Biblio

This paper considers a decentralized switched control problem where exact conditions for controller synthesis are obtained in the form of semidefinite programming (SDP). The formulation involves a discrete-time switched linear plant that has a nested structure, and whose system matrices switch between a finite number of values according to finite-state automation. The goal of this paper is to synthesize a commensurately nested switched controller to achieve a desired level of 2-induced norm performance. The nested structures of both plant and controller are characterized by block lower-triangular system matrices. For this setup, exact conditions are provided for the existence of a finite path-dependent synthesis. These include conditions for the completion of scaling matrices obtained through an extended matrix completion lemma.When individual controller dimensions are chosen at least as large as the plant, these conditions reduce to a set of linear matrix inequalities. The completion lemma also provides an algorithm to complete closed-loop scaling matrices, leading to inequalities for  ontroller synthesis that are solvable either algebraically or numerically through SDP.

We consider a three-step three-player complete information Colonel Blotto game in this paper, in which the first two players fight against a common adversary. Each player is endowed with a certain amount of resources at the beginning of the game, and the number of battlefields on which a player and the adversary fights is specified. The first two players are allowed to form a coalition if it improves their payoffs. In the first stage, the first two players may add battlefields and incur costs. In the second stage, the first two players may transfer resources among each other. The adversary observes this transfer, and decides on the allocation of its resources to the two battles with the players. At the third step, the adversary and the other two players fight on the updated number of battlefields and receive payoffs. We characterize the subgame-perfect Nash equilibrium (SPNE) of the game in various parameter regions. In particular, we show that there are certain parameter regions in which if the players act according to the SPNE strategies, then (i) one of the first two players add battlefields and transfer resources to the other player (a coalition is formed), (ii) there is no addition of battlefields and no transfer of resources (no coalition is formed). We discuss the implications of the results on resource allocation for securing cyberphysical systems.

This paper is concerned with the tradeoffs between low-cost heterogenous designs and optimality. We study a class of constrained myopic strategic games on networks which approximate the solutions to a constrained quadratic optimization problem; the Nash equilibria of these games can be found using best-response dynamical systems, which only use local information. The notion of price of heterogeneity captures the quality of our approximations. This notion relies on the structure and the strength of the interconnections between agents. We study the stability properties of these dynamical systems and demonstrate their complex characteristics, including abundance of equilibria on graphs with high sparsity and heterogeneity. We also introduce the novel notions of social equivalence and social dominance, and show some of their interesting implications, including their correspondence to consensus. Finally, using a classical result of Hirsch [1], we fully characterize the stability of these dynamical systems for the case of star graphs with asymmetric interactions. Various examples illustrate our results.