Keywords: Control and analysis of Nonlinear Systems

Keywords: Control and analysis of Nonlinear Systems

Keywords: Nonlinear Model Predictive Control, Machine Learning, Power and Energy Control
Abstract: Recently, data-enabled predictive control (DeePC) schemes based on Willems' fundamental lemma have attracted considerable attention. At the core are computations using Hankel-like matrices and their connection to the concept of persistency of excitation. We propose an iterative solver for the underlying data-driven optimal control problems resulting from linear discrete-time systems. To this end, we apply factorizations based on the discrete Fourier transform of the Hankel-like matrices, which enable fast and memory-efficient computations. To take advantage of this factorization in an optimal control solver and to reduce the effect of inherent bad conditioning of the Hankel-like matrices, we propose an augmented Lagrangian BFGS-method. We illustrate the performance of our method by means of a numerical study.

Keywords: Modeling and Identification of Nonlinear Systems, Nonlinear Model Predictive Control
Abstract: This article proposes a non-parametric representation for a class of high-order unknown nonlinear systems comprising polynomial functions. A data-driven approach is introduced that uses pure data for future simulation based on any given input set. We also consider a comprehensive class of nonlinear autoregressive exogenous (NARX) models which covers other existing representations as special cases. Then, a non-parametric representation of this class of NARX models are investigated by leveraging the idea of re-expressing the system in the context of a non-minimal state-space reformulation. A data-driven predictive control (DDPC) approach is as a result introduced that uses the fundamental lemma for future prediction during the open-loop optimization. The recursive feasibility analysis and the proof of stability are also given. Finally, the simulation results quantify the effectiveness of the proposed approach in different scenarios.

Keywords: Control with Limited Information, Stability and Complex Dynamics
Abstract: We consider the problem of designing feedback controllers, using measured data, such that the eigenvalues of the closed-loop system lie in a predefined stability region D of the complex plane. We consider a general convex region D defined by quadratic matrix inequality (QMI). First, considering the case of noise-free input/state data we provide non-conservative design conditions in terms of data-based linear matrix inequalities. For the case when the input/state data are affected by noise, the data-based design conditions are only sufficient. We further discuss the case of noise-free input/output data. We illustrate our results with a numerical example.

Keywords: Modeling and Identification of Nonlinear Systems
Abstract: This paper presents a modeling methodology to enhance the dynamic performance of the mechanical component of finite-dimensional curling HASEL (Hydraulically Amplified Self-Healing Electrostatic) actuators within the port-Hamiltonian systems framework. The proposed approach entails replacing the sheet dynamics that limit deformation in a low-scale model with those derived from a large-scale discretized beam model. By making a few additional assumptions compared to the original low-scale HASEL model, the resulting interconnected system is established by aligning the states of the mechanical component in the low-scale model with those of the large-scale beam model in a straightforward manner. To validate the effectiveness of the methodology, simulated examples are provided along with a comparison to experimental results.

Keywords: Modeling and Identification of Nonlinear Systems, Control and analysis of Nonlinear Systems
Abstract: We give insight in the structure of port-Hamiltonian systems as control systems in between two closed Hamiltonian systems. Using the language of category theory, we identify systems with their behavioural representation and view a port-control structure with desired structural properties on a given closed system as an extension of this system which itself may be embedded in a ``larger'' closed system. The latter system describes the nature of the ports (e.g. Hamiltonian, metriplectic etc.). This point of view allows us to describe meaningful port-control structures for a large family of systems, which is illustrated with Hamiltonian and metriplectic systems.

Keywords: Control and analysis of Nonlinear Systems, Stability and Complex Dynamics
Abstract: This paper is intended as a preliminary work in which we describe a connection between contractive systems and dissipative Hamiltonian dynamics. In particular, we show that it is always possible to obtain from the Jacobian of the autonomous system, given the contraction metric, the structural matrices of a Hamiltonian dynamics. We show how to obtain in closed-form such matrices for stable linear systems, by exploiting a modification of the Jordan block form. We then conclude the paper by analytically performing the analysis on an example of nonlinear contractive system.

