Fast auto-generated ACADO integrators and application to MHE with multi-rate measurements

Abstract: Algorithms for real-time, embedded optimization need to run within tight computational times, and preferably on embedded control hardware for which only limited computational power and memory is available. A computationally demanding step of these algorithms is the model simulation with sensitivity generation. This paper presents an implementation of code generation for Implicit Runge-Kutta (IRK) methods with efficient sensitivity generation, which outperforms other solvers for the targeted applications. The focus of this paper will be on the extension of the proposed tool to the integration of index-1 Differential Algebraic Equations (DAE), and continuous output functions, which are crucial for e.g. performing sensor fusion with measurements provided at very high sampling rates. The new tool is provided with a powerful MATLAB interface. It is illustrated in simulation for the trajectory estimation of a mechanical system modeled by complex Differential-Algebraic equations, using sensor information provided at fast, multi-rate sampling frequencies

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