2,590 research outputs found
Augmented Lagrangian Approach to Design of Structured Optimal State Feedback Gains
We consider the design of optimal state feedback gains subject to structural constraints on the distributed controllers. These constraints are in the form of sparsity requirements for the feedback matrix, implying that each controller has access to information from only a limited number of subsystems. The minimizer of this constrained optimal control problem is sought using the augmented Lagrangian method. Notably, this approach does not require a stabilizing structured gain to initialize the optimization algorithm. Motivated by the structure of the necessary conditions for optimality of the augmented Lagrangian, we develop an alternating descent method to determine the structured optimal gain. We also utilize the sensitivity interpretation of the Lagrange multiplier to identify favorable communication architectures for structured optimal design. Examples are provided to illustrate the effectiveness of the developed method
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
Enhanced gradient tracking algorithms for distributed quadratic optimization via sparse gain design
In this paper we propose a new control-oriented design technique to enhance the algorithmic performance of the distributed gradient tracking algorithm. We focus on a scenario in which agents in a network aim to cooperatively minimize the sum of convex, quadratic cost functions depending on a common decision variable. By leveraging a recent system-theoretical reinterpretation of the considered algorithmic framework as a closed-loop linear dynamical system, the proposed approach generalizes the diagonal gain structure associated to the existing gradient tracking algorithms. Specifically, we look for closed-loop gain matrices that satisfy the sparsity constraints imposed by the network topology, without however being necessarily diagonal, as in existing gradient tracking schemes. We propose a novel procedure to compute stabilizing sparse gain matrices by solving a set of nonlinear matrix inequalities, based on the solution of a sequence of approximate linear versions of such inequalities. Numerical simulations are presented showing the enhanced performance of the proposed design compared to existing gradient tracking algorithms
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