Stabilizability of nonlinear infinite dimensional switched systems by measures of noncompactness in the space

This article studies the problem of stabilizability of nonlinear infinite dimensional switched systems. The switching rule is arbitrary and takes place between a countably infinite number of subsystems, each of which is represented by a differential equation in some Banach space. Using a topological notion of a (locally finite) cover and the Hausdorff measure of noncompactness in the c 0 space, we show how the problem of approximate stabilizability of switched systems can be cast into a sequential framework and dealt with. Examples of application are given

Laplace--Carleson embeddings on model spaces and boundedness of truncated Hankel and Toeplitz operators

A characterisation is given of bounded embeddings from weighted $L^2$ spaces on bounded intervals into $L^2$ spaces on the half-plane, induced by isomorphisms given by the Laplace transform onto weighted Hardy and Bergman spaces (Zen spaces). As an application necessary and sufficient conditions are given for the boundedness of truncated Hankel and Toeplitz integral operators, including the weighted case.Comment: 19 pages. Some minor revision

Admissibility of retarded diagonal systems with one-dimensional input space

We investigate infinite-time admissibility of a control operator $B$ in a Hilbert space state-delayed dynamical system setting of the form $\dot{z}(t)=Az(t)+A_1 z(t-\tau)+Bu(t)$, where $A$ generates a diagonal $C_0$-semigroup, $A_1\in\mathcal{L}(X)$ is also diagonal and $u\in L^2(0,\infty;\mathbb{C})$. Our approach is based on the Laplace embedding between $L^2$ and the Hardy space $H^2(\mathbb{C}_+)$. The results are expressed in terms of the eigenvalues of $A$ and $A_1$ and the sequence representing the control operator.Comment: 25 pages, 2 figure

Admissibility of Diagonal State-Delayed Systems with a One-Dimensional Input Space

In this paper we investigate admissibility of the control operator B in a Hilbert space state-delayed dynamical system setting of the form z˙(t)=Az(t−τ)+Bu(t) , where A generates a diagonal semigroup and u is a scalar input function. Our approach is based on the Laplace embedding between L2 and the Hardy space. The sufficient conditions for infinite-time admissibility are stated in terms of eigenvalues of the generator and in terms of the control operator itself

Exact controllability of non-Lipschitz semilinear systems

We present sufficient conditions for exact controllability of a semilinear infinite-dimensional dynamical system. The system mild solution is formed by a noncompact semigroup and a nonlinear disturbance that does not need to be Lipschitz continuous. Our main result is based on a fixed point-type application of the Schmidt existence theorem and illustrated by a nonlinear transport partial differential equation

Modelling and optimal control system design for quadrotor platform – an extended approach

This article presents the development of a mathematical model of a quadrotor platform and the design of a dedicated control system based on an optimal approach. It describes consecutive steps in development of equations forming the model and including all its physical aspects without commonly used simplifications. Aerodynamic phenomena, such as Vortex Ring State or blade flapping are accounted for during the modelling process. The influence of rotors’ gyroscopic effect is exposed. The structure of a control system is described with an application of the optimal LQ regulator and an intuitive way of creating various flight trajectories. Simulation tests of the control system performance are conducted. Comparisons with models available in the literature are made. Based on above, conclusions are drawn about the level of insight necessary in creation of control-oriented and useable model of a quadrotor platform. New possibilities of designing and verifying models of quadrotor platforms are also discussed

Modelling and optimal control system design for quadrotor platform – an extended approach

This article presents the development of a mathematical model of a quadrotor platform and the design of a dedicated control system based on an optimal approach. It describes consecutive steps in development of equations forming the model and including all its physical aspects without commonly used simplifications. Aerodynamic phenomena, such as Vortex Ring State or blade flapping are accounted for during the modelling process. The influence of rotors’ gyroscopic effect is exposed. The structure of a control system is described with an application of the optimal LQ regulator and an intuitive way of creating various flight trajectories. Simulation tests of the control system performance are conducted. Comparisons with models available in the literature are made. Based on above, conclusions are drawn about the level of insight necessary in creation of control-oriented and useable model of a quadrotor platform. New possibilities of designing and verifying models of quadrotor platforms are also discussed

On controllability of second order dynamical systems – a survey

The paper presents a survey of recent results in the area of controllability of second order dynamical systems. Controllability problem for finite and infinite dimensional, linear, semilinear, deterministic and stochastic dynamical systems (with delays and undelayed) is taken into consideration. Different types of controllability are discussed

Laplace–Carleson Embeddings on Model Spaces and Boundedness of Truncated Hankel and Toeplitz Operators

A characterisation is given of bounded embeddings from weighted L2 spaces on bounded intervals into L2 spaces on the half-plane, induced by isomorphisms given by the Laplace transform onto weighted Hardy and Bergman spaces (Zen spaces). As an application necessary and sufficient conditions are given for the boundedness of truncated Hankel and Toeplitz integral operators, including the weighted case, and on model spaces