Blind Identification via Lifting

Blind system identification is known to be an ill-posed problem and without further assumptions, no unique solution is at hand. In this contribution, we are concerned with the task of identifying an ARX model from only output measurements. We phrase this as a constrained rank minimization problem and present a relaxed convex formulation to approximate its solution. To make the problem well posed we assume that the sought input lies in some known linear subspace.Comment: Submitted to the IFAC World Congress 2014. arXiv admin note: text overlap with arXiv:1303.671

Safe Experimentation Dynamics Algorithm for Identification of Cupping Suction Based on the Nonlinear Hammerstein Model

The use of cupping therapy for various health benefits has increased in popularity recently. Potential advantages of cupping therapy include pain reduction, increased circulation, relaxation, and skin health. The increased blood flow makes it easier to supply nutrients and oxygen to the tissues, promoting healing. Nevertheless, the effectiveness of this technique greatly depends on the negative pressure's ability to create the desired suction effect on the skin. This research paper suggests a method to detect the cupping suction model by employing the Hammerstein model and utilizing the Safe Experimentation Dynamics (SED) algorithm. The problem is that the cupping suction system experiences pressure leaks and is difficult to control. Although, stabilizing the suction pressure and developing an effective controller requires an accurate model. The research contribution lies in utilizing the SED algorithm to tune the parameters of the Hammerstein model specifically for the cupping suction system and figure out the real system with a continuous-time transfer function. The experimental data collected for cupping therapy exhibited nonlinearity attributed to the complex dynamics of the system, presenting challenges in developing a Hammerstein model. This work used a nonlinear model to study the cupping suction system. Input and output data were collected from the differential pressure sensor for 20 minutes, sampling every 0.1 seconds. The single-agent method SED has limited exploration capabilities for finding optimum value but excels in exploitation. To address this limitation, incorporating initial values leads to improved performance and a better match with the real experimental observations. Experimentation was conducted to find the best model parameters for the desired suction pressure. The therapy can be administered with greater precision and efficacy by accurately identifying the suction pressure. Overall, this research represents a promising development in cupping therapy. In particular, it has been demonstrated that the proposed nonlinear Hammerstein models improve accuracy by 84.34% through the tuning SED algorithm

Oxygen uptake estimation in humans during exercise using a Hammerstein model

This paper aims to establish a block-structured model to predict oxygen uptake in humans during moderate treadmill exercises. To model the steady state relationship between oxygen uptake (oxygen consumption) and walking speed, six healthy male subjects walked on a motor driven treadmill with constant speed from 2 to 7 km/h. The averaged oxygen uptake at steady state (VO 2) was measured by a mixing chamber based gas analysis and ventilation measurement system (AEI Moxus Metabolic Cart). Based on these reliable date, a nonlinear steady state relationship was successfully established using Support Vector Regression methods. In order to capture the dynamics of oxygen uptake, the treadmill velocity was modulated using a Pseudo Random Binary Signal (PRBS) input. Breath by breath analysis of all subjects was performed. An ARX model was developed to accurately reproduce the measured oxygen uptake dynamics within the aerobic range. Finally, a Hammerstein model was developed, which may be useful for implementing a control system for the regulation of oxygen uptake during treadmill exercises. © 2007 Biomedical Engineering Society

Networked Control System Design and Parameter Estimation

Networked control systems (NCSs) are a kind of distributed control systems in which the data between control components are exchanged via communication networks. Because of the attractive advantages of NCSs such as reduced system wiring, low weight, and ease of system diagnosis and maintenance, the research on NCSs has received much attention in recent years. The first part (Chapter 2 - Chapter 4) of the thesis is devoted to designing new controllers for NCSs by incorporating the network-induced delays. The thesis also conducts research on filtering of multirate systems and identification of Hammerstein systems in the second part (Chapter 5 - Chapter 6). Network-induced delays exist in both sensor-to-controller (S-C) and controller-to-actuator (C-A) links. A novel two-mode-dependent control scheme is proposed, in which the to-be-designed controller depends on both S-C and C-A delays. The resulting closed-loop system is a special jump linear system. Then, the conditions for stochastic stability are obtained in terms of a set of linear matrix inequalities (LMIs) with nonconvex constraints, which can be efficiently solved by a sequential LMI optimization algorithm. Further, the control synthesis problem for the NCSs is considered. The definitions of H₂ and H∞ norms for the special system are first proposed. Also, the plant uncertainties are considered in the design. Finally, the robust mixed H₂/H∞ control problem is solved under the framework of LMIs. To compensate for both S-C and C-A delays modeled by Markov chains, the generalized predictive control method is modified to choose certain predicted future control signal as the current control effort on the actuator node, whenever the control signal is delayed. Further, stability criteria in terms of LMIs are provided to check the system stability. The proposed method is also tested on an experimental hydraulic position control system. Multirate systems exist in many practical applications where different sampling rates co-exist in the same system. The l₂-l∞ filtering problem for multirate systems is considered in the thesis. By using the lifting technique, the system is first transformed to a linear time-invariant one, and then the filter design is formulated as an optimization problem which can be solved by using LMI techniques. Hammerstein model consists of a static nonlinear block followed in series by a linear dynamic system, which can find many applications in different areas. New switching sequences to handle the two-segment nonlinearities are proposed in this thesis. This leads to less parameters to be estimated and thus reduces the computational cost. Further, a stochastic gradient algorithm based on the idea of replacing the unmeasurable terms with their estimates is developed to identify the Hammerstein model with two-segment nonlinearities. Finally, several open problems are listed as the future research directions

Model-predictive control for non-domestic buildings: a critical review and prospects

Model-predictive control (MPC) has recently excited a great deal of interest as a new control paradigm for non-domestic buildings. Since it is based on the notion of optimisation, MPC is, in principle, well-placed to deliver significant energy savings and reduction in carbon emissions compared to existing rule-based control systems. In this paper, we critically review the prospects for buildings MPC and, in particular, the central role of the predictive mathematical model that lies at its heart; our clear emphasis is on practical implementation rather than control-theoretic aspects, and covers the role of occupants as well as the form of the predictive model. The most appropriate structure for such a model is still an open question, which we discuss alongside the development of the initial model, and the process of updating the model during the building’s operational life. The importance of sensor placement is highlighted alongside the possibility of updating the model with occupants’ comfort perception. We conclude that there is an urgent need for research on the automated creation and updating of predictive models if MPC is to become an economically-viable control methodology for non-domestic buildings. Finally, more evidence through operating full scale buildings with MPC is required to demonstrate the viability of this method

An empirical Bayes approach to identification of modules in dynamic networks

We present a new method of identifying a specific module in a dynamic network, possibly with feedback loops. Assuming known topology, we express the dynamics by an acyclic network composed of two blocks where the first block accounts for the relation between the known reference signals and the input to the target module, while the second block contains the target module. Using an empirical Bayes approach, we model the first block as a Gaussian vector with covariance matrix (kernel) given by the recently introduced stable spline kernel. The parameters of the target module are estimated by solving a marginal likelihood problem with a novel iterative scheme based on the Expectation-Maximization algorithm. Additionally, we extend the method to include additional measurements downstream of the target module. Using Markov Chain Monte Carlo techniques, it is shown that the same iterative scheme can solve also this formulation. Numerical experiments illustrate the effectiveness of the proposed methods