Abstract
This article revisits the inverted pendulum-in particular, analyses a simplified model of a Segway, with a view to exploring its capabilities in Control Systems Engineering education. The integration between the theoretic and practical side is achieved through simulation, and in particular by using MathWorks software. We also present a structure for the work to be done in the Laboratory class and propose a solution for the problem. © 2018 IEEE.

Abstract
Knowledge of the Kalman filter is very important in machine learning since is the basis for understanding more advanced concepts. Towards this end, control and estimation courses should assure the understanding of the concept and its correct application. A tutorial on the design, implementation and test of the KF to denoise the discharge current of a Li-ion cell is presented in this article. The students are also meant to acquire the discharge data used in the case study - Discharge of a Li-ion cell. The Battery Discharger Board is a low cost device to discharge Li-ion cells with a user programmable current discharge profile. The discharge is controlled and monitored by an external microcontroller connected to a host computer that stores and processes the discharge data. This board has been constructed to help students to gain insight into batteries. The current is measured by ACS712 Hall sensors, which are low cost but also very noisy. To de-noise the current measurements two different KF are used with the current being modelled as the state of a first order integrator. In the first approach, the KF assumes that the system is disturbed by process and measurement noises while in the second it only assumes measurement noise, The operation of the discharge board is illustrated in two experiments: (i) one with a constant discharge current and (ii) the other with a pulsed current. In both experiments, the filters performance was very good. Copyright (c) 2023 The Authors.

Abstract
In this work, the prediction of a time series is formulated as a gaussian process regression, for different levels of noise. The gaussian regressor is translated into lower rank Dynamic Mode Decomposition methods that use kernels (K-DMD) - Kernel regression and Least Squares Support Vector Machines. The presented unified approach delivers an algorithm where the optimisation of the marginal likelihood function can be used to find the parameters of the kernel regression. The viability of the procedure is demonstrated on a chaotic series, with quite good adjustment results being obtained. Copyright (c) 2023 The Authors.

Abstract

Abstract
A kernel regressor to estimate a six-degree-of-fredoom non linear model of an autonomous underwater vehicle is proposed. Although this estimator assumes that the model coefficients are linear combinations of basis functions, it circumvents the problem of specifying the basis functions by using the kernel trick. The Gaussian radial basis function is the chosen kernel, with the Kernel matrix being regularized by its principal components. The variance of the Gaussian radial basis function and the number of principal components are hyper-parameters to be determined by the minimisation of a final prediction error criterion and using the training data. A simulated autonomous underwater vehicle is proposed was used as case study.

Abstract
The successive approximation Linear Parameter Varying systems subspace identification algorithm for discrete-time systems is based on a convergent sequence of linear time invariant deterministic-stochastic state-space approximations. In this chapter, this method is modified to cope with continuous-time LPV state-space models. To do this, the LPV system is discretised, the discrete-time model is identified by the successive approximations algorithm and then converted to a continuous-time model. Since affine dependence is preserved only for fast sampling, a subspace downsampling approach is used to estimate the linear time invariant deterministic-stochastic state-space approximations. A second order simulation example, with complex poles, illustrates the effectiveness of the new algorithm. © 2012 by World Scientific Publishing Co. Pte. Ltd.