MAX-consensus in open multi-agent systems with gossip interactions

We study the problem of distributed maximum computation in an open multi-agent system, where agents can leave and arrive during the execution of the algorithm. The main challenge comes from the possibility that the agent holding the largest value leaves the system, which changes the value to be computed. The algorithms must as a result be endowed with mechanisms allowing to forget outdated information. The focus is on systems in which interactions are pairwise gossips between randomly selected agents. We consider situations where leaving agents can send a last message, and situations where they cannot. For both cases, we provide algorithms able to eventually compute the maximum of the values held by agents.Comment: To appear in the proceedings of the 56th IEEE Conference on Decision and Control (CDC 17). 8 pages, 3 figure

On the relationship between control barrier functions and projected dynamical systems

In this paper, we study the relationship between systems controlled via Control Barrier Function (CBF) approaches and a class of discontinuous dynamical systems, called Projected Dynamical Systems (PDSs). In particular, under appropriate assumptions, we show that the vector field of CBF-controlled systems is a Krasovskii-like perturbation of the set-valued map of a differential inclusion, that abstracts PDSs. This result provides a novel perspective to analyze and design CBF-based controllers. Specifically, we show how, in certain cases, it can be employed for designing CBF-based controllers that, while imposing safety, preserve asymptotic stability and do not introduce undesired equilibria or limit cycles. Finally, we briefly discuss about how it enables continuous implementations of certain projection-based controllers, that are gaining increasing popularity.Comment: To be presented at the 62nd IEEE Conference on Decision and Control, Dec. 13-15, 2023, Singapor

Constraint-Adaptive MPC for linear systems: A system-theoretic framework for speeding up MPC through online constraint removal

Reducing the computation time of model predictive control (MPC) is important, especially for systems constrained by many state constraints. In this paper, we propose a new online constraint removal framework for linear systems, for which we coin the term constraint-adaptive MPC (ca-MPC). In so-called exact ca-MPC, we adapt the imposed constraints by removing, at each time-step, a subset of the state constraints in order to reduce the computational complexity of the receding-horizon optimal control problem, while ensuring that the closed-loop behavior is {\em identical} to that of the original MPC law. We also propose an approximate ca-MPC scheme in which a further reduction of computation time can be accomplished by a tradeoff with closed-loop performance, while still preserving recursive feasibility, stability, and constraint satisfaction properties. The online constraint removal exploits fast backward and forward reachability computations combined with optimality properties

Urgency-aware optimal routing in repeated games through artificial currencies

When people choose routes minimizing their individual delay, the aggregate congestion can be much higher compared to that experienced by a centrally-imposed routing. Yet centralized routing is incompatible with the presence of self-interested users. How can we reconcile the two? In this paper we address this question within a repeated game framework and propose a fair incentive mechanism based on artificial currencies that routes selfish users in a system-optimal fashion, while accounting for their temporal preferences. We instantiate the framework in a parallel-network whereby users commute repeatedly (e.g., daily) from a common start node to the end node. Thereafter, we focus on the specific two-arcs case whereby, based on an artificial currency, the users are charged when traveling on the first, fast arc, whilst they are rewarded when traveling on the second, slower arc. We assume the users to be rational and model their choices through a game where each user aims at minimizing a combination of today's discomfort, weighted by their urgency, and the average discomfort encountered for the rest of the period (e.g., a week). We show that, if prices of artificial currencies are judiciously chosen, the routing pattern converges to a system-optimal solution, while accommodating the users’ urgency. We complement our study through numerical simulations. Our results show that it is possible to achieve a system-optimal solution whilst significantly reducing the users’ perceived discomfort when compared to a centralized optimal but urgency-unaware policy

Learning the cost-to-go for mixed-integer nonlinear model predictive control

Application of nonlinear model predictive control (NMPC) to problems with hybrid dynamical systems, disjoint constraints, or discrete controls often results in mixed-integer formulations with both continuous and discrete decision variables. However, solving mixed-integer nonlinear programming problems (MINLP) in real-time is challenging, which can be a limiting factor in many applications. To address the computational complexity of solving mixed integer nonlinear model predictive control problem in real-time, this paper proposes an approximate mixed integer NMPC formulation based on value function approximation. Leveraging Bellman's principle of optimality, the key idea here is to divide the prediction horizon into two parts, where the optimal value function of the latter part of the prediction horizon is approximated offline using expert demonstrations. Doing so allows us to solve the MINMPC problem with a considerably shorter prediction horizon online, thereby reducing the online computation cost. The paper uses an inverted pendulum example with discrete controls to illustrate this approach