Keywords: Modeling and Identification of Nonlinear Systems, Disturbance Rejection, Adaptive Control and Signal Processing for Nonlinear Systems
Abstract: This paper addresses state estimation for dynamical systems involving localized unknown nonlinearities. Direct application of linear state estimation techniques, e.g., the Kalman filter, would yield erroneous state estimates. Existing approaches in the literature either assume or estimate the nonlinearities. Alternatively, the present paper proposes to reject the unknown nonlinearities as if they were unknown disturbances. By applying an existing disturbance rejection technique, the need to know or to estimate the nonlinearities is avoided. The efficiency of the proposed method is demonstrated through numerical simulations on a nonlinear mechanical system

Keywords: Control and analysis of Nonlinear Systems, Modeling and Identification of Nonlinear Systems, Stability and Complex Dynamics
Abstract: KKL (Kazantzis-Kravaris/Luenberger) observers are based on the idea of immersing a given nonlinear system into a target system that is a linear stable filter of the measured output. In the present paper, we extend this theory by allowing this target system to be a nonlinear contracting filter of the output. We prove, under a differential observability condition, the existence of these new KKL observers. We motivate their introduction by showing numerically the possibility of combining convergence speed and robustness to noise, unlike what is known for linear filtering.

Keywords: Observers Design
Abstract: This paper proposes a new observer design approach for a class of nonlinear systems which are not observable for all inputs. This provides an alternative to the already available solution for such systems based on Kalman with high gain, by relying here on several high gains instead of the standard single one. This can result in less conservative gains on the one hand, and excitation conditions ensuring convergence more easily checked on the other hand. A related convergence analysis is provided, and a simulation example illustrates the approach.

Keywords: Power and Energy Control, Control and analysis of Distributed Systems, Process Control
Abstract: The estimation of the temperature distribution in solar concentration plants is crucial for monitoring and control purposes. These plants cover large surfaces, and therefore, partial shading can occur. Under such conditions, solar irradiance varies according to the location of the collectors. This work addresses the problem of designing an observer to estimate the temperature profile of several parabolic solar concentrators based on multiple measurements. The convergence of the proposed observer is analyzed using Lyapunov theory, and its performance is illustrated through simulations. These results demonstrate that the use of additional measurements improves the observer’s convergence under partial shading. Further work is proposed to address tuning issues and the effects of uncertain irradiance measurements.

Keywords: Nonlinear Model Predictive Control, Modeling and Identification of Nonlinear Systems, Systems Biology
Abstract: Moving-horizon estimation performance depends on the arrival-cost approximation. Different methods exist to approximate the arrival cost with different trade-offs, such as limited performance, complex implementation, or abusive computational cost. In particular, we can distinguish two different methods based on using an external filter or the optimality conditions to calculate the covariance of the estimations. This paper presents a simpler alternative for the arrival-cost approximation based on maximum-likelihood estimation. The performance of this approximation is assessed using a mammalian cell culture case study where biomass and glutamine concentrations are estimated.

Keywords: Control and analysis of Nonlinear Systems, Modeling and Identification of Nonlinear Systems, Observers Design
Abstract: This article delves into the design of a proportional observer scheme for a class of Nonlinear Parameter-Varying (NLPV) systems. The objective is to formulate a less conservative Linear Matrix Inequality (LMI) condition than the existing ones, ensuring the exponential stability of the error dynamics in the proposed observer. Through the incorporation of the reformulated Lipschitz property, Young’s inequalities and a generalized matrix multiplier, two new LMI conditions are established. Due to the judicious use of these mathematical tools, the obtained LMI conditions contain a larger number of decision variables. As a result, these LMIs have enhanced feasibility than the one presented in the literature. The effectiveness of the newly designed LMI-based proportional observer is highlighted through a numerical example.

Keywords: Control and analysis of Distributed Parameter Systems