Compositional Set Invariance in Network Systems with Assume-Guarantee Contracts

Abstract

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.

Safety-Critical Control Synthesis for Network Systems With Control Barrier Functions and Assume-Guarantee Contracts

“…The paper significantly extends the conference version [18] in the following aspects. (1) We include more detail of the network assume-guarantee contract (2) We present the contingency tube MPC algorithm based on the RCI algorithm, which is able to handle contingencies that cause the operating point to change.…”

Compositional safety rules for inter-triggering hybrid automata

“…The value of the reset depends on the triggering actions of all agents ( ), which can possibly affect agent at time . This determines the new lead car and hence the new values of ℎ and , while evolves according to individual dynamics in (5). Controlled invariant sets for the system defined in (5) can be computed using polyhedral set computation methods such as those discussed in [18,25].…”

“…and executing ( 0 ), where the prediction horizon = 25, the predicted disturbance˜( ) = 0 if > 0 and˜( ) = −10 if = 0 , and the continuous dynamics (•, •, •) are as in (5), where Δ = 0.1. Furthermore, U = [−10, 10] for all agents , and we defineˆ− ( ) = { ∈ I | ∃ ∈ˆ( ), ∩{ } ≠ ∅} as an over-approximation of the set of all agents that can trigger at time .…”

“…On the other extreme, one can analyze agents individually, assuming all of the remaining agents act adversarially, in which case safety is hard to attain, if at all possible. Several frameworks have been developed between these two extremes to capture various notions of coordination, collaboration, or contracts [5,6,9,14,17,23,25,28].…”

System Level Synthesis with State and Input Constraints

“…Compared to the invariant set method [3], [4], [7], [11], that also guarantees closed-loop state bounds under a bounded disturbance signal, the SLS method proposed in this paper does not use the invariance condition of a set, but rather directly parameterize the closed-loop response. Therefore, the bound obtained is tight, as is shown in Section IV.…”