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

Putting reaction-diffusion systems into port-Hamiltonian framework

Reaction-diffusion systems model the evolution of the constituents distributed in space under the influence of chemical reactions and diffusion [6], [10]. These systems arise naturally in chemistry [5], but can also be used to model dynamical processes beyond the realm of chemistry such as biology, ecology, geology, and physics. In this paper, by adopting the viewpoint of port-controlled Hamiltonian systems [7] we cast reaction-diffusion systems into the portHamiltonian framework. Aside from offering conceptually a clear geometric interpretation formalized by a Stokes-Dirac structure [8], a port-Hamiltonian perspective allows to treat these dissipative systems as interconnected and thus makes their analysis, both quantitative and qualitative, more accessible from a modern dynamical systems and control theory point of view. This modeling approach permits us to draw immediately some conclusions regarding passivity and stability of reaction-diffusion systems. It is well-known that adding diffusion to the reaction system can generate behaviors absent in the ode case. This primarily pertains to the problem of diffusion-driven instability which constitutes the basis of Turing’s mechanism for pattern formation [11], [5]. Here the treatment of reaction-diffusion systems as dissipative distributed portHamiltonian systems could prove to be instrumental in supply of the results on absorbing sets, the existence of the maximal attractor and stability analysis. Furthermore, by adopting a discrete differential geometrybased approach [9] and discretizing the reaction-diffusion system in port-Hamiltonian form, apart from preserving a geometric structure, a compartmental model analogous to the standard one [1], [2] is obtaine

Compositional Analysis for Linear Control Systems

The complexity of physical and engineering systems, both in terms of the governing physical phenomena and the number of subprocesses involved, is mirrored in ever more complex mathematical models. While the demand for precise models is indisputable, the analysis of such system models remains challenging. Adopting techniques from computer science makes available a framework for compositional analysis of interconnected control systems. Simulation relations relate process models with their specifications thus checking whether the derived model behaves as desired. Based on that, compositional and assume-guarantee reasoning rules decompose the actual verification task into several subtasks that can be checked with less computational effort. Thus, modularly composed system models can be treated with modular analysis techniques. In this paper, we want to give an overview of how these concepts can be applied to analyze linear continuous-time systems (LTI). Motivated by the underlying physics, we introduce a general type of interconnection that can also be interpreted as a feedback control configuration in the spirit of decentralized control. Additionally, parallel composition of LTI systems is discussed with special emphasis on decomposition strategies for a given specification. The proposed methodology could be extended further to classes of hybrid systems where compositional analysis techniques are of particular interest.