Distributed Robust Set-Invariance for Interconnected Linear Systems

We introduce a class of distributed control policies for networks of discrete-time linear systems with polytopic additive disturbances. The objective is to restrict the network-level state and controls to user-specified polyhedral sets for all times. This problem arises in many safety-critical applications. We consider two problems. First, given a communication graph characterizing the structure of the information flow in the network, we find the optimal distributed control policy by solving a single linear program. Second, we find the sparsest communication graph required for the existence of a distributed invariance-inducing control policy. Illustrative examples, including one on platooning, are presented.Comment: 8 Pages. Submitted to American Control Conference (ACC), 201

Robust Connectivity Analysis for Multi-Agent Systems

In this report we provide a decentralized robust control approach, which guarantees that connectivity of a multi-agent network is maintained when certain bounded input terms are added to the control strategy. Our main motivation for this framework is to determine abstractions for multi-agent systems under coupled constraints which are further exploited for high level plan generation.Comment: 20 page

Distributed Control of Spatially Reversible Interconnected Systems with Boundary Conditions

We present a class of spatially interconnected systems with boundary conditions that have close links with their spatially invariant extensions. In particular, well-posedness, stability, and performance of the extension imply the same characteristics for the actual, finite extent system. In turn, existing synthesis methods for control of spatially invariant systems can be extended to this class. The relation between the two kinds of systems is proved using ideas based on the "method of images" of partial differential equations theory and uses symmetry properties of the interconnection as a key tool

Compositional Set Invariance in Network Systems with Assume-Guarantee Contracts

This paper presents an assume-guarantee reasoning approach to the computation of robust invariant sets for network systems. Parameterized signal temporal logic (pSTL) is used to formally describe the behaviors of the subsystems, which we use as the template for the contract. We show that set invariance can be proved with a valid assume-guarantee contract by reasoning about individual subsystems. If a valid assume-guarantee contract with monotonic pSTL template is known, it can be further refined by value iteration. When such a contract is not known, an epigraph method is proposed to solve for a contract that is valid, ---an approach that has linear complexity for a sparse network. A microgrid example is used to demonstrate the proposed method. The simulation result shows that together with control barrier functions, the states of all the subsystems can be bounded inside the individual robust invariant sets.Comment: Submitted to 2019 American Control Conferenc

Provably safe cruise control of vehicular platoons

We synthesize performance-aware safe cruise control policies for longitudinal motion of platoons of autonomous vehicles. Using set-invariance theories, we guarantee infinite-time collision avoidance in the presence of bounded additive disturbances, while ensuring that the length and the cruise speed of the platoon are bounded within specified ranges. We propose: 1) a centralized control policy and 2) a distributed control policy, where each vehicle's control decision depends solely on its relative kinematics with respect to the platoon leader. Numerical examples are included.NSF; CPS-1446151; CMMI-1400167; FA 9550-15-1-0186 - AFOSR; Schlumberger Foundation Faculty for the Future Fellowship; FA 9550-15-1-0186 - AFOSR; NSF; ECCS-1550016; CNS 123922