Contracts as specifications for dynamical systems in driving variable form

Abstract

This paper introduces assume/guarantee contracts on continuous-time control systems, hereby extending contract theories for discrete systems to certain new model classes and specifications. Contracts are regarded as formal characterizations of control specifications, providing an alternative to specifications in terms of dissipativity properties or setinvariance. The framework has the potential to capture a richer class of specifications more suitable for complex engineering systems. The proposed contracts are supported by results that enable the verification of contract implementation and the comparison of contracts. These results are illustrated by an example of a vehicle following system.

Behavioural assume-guarantee contracts for linear dynamical systems

“…Remark 2: Suppose that Σ, A and Γ are given by ( 3), ( 6) and (7), respectively. Using Theorem 1 with w = [y u ] shows that B(A ∧ Σ) ⊂ B(Γ) if and only if there exist polynomial matrices M 1 (s) and M 2 (s) such that…”

“…We proceed with finding guarantees Γ of the form ( 9) such that G (s) has full row rank and B(A ∧ Γ ) = B(A ∧ Γ). Let Γ be given by (7). If G(s) has full row rank, then we can take Γ = Γ.…”

“…The contracts presented in this paper are a generalization of the contracts in [6], and are closely related to the contracts in [7]. In contrast to [6], where the guarantees specify only a set of admissible output trajectories, the guarantees in this paper can also specify a particular relationship between input and output trajectories.…”

Verifying Contracts for Perturbed Control Systems using Linear Programming

“…It has been successfully applied to the design of the "cyber" aspects of cyber-physical systems, see [24], [25] and references therein. More recently, several frameworks have been proposed for contract theory for dynamical control systems, see e.g., [26]- [32]. In [26], [27], the authors propose methods for prescribing contracts on continuous-time systems, and verify these contracts either using geometric control theory methods, or using behavioural systems theory, respectively.…”

“…More recently, several frameworks have been proposed for contract theory for dynamical control systems, see e.g., [26]- [32]. In [26], [27], the authors propose methods for prescribing contracts on continuous-time systems, and verify these contracts either using geometric control theory methods, or using behavioural systems theory, respectively. Discrete-time systems are considered in [28]- [31], where assumptions are put on the input signal to the system, and guarantees are put on the state and the output of the system.…”