Model predictive control for singular differential-algebraic equations. - In: International journal of control, ISSN 1366-5820, Bd. 95 (2022), 8, S. 2141-2150
We study model predictive control for singular differential-algebraic equations with higher index. This is a novelty when compared to the literature where only regular differential-algebraic equations with additional assumptions on the index and/or controllability are considered. By regularisation techniques, we are able to derive an equivalent optimal control problem for an ordinary differential equation to which well-known model predictive control techniques can be applied. This allows the construction of terminal constraints and costs such that the origin is asymptotically stable w.r.t. the resulting closed-loop system.
On a class of integral systems. - In: Complex analysis and operator theory, ISSN 1661-8262, Bd. 15 (2021), 6, 103, insges. 39 S.
We study spectral problems for two-dimensional integral system with two given non-decreasing functions R, W on an interval [0, b) which is a generalization of the Krein string. Associated to this system are the maximal linear relation Tmax and the minimal linear relation Tmin in the space L2(dW) which are connected by Tmax=T*min. It is shown that the limit point condition at b for this system is equivalent to the strong limit point condition for the linear relation Tmax. In the limit circle case the Evans-Everitt condition is proved to hold on a subspace T*N of Tmax characterized by the Neumann boundary condition at b. The notion of the principal Titchmarsh-Weyl coefficient of this integral system is introduced. Boundary triple for the linear relation Tmax in the limit point case (and for T*N in the limit circle case) is constructed and it is shown that the corresponding Weyl function coincides with the principal Titchmarsh-Weyl coefficient of the integral system. The notion of the dual integral system is introduced by reversing the order of R and W and the formula relating the principal Titchmarsh-Weyl coefficients of the direct and the dual integral systems is proved. For every integral system with the principal Titchmarsh-Weyl coefficients q a canonical system is constructed so that its Titchmarsh-Weyl coefficient Q is the unwrapping transform of q: Q(z)=zq(z2).
Differential-algebraic systems are generically controllable and stabilizable. - In: Mathematics of control, signals, and systems, ISSN 1435-568X, Bd. 33 (2021), 3, S. 359-377
We investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1-61. https://doi.org/10.1007/978-3-642-34928-7_1)), we use tools from algebraic geometry to characterize genericity of controllability and stabilizability in terms of matrix formats.
Funnel control of nonlinear systems. - In: Mathematics of control, signals, and systems, ISSN 1435-568X, Bd. 33 (2021), 1, S. 151-194
Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by r-th-order functional differential equations, encompassing inter alia systems with unknown "control direction" and dead-zone input effects. A control structure is developed which ensures that, for every member of the underlying system class and every admissible reference signal, the tracking error evolves in a prescribed funnel chosen to reflect transient and asymptotic accuracy objectives. Two fundamental properties underpin the system class: bounded-input bounded-output stable internal dynamics, and a high-gain property (an antecedent of which is the concept of sign-definite high-frequency gain in the context of linear systems).
Applications of differential-algebraic equations: examples and benchmarks. - Cham : Springer, 2019. - vii, 320 Seiten. - (Differential-algebraic equations forum) ISBN 3-030-03717-7
General Nonlinear Differential Algebraic Equations and Tracking Problems: A Robotics Example -- DAE Aspects in Vehicle Dynamics and Mobile Robotics -- Open-loop Control of Underactuated Mechanical Systems Using Servo-constraints: Analysis and Some Examples -- Systems of Differential Algebraic Equations in Computational Electromagnetics -- Gas Network Benchmark Models -- Topological Index Analysis Applied to Coupled Flow Networks -- Nonsmooth DAEs with Applications in Modeling Phase Changes -- Continuous, Semi-Discrete, and Fully Discretized Navier-Stokes Equations
Optimal control of differential-algebraic equations from an ordinary differential equation perspective. - In: Optimal control, applications and methods, ISSN 1099-1514, Bd. 40 (2019), 2, S. 351-366
The gap distance to the set of singular matrix pencils. - In: Linear algebra and its applications, Bd. 564 (2019), S. 28-57
Die Baugeschichte eines Rokoko-Stadthauses. - Erfurt : Ulenspiegel, 2018. - 253 Seiten ISBN 978-3-932655-56-2
Model predictive control for linear DAEs without terminal constraints and costs. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 51 (2018), 20, S. 116-121
Model predictive control for linear differential-algebraic equations. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 51 (2018), 20, S. 98-103