structure of feedback gains is identified using the
alternating direction method of multipliers, which is a powerful algorithm
well-suited to large optimization problems. This method alternates between
promoting the sparsity of the controller and optimizing the closed-loop
performance, which allows us to exploit the structure of the corresponding
objective functions. In particular, we take advantage of the separability of
the sparsity-promoting penalty functions to decompose the minimization problem
into sub-problems that can be solved analytically. Several examples are
provided to illustrate the effectiveness of the developed approach.Comment: To appear in IEEE Trans. Automat. Contro
Stochastic and Optimal Distributed Control for Energy Optimization and Spatially Invariant Systems
Improving energy efficiency and grid responsiveness of buildings requires sensing, computing and communication to enable stochastic decision-making and distributed operations. Optimal control synthesis plays a significant role in dealing with the complexity and uncertainty associated with the energy systems.
The dissertation studies general area of complex networked systems that consist of interconnected components and usually operate in uncertain environments. Specifically, the contents of this dissertation include tools using stochastic and optimal distributed control to overcome these challenges and improve the sustainability of electric energy systems.
The first tool is developed as a unifying stochastic control approach for improving energy efficiency while meeting probabilistic constraints. This algorithm is applied to demonstrate energy efficiency improvement in buildings and improving operational efficiency of virtualized web servers, respectively. Although all the optimization in this technique is in the form of convex optimization, it heavily relies on semidefinite programming (SP). A generic SP solver can handle only up to hundreds of variables. This being said, for a large scale system, the existing off-the-shelf algorithms may not be an appropriate tool for optimal control. Therefore, in the sequel I will exploit optimization in a distributed way.
The second tool is itself a concrete study which is optimal distributed control for spatially invariant systems. Spatially invariance means the dynamics of the system do not vary as we translate along some spatial axis. The optimal H2 [H-2] decentralized control problem is solved by computing an orthogonal projection on a class of Youla parameters with a decentralized structure. Optimal H∞ [H-infinity] performance is posed as a distance minimization in a general L∞ [L-infinity] space from a vector function to a subspace with a mixed L∞ and H∞ space structure. In this framework, the dual and pre-dual formulations lead to finite dimensional convex optimizations which approximate the optimal solution within desired accuracy. Furthermore, a mixed L2 [L-2] /H∞ synthesis problem for spatially invariant systems as trade-offs between transient performance and robustness. Finally, we pursue to deal with a more general networked system, i.e. the Non-Markovian decentralized stochastic control problem, using stochastic maximum principle via Malliavin Calculus
Fault detection and isolation of malicious nodes in MIMO Multi-hop Control Networks
A MIMO Multi-hop Control Network (MCN) consists of a MIMO LTI system where
the communication between sensors, actuators and computational units is
supported by a (wireless) multi-hop communication network, and data flow is
performed using scheduling and routing of sensing and actuation data. We
provide necessary and sufficient conditions on the plant dynamics and on the
communication protocol configuration such that the Fault Detection and
Isolation (FDI) problem of failures and malicious attacks to communication
nodes can be solved.Comment: 6 page
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