Robust nonlinear receding horizon control with constraint tightening: off line approximation and application to networked control system

2007/2008Nonlinear Receding Horizon (RH) control, also known as moving horizon control or nonlinear Model Predictive Control (MPC), refers to a class of algorithms that make explicit use of a nonlinear process model to optimize the plant behavior, by computing a sequence of future ma- nipulated variable adjustments. Usually the optimal control sequence is obtained by minimizing a multi-stage cost functional on the basis of open-loop predictions. The presence of uncertainty in the model used for the optimization raises the question of robustness, i.e., the maintenance of certain properties such as stability and performance in the presence of uncertainty. The need for guaranteeing the closed-loop stability in presence of uncertainties motivates the conception of robust nonlinear MPC, in which the perturbations are explicitly taken in account in the design of the controller. When the nature of the uncertainty is know, and it is assumed to be bounded in some compact set, the robust RH control can be determined, in a natural way, by solving a min–max optimal control problem, that is, the performance objective is optimized for the worst-case scenario. However, the use of min-max techniques is limited by the high computational burden required to solve the optimization problem. In the case of constrained system, a possibility to ensure the robust constraint satisfaction and the closed-loop stability without resorting to min-max optimization consists in imposing restricted (tightened) constraints on the the predicted trajectories during the optimization. In this framework, an MPC scheme with constraint tightening for discrete-time nonlinear systems affected by state-dependent and norm bounded uncertainties is proposed and discussed. A novel method to tighten the constraints relying on the nominal state prediction is described, leading to less conservative set contractions than in the existing approaches. Moreover, by imposing a stabilizing state constraint at the end of the control horizon (in place of the usual terminal one placed at the end of the prediction horizon), less stringent assumptions can be posed on the terminal region, while improving the robust stability properties of the MPC closed-loop system. The robust nonlinear MPC formulation with tightened constraints is then used to design off- line approximate feedback laws able to guarantee the practical stability of the closed-loop system. By using off-line approximations, the computational burden due to the on-line optimization is removed, thus allowing for the application of the MPC to systems with fast dynamics. In this framework, we will also address the problem of approximating possibly discontinuous feedback functions, thus overcoming the limitation of existent approximation scheme which assume the continuity of the RH control law (whereas this condition is not always verified in practice, due to both nonlinearities and constraints). Finally, the problem of stabilizing constrained systems with networked unreliable (and de- layed) feedback and command channels is also considered. In order to satisfy the control ob- jectives for this class of systems, also referenced to as Networked Control Systems (NCS’s), a control scheme based on the combined use of constraint tightening MPC with a delay compen- sation strategy will be proposed and analyzed. The stability properties of all the aforementioned MPC schemes are characterized by using the regional Input-to-State Stability (ISS) tool. The ISS approach allows to analyze the depen- dence of state trajectories of nonlinear systems on the magnitude of inputs, which can represent control variables or disturbances. Typically, in MPC the ISS property is characterized in terms of Lyapunov functions, both for historical and practical reasons, since the optimal finite horizon cost of the optimization problem can be easily used for this task. Note that, in order to study the ISS property of MPC closed-loop systems, global results are in general not useful because, due to the presence of state and input constraints, it is impossible to establish global bounds for the multi-stage cost used as Lyapunov function. On the other hand local results do not allow to analyze the properties of the predictive control law in terms of its region of attraction. There- fore, regional ISS results have to employed for MPC controlled systems. Moreover, in the case of NCS, the resulting control strategy yields to a time-varying closed-loop system, whose stability properties can be analyzed using a novel regional ISS characterization in terms of time-varying Lyapunov functions.XXI Ciclo198

Induction hob and method for operating an induction hob

The invention relates to an induction hob comprising a circuitry (1a) for powering at least one induction coil (6), the circuitry (1a) comprising a power circuit portion (7) with at least one switching element (4, 5) adapted to provide pulsed electric power to said induction coil (6) and an oscillating circuit portion (9), said induction coil (6) being electrically coupled with said power circuit portion (7) and said oscillating circuit (9), wherein said induction hob comprises a control entity (10), said control entity (10) being configured to receive first information correlated with a first voltage provided at said power circuit portion (7) and second information correlated with a second voltage correlated with said oscillating circuit (9), said control entity (10) being further configured to calculate information regarding a peak value and a power factor of the electric current provided through said induction coil (6) based on said received first and second information

Identification of multi-sinusoidal signals with direct frequency estimation: An adaptive observer approach

This paper addresses the problem of estimating the frequencies, amplitudes and phases of the n sinusoidal components of a possibly biased multi-sinusoidal signal. The proposed adaptive observer allows the direct adaptation of the frequency estimates with a relatively low dynamic order 3n+1 (3n for an unbiased signal). The stability analysis proves the global exponential convergence of the estimation error and the robustness to additive norm-bounded measurement perturbations

Machine learning for computationally efficient electrical loads estimation in consumer washing machines

Estimating the wear of the single electrical parts of a home appliance without resorting to a large number of sensors is desirable for ensuring a proper level of maintenance by the manufacturers. Deep learning techniques can be effective tools for such estimation from relatively poor measurements, but their computational demands must be carefully considered, for the actual deployment. In this work, we employ one-dimensional Convolutional Neural Networks and Long Short-Term Memory networks to infer the status of some electrical components of different models of washing machines, from the electrical signals measured at the plug. These tools are trained and tested on a large dataset (502 washing cycles 1000 h) collected from four different washing machines and are carefully designed in order to comply with the memory constraints imposed by available hardware selected for a real implementation. The approach is end-to-end; i.e., it does not require any feature extraction, except the harmonic decomposition of the electrical signals, and thus it can be easily generalized to other appliances