This paper presents the numerical discretization methods of the continuous-time linear-quadratic optimal control problems (LQ-OCPs) with time delays. We describe the weight matrices of the LQ-OCPs as differential equations systems, allowing us to derive the discrete equivalent of the continuous-time LQ-OCPs. Three numerical methods are introduced for solving proposed differential equations systems: 1) the ordinary differential equation (ODE) method, 2) the matrix exponential method, and 3) the step-doubling method. We implement a continuous-time model predictive control (CT-MPC) on a simulated cement mill system, and the objective function of the CT-MPC is discretized using the proposed LQ discretization scheme. The closed-loop results indicate that the CT-MPC successfully stabilizes and controls the simulated cement mill system, ensuring the viability and effectiveness of LQ discretization.

In this paper, we extend a classical approach to linear quadratic (LQ) optimal control via Popov operators to abstract linear differential-algebraic equations (ADAEs) in Hilbert spaces. To ensure existence of solutions, we assume that the underlying differential-algebraic equation has index one in the pseudo-resolvent sense. This leads to the existence of a degenerate semigroup that can be used to define a Popov operator for our system. It is shown that under a suitable coercivity assumption for the Popov operator the optimal costs can be described by a bounded Riccati operator and that the optimal control input is of feedback form. Furthermore, we characterize exponential stability of ADAEs which is required to solve the infinite horizon LQ problem.

Perfect adaptation is a ubiquitous phenomenon in biology, characterized by the ability of living cells to maintain chemical levels despite disturbances. This adaptation is said to be robust when it holds even after parameter variations. This property of the system is called Robust Perfect Adaptation (RPA). When certain variables lose this property or undesired chemical species acquire RPA property, it results in disease conditions. Metabolic adaptation in extreme tumor microenvironment is a hallmark of cancer cells and allows them to evade death and develop drug resistance. Hence, it is important to investigate the robustness properties of cancer metabolism using a system-theoretical approach. In this work, we topologically investigate the robust perfect adaptation property of large-scale metabolic reaction networks of three types of cancers using the theory proposed by Hirono, Gupta, and Khammash, 2023 (https://arxiv.org/abs/2307.07444). We enumerate the RPA properties of all biologically relevant reactions in large-scale metabolic models of cancer cells, along with the corresponding healthy cells. Finally, perform a comparative analysis to identify drug targets based on the differences in the RPA properties between healthy and cancer cell metabolisms.

A finite-time cascaded control is designed for grid-forming inverters to establish and support the frequency and voltage of an islanded microgrid under uncertainties. Firstly, a fast integral terminal sliding manifold is developed to attain fast tracking convergence, minimize the tracking-error, and improve the integrity of current by mitigating total harmonic distortion. Secondly, an exponential reaching law is added in the control schema to increase the robustness of the system. Lyapunov theory is employed to establish finite-time stability. Finally, simulation results demonstrate that the proposed control exhibits superior tracking accuracy, mitigates the chattering phenomenon, and enhances support for the frequency and voltage of an island microgrid compared to sliding mode control.

Emerging “New Space” paradigms raise challenges in satellite design by appropriate use of miniaturization, Commercial-of-the-Shelf and multi-satellite systems technologies. Related education in space technology has to reflect not only related theoretical background, but should also teach practical problem solution capabilities. Here the CubeSat standard is used to practice system engineering skills at satellite level by a “FlatSat” with subsystem hardware providing access to space simulation environment, measurement and test equipment. In the “Satellite Technology” program at University Würzburg hands-on experiments accompany students in tasks of increasing complexity to apply system engineering and control skills to satellite realization problems.

We consider the growth rate of a switching max-min-plus-scaling (S-MMPS) system in a discrete-event framework. We show that an explicit, time-invariant, monotone, and arbitrarily switching MMPS system has a bounded growth rate. Further, we propose a mixed-integer linear programming problem to calculate the estimates of the smallest upper bound and the largest lower bound of the growth rate of an S-MMPS system.