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

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

Safety-Critical Control Synthesis for network systems with Control Barrier Functions and Assume-Guarantee Contracts

This paper presents a contract based framework for safety-critical control synthesis for network systems. To handle the large state dimension of such systems, an assume-guarantee contract is used to break the large synthesis problem into smaller subproblems. 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 robust control invariant sets (RCIs) for the subsystems can be composed to form a robust control invariant set for the whole network system under a valid assume-guarantee contract. An epigraph algorithm is proposed to solve for a contract that is valid, ---an approach that has linear complexity for a sparse network, which leads to a robust control invariant set for the whole network. Implemented with control barrier function (CBF), the state of each subsystem is guaranteed to stay within the safe set. Furthermore, we propose a contingency tube Model Predictive Control (MPC) approach based on the robust control invariant set, which is capable of handling severe contingencies, including topology changes of the network. A power grid example is used to demonstrate the proposed method. The simulation result includes both set point control and contingency recovery, and the safety constraint is always satisfied

Abstracting Partially Feedback Linearizable Systems Compositionally

Symbolic controller synthesis offers the ability to design controllers enforcing a rich class of specifications such as those expressible in temporal logic. Despite the promise of symbolic controller synthesis and correct-by-design control software, this design methodology is not yet widely applicable due to the complexity of constructing finite-state abstractions for large continuous systems. In this letter, we investigate a compositional approach to the construction of abstractions by exploiting the cascading structure of partially feedback linearizable systems. We show how the linearized part and the zero dynamics can be independently abstracted and subsequently composed to obtain an abstraction of the original continuous system. We also illustrate through examples how this compositional approach significantly reduces the time required for construction of abstractions