We present semi-decentralized and distributed algorithms, designed via a preconditioned forward-backward operator splitting, for solving large-scale, decomposable semi-definite programs (SDPs). We exploit a chordal aggregate sparsity pattern assumption on the original SDP to obtain a set of mutually coupled SDPs defined on positive semidefinite (PSD) cones of reduced dimensions. We show that the proposed algorithms converge to a solution of the original SDP via iterations of reasonable computational cost, numerically comparing their performances with respect to others available in the literature.

State convergence is essential in many scientific areas, e.g. multi-agent consensus/disagreement, distributed optimization, computational game theory, multi-agent learning over networks. In this paper, we study for the first time the state convergence problem in uncertain linear systems. Preliminarily, we characterize state convergence in linear systems via equivalent linear matrix inequalities. In the presence of uncertainty, we complement the canonical definition of (weak) convergence with a stronger notion of convergence, which requires the existence of a common kernel among the generator matrices of the difference/differential inclusion (strong convergence). We investigate under which conditions the two definitions are equivalent. Then, we characterize strong and weak convergence via Lyapunov arguments, (linear) matrix inequalities and separability of the eigenvalues of the generator matrices. Finally, we show that, unlike asymptotic stability, state convergence lacks of duality.

To control the flow in a dynamical network where the nodes are associated with buffer variables and the arcs with controlled flows, we consider a network-decentralised strategy such that each arc controller makes its decision exclusively based on local information about the levels of the buffers that it connects. We seek a flow control law that asymptotically minimises a cost specified in terms of a weighted L₁-norm. This approach has the advantage of providing a solution that is generally sparse, because it uses a limited number of controlled flows. In particular, in the presence of a resource demand applied on a single node, the asymptotic flow is concentrated along the shortest path.

In this paper, we show the equivalence between a constrained, multi-agent control problem, modeled within the port-Hamiltonian framework, and an exact potential game. Specifically, critical distance-based constraints determine a network of double-integrator agents, which can be represented as a graph. Virtual couplings, i.e., pairs of spring-damper, assigned to each edge of the graph, allow to synthesize a distributed, gradient-based control law that steers the network to an invariant set of stable configurations. We characterize the points belonging to such set as Nash equilibria of the associated potential game, relating the parameters of the virtual couplings with the equilibrium seeking problem, since they are crucial to shape the transient behavior (i.e., the convergence) and, ideally, the set of achievable equilibria.

This paper proposes a decentralised explicit (closed-form) iterative formula that solves convex programming problems with linear equality constraints and interval bounds on the decision variables. In particular, we consider a team of decision agents, each setting the value of a subset of the variables, and a team of information agents, in charge of ensuring that the equality constraints are fulfilled. The structure of the constraint matrix imposes a communication pattern between decision and information agents, which can be represented as a bipartite graph. We associate each information agent with an integral variable and each decision agent with a saturated function, which takes the interval bounds into account, and we design a decentralised dynamic mechanism that globally converges to the optimal solution. Under mild conditions, the convergence is shown to be exponential. We also provide a discrete-time algorithm, based on the Euler system, and we give an upper bound for the step parameter to ensure convergence. Although the considered optimisation problem is static, we show that the proposed scheme can be successfully applied to find the optimal solution of network-decentralised dynamic control problems.

We consider the charge scheduling coordination of a fleet of plug-in electric vehicles, developing a hybrid decision-making framework for efficient and profitable usage of the distribution grid. Each charging dynamics, affected by the aggregate behavior of the whole fleet, is modelled as an inter-dependent, mixed-logical-dynamical system. The coordination problem is formalized as a generalized mixed-integer aggregative potential game, and solved via semi-decentralized implementation of a sequential best-response algorithm that leads to an approximated equilibrium of the game.

We propose a hybrid decision-making framework for safe and efficient autonomous driving of selfish vehicles on highways. Specifically, we model the dynamics of each vehicle as a Mixed-Logical-Dynamical system and propose driving rules to prevent potential sources of conflict among neighboring vehicles. We formalize the coordination problem as a generalized mixed-integer potential game, where an equilibrium solution generates a sequence of mixed-integer decisions for the vehicles that trade off individual optimality and overall safety.

Merging two Control Lyapunov Functions (CLFs) means creating a single 'new-born' CLF by starting from two parents functions. Specifically, given a 'father' function, shaped by the state constraints, and a 'mother' function, designed with some optimality criterion, the merging CLF should be similar to the father close to the constraints and similar to the mother close to the origin. To successfully merge two CLFs, the control-sharing condition is crucial: the two functions must have a common control law that makes both Lyapunov derivatives simultaneously negative. Unfortunately, it is difficult to guarantee this property a-priori, i.e., while computing the two parents functions. To create a constraint-shaped 'father' function that has the control-sharing property with the 'mother' function, we introduce a partial control-sharing i.e., the control-sharing only in the regions where the constraints are active. We show that imposing partial control-sharing is a convex optimization problem. Finally, the partial control-sharing is used to merge constraint-shaped and the Riccati-optimal functions, thus generating a CLF with bounded complexity that solves the constrained linear-quadratic stabilization problem with local optimality.