Urgency-aware Optimal Routing in Repeated Games through Artificial Currencies

When people choose routes minimizing their individual delay, the aggregate congestion can be much higher compared to that experienced by a centrally-imposed routing. Yet centralized routing is incompatible with the presence of self-interested agents. How can we reconcile the two? In this paper we address this question within a repeated game framework and propose a fair incentive mechanism based on artificial currencies that routes selfish agents in a system-optimal fashion, while accounting for their temporal preferences. We instantiate the framework in a parallel-network whereby agents commute repeatedly (e.g., daily) from a common start node to the end node. Thereafter, we focus on the specific two-arcs case whereby, based on an artificial currency, the agents are charged when traveling on the first, fast arc, whilst they are rewarded when traveling on the second, slower arc. We assume the agents to be rational and model their choices through a game where each agent aims at minimizing a combination of today's discomfort, weighted by their urgency, and the average discomfort encountered for the rest of the period (e.g., a week). We show that, if prices of artificial currencies are judiciously chosen, the routing pattern converges to a system-optimal solution, while accommodating the agents' urgency. We complement our study through numerical simulations. Our results show that it is possible to achieve a system-optimal solution whilst reducing the agents' perceived discomfort by 14-20% when compared to a centralized optimal but urgency-unaware policy.Comment: Accepted for presentation at the European Control Conference 202

Fair Artificial Currency Incentives in Repeated Weighted Congestion Games: Equity vs. Equality

When users access shared resources in a selfish manner, the resulting societal cost and perceived users' cost is often higher than what would result from a centrally coordinated optimal allocation. While several contributions in mechanism design manage to steer the aggregate users choices to the desired optimum by using monetary tolls, such approaches bear the inherent drawback of discriminating against users with a lower income. More recently, incentive schemes based on artificial currencies have been studied with the goal of achieving a system-optimal resource allocation that is also fair. In this resource-sharing context, this paper focuses on repeated weighted congestion game with two resources, where users contribute to the congestion to different extents that are captured by individual weights. First, we address the broad concept of fairness by providing a rigorous mathematical characterization of the distinct societal metrics of equity and equality, i.e., the concepts of providing equal outcomes and equal opportunities, respectively. Second, we devise weight-dependent and time-invariant optimal pricing policies to maximize equity and equality, and prove convergence of the aggregate user choices to the system-optimum. In our framework it is always possible to achieve system-optimal allocations with perfect equity, while the maximum equality that can be reached may not be perfect, which is also shown via numerical simulations

Projection-based Controllers with Inherent Dissipativity Properties

Projection-based Controllers (PBCs) are currently gaining traction in both scientific and engineering communities. In PBCs, the input-output signals of the controller are kept in sector-bounded sets by means of projection. In this paper, we will show how this projection operation can be used to induce useful passivity or general dissipativity properties on broad classes of (unprojected) nonlinear controllers that otherwise would not have these properties. The induced dissipativity properties of PBC will be exploited to guarantee asymptotic stability of negative feedback interconnections of passive nonlinear plants and suitably designed PBC, under mild conditions. Proper generalizations to so-called $(q,s,r)$-dissipativity will be presented as well. For illustrating the effectiveness of PBC control design via these passivity-based techniques, two numerical examples are provided.Comment: to be presented at IEEE CDC 2023 (Singapore

Decentralized event-triggered estimation of nonlinear systems

We investigate the scenario where a perturbed nonlinear system transmits its output measurements to a remote observer via a packet-based communication network. The sensors are grouped into N nodes and each of these nodes decides when its measured data is transmitted over the network independently. The objective is to design both the observer and the local transmission policies in order to obtain accurate state estimates, while only sporadically using the communication network. In particular, given a general nonlinear observer designed in continuous-time satisfying an input-to-state stability property, we explain how to systematically design a dynamic event-triggering rule for each sensor node that avoids the use of a copy of the observer, thereby keeping local calculation simple. We prove the practical convergence property of the estimation error to the origin and we show that there exists a uniform strictly positive minimum inter-event time for each local triggering rule under mild conditions on the plant. The efficiency of the proposed techniques is illustrated on a numerical case study of a flexible robotic arm