716 research outputs found
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
Compositional Synthesis via a Convex Parameterization of Assume-Guarantee Contracts
We develop an assume-guarantee framework for control of large scale linear
(time-varying) systems from finite-time reach and avoid or infinite-time
invariance specifications. The contracts describe the admissible set of states
and controls for individual subsystems. A set of contracts compose correctly if
mutual assumptions and guarantees match in a way that we formalize. We propose
a rich parameterization of contracts such that the set of parameters that
compose correctly is convex. Moreover, we design a potential function of
parameters that describes the distance of contracts from a correct composition.
Thus, the verification and synthesis for the aggregate system are broken to
solving small convex programs for individual subsystems, where correctness is
ultimately achieved in a compositional way. Illustrative examples demonstrate
the scalability of our method
Compositional Synthesis for Linear Systems via Convex Optimization of Assume-Guarantee Contracts
We take a divide and conquer approach to design controllers for reachability
problems given large-scale linear systems with polyhedral constraints on
states, controls, and disturbances. Such systems are made of small subsystems
with coupled dynamics. We treat the couplings as additional disturbances and
use assume-guarantee (AG) contracts to characterize these disturbance sets. For
each subsystem, we design and implement a robust controller locally, subject to
its own constraints and contracts. The main contribution of this paper is a
method to derive the contracts via a novel parameterization and a corresponding
potential function that characterizes the distance to the correct composition
of controllers and contracts, where all contracts are held. We show that the
potential function is convex in the contract parameters. This enables the
subsystems to negotiate the contracts with the gradient information from the
dual of their local synthesis optimization problems in a distributed way,
facilitating compositional control synthesis that scales to large systems. We
present numerical examples, including a scalability study on a system with tens
of thousands of dimensions, and a case study on applying our method to a
distributed Model Predictive Control (MPC) problem in a power system
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
Formal methods for resilient control
Many systems operate in uncertain, possibly adversarial environments, and their successful operation is contingent upon satisfying specific requirements, optimal performance, and ability to recover from unexpected situations. Examples are prevalent in many engineering disciplines such as transportation, robotics, energy, and biological systems. This thesis studies designing correct, resilient, and optimal controllers for discrete-time complex systems from elaborate, possibly vague, specifications.
The first part of the contributions of this thesis is a framework for optimal control of non-deterministic hybrid systems from specifications described by signal temporal logic (STL), which can express a broad spectrum of interesting properties. The method is optimization-based and has several advantages over the existing techniques. When satisfying the specification is impossible, the degree of violation - characterized by STL quantitative semantics - is minimized. The computational limitations are discussed.
The focus of second part is on specific types of systems and specifications for which controllers are synthesized efficiently. A class of monotone systems is introduced for which formal synthesis is scalable and almost complete. It is shown that hybrid macroscopic traffic models fall into this class. Novel techniques in modular verification and synthesis are employed for distributed optimal control, and their usefulness is shown for large-scale traffic management. Apart from monotone systems, a method is introduced for robust constrained control of networked linear systems with communication constraints. Case studies on longitudinal control of vehicular platoons are presented.
The third part is about learning-based control with formal guarantees. Two approaches are studied. First, a formal perspective on adaptive control is provided in which the model is represented by a parametric transition system, and the specification is captured by an automaton. A correct-by-construction framework is developed such that the controller infers the actual parameters and plans accordingly for all possible future transitions and inferences. The second approach is based on hybrid model identification using input-output data. By assuming some limited knowledge of the range of system behaviors, theoretical performance guarantees are provided on implementing the controller designed for the identified model on the original unknown system
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