Extremum Seeking for Stefan PDE with Moving Boundary

This paper presents the design and analysis of the extremum seeking for static maps with input passed through a partial differential equation (PDE) of the diffusion type defined on a time-varying spatial domain whose boundary position is governed by an ordinary differential equation (ODE). This is the first effort to pursue an extension of extremum seeking from the heat PDE to the Stefan PDE. We compensate the average-based actuation dynamics by a controller via backstepping transformation for the moving boundary, which is utilized to transform the original coupled PDE-ODE into a target system whose exponential stability of the average equilibrium of the average system is proved. The discussion for the delay-compensated extremum seeking control of the Stefan problem is also presented and illustrated with numerical simulations.Comment: 10 pages and 10 figure

On the classical and fractional control of a nonlinear inverted cart-pendulum system: a comparative analysis

International audienceFractional-order control is based on the fractional calculus and its use is being explored for many researchers in order to improve the performance of control systems. In this paper, fractional integrators are employed in a state-feedback controller and applied to an inverted cart-pendulum system. Faster transient responses and increased (local) attraction domains are achieved when compared to the integer integrator based implementation of the proposed control law

Extremum Seeking-based Adaptive PID Control applied to Neuromuscular Electrical Stimulation

Abstract A multivariable deterministic extremum seeking (ES) is being evaluated to construct an adaptive Proportional-Integral-Derivative (PID) control law for the functional Neuromuscular Electrical Stimulation (NMES) of stroke patients. The developed scheme is applied to control the position of the patient’s arm so that movements of flexion/extension for its elbow can be produced. The true limitations of a PID controller for these types of applications is that a PID controller is designed for linear systems, but the system which is being controlled is nonlinear. Moreover, it is worth mention that clinicians’ knowledge of control systems is limited. Therefore, their expertise in tuning controllers is limited. Also, in NMES applications each patient is unique and requires a unique set of PID parameters. Since it can be time consuming and difficult to find proper parameters for each patient, a better procedure, or a more intelligent adaptive controller, is needed. The PID parameters are updated by means of ES in order to minimize a cost function which brings the desired performance attributes. Experiments are performed with healthy volunteers and stroke patients, including significant advances based on real data and validation. Quantitative results show a reduction of 64:1% in terms of RMSE (Root-Mean-Square Error) – from 8:94º to 3:21º – when comparing the tracking curves of the last cycle to the first cycle in the experiments with all stroke patients