Eric Rogers

Iterative learning control using optimal feedback and feedforward actions

An algorithm for iterative learning control is developed on the basis of an optimization principle which has been used previously to derive gradient-type algorithms. The new algorithm has numerous benefits which include realization in terms of Riccati feedback and feedforward components. This realization also has the advantage of implicitly ensuring automatic step size selection and hence guaranteeing convergence without the need for empirical choice of parameters. The algorithm is expressed as a very general norm optimization problem in a Hilbert space setting and hence, in principle, can be used for both continuous and discrete time systems. A basic relationship with almost singular optimal control is outlined. The theoretical results are illustrated by simulation studies which highlight the dependence of the speed of convergence on parameters chosen to represent the norm of the signals appearing in the optimization problem.

Predictive optimal iterative learning control

A new optimization-based iterative learning control algorithm is proposed and its properties derived. An important characteristic of this algorithm is that it uses present and future predicted errors to compute the current control, in a similar manner to model-based predictive control using a receding horizon. In particular, it enables the algorithm designer to achieve good control over convergence rate. The actual implementation has a multimodel structure but uses standard linear quadratic regulator methods for a causal formulation (in the iterative learning sense) of what is originally a non-causal algorithm. The results are illustrated by simulations.

Non-linear iterative learning by an adaptive Lyapunov technique

We consider the iterative learning control problem from an adaptive control viewpoint. It is shown that some standard Lyapunov adaptive designs can be modified in a straightforward manner to give a solution to either the feedback or feedforward ILC problem. Some of the common assumptions of non-linear iterative learning control are relaxed: e.g. we relax the common linear growth asssumption on the non-linearities and handle systems of arbitrary relative degree. It is shown that generally a linear rate of convergence of the MSE can be achieved, and a simple robustness analysis is given. For linear plants we show that a linear rate of MSE convergence can be achieved for non-minimum phase plants.

Analysis of Linear Iterative Learning Control Schemes -A 2D Systems/Repetitive Processes Approach

This paper first develops results on the stability and convergence properties of a general class of iterative learning control schemes using, in the main, theory first developed for the branch of 2D linear systems known as linear repetitive processes. A general learning law that uses information from the current and a finite number of previous trials is considered and the results, in the form of fundamental limitations on the benefits of using this law, are interpreted in terms of basic systems theoretic concepts such as the relative degree and minimum phase characteristics of the example under consideration. Following this, previously reported powerful 2D predictive and adaptive control algorithms are reviewed. Finally, new iterative adaptive learning control laws which solve iterative learning control algorithms under weak assumptions are developed.

Iterative Learning Control in Health Care: Electrical Stimulation and Robotic-Assisted Upper-Limb Stroke Rehabilitation

Annually, 15 million people worldwide suffer a stroke, and 5 million are left permanently disabled. A stroke is usually caused when a blood clot blocks a vessel in the brain and acts like a dam, stopping the blood reaching the regions downstream. Alternatively, it may be caused by a hemorrhage, in which a vessel ruptures and leaks blood into surrounding areas. As a result, some of the connecting nerve cells die, and the person commonly suffers partial paralysis on one side of the body, termed hemiplegia. Cells killed in this way cannot regrow, but the brain has some spare capacity and, hence, new connections can be made. The brain is continually and rapidly changing as new skills are learned, new connections are formed, and redundant ones disappear. A person who relearns skills after a stroke goes through the same process as someone learning to play tennis or a baby learning to walk, requiring sensory feedback during the repeated practice of a task. Unfortunately, the problem is that they can hardly move and, therefore, do not receive feedback on their performance.

LMIs - a fundamental tool in analysis and controller design for discrete linear repetitive processes

Discrete linear repetitive processes are a distinct class of two-dimensional (2-D) linear systems with applications in areas ranging from long-wall coal cutting through to iterative learning control schemes. The feature which makes them distinct from other classes of 2-D linear systems is that information propagation in one of the two distinct directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them. In this paper, an LMI approach is used to produce highly significant new results on the stability analysis of these processes and the design of control schemes for them. These results are, in the main, for processes with singular dynamics and for those with so-called dynamic boundary conditions. Unlike other classes of 2-D linear systems, these feedback control laws have a firm physical basis, and the LMI setting is also shown to provide a (potentially) very powerful setting in which to characterize the robustness properties of these processes.

Feasibility of Iterative Learning Control Mediated by Functional Electrical Stimulation for Reaching After Stroke

Background. An inability to perform tasks involving reaching is a common problem following stroke. Evidence supports the use of robotic therapy and functional electrical stimulation (FES) to reduce upper limb impairments, but current systems may not encourage maximal voluntary contribution from the participant because assistance is not responsive to performance. Objective. This study aimed to investigate whether iterative learning control (ILC) mediated by FES is a feasible intervention in upper limb stroke rehabilitation. Methods. Five hemiparetic participants with reduced upper limb function who were at least 6 months poststroke were recruited from the community. No participants withdrew. Intervention. Participants undertook supported tracking tasks using 27 different trajectories augmented by responsive FES to their triceps brachii muscle, with their hand movement constrained in a 2-dimensional plane by a robot. Eighteen 1-hour treatment sessions were used with 2 participants receiving an additional 7 treatment sessions. Outcome measures. The primary functional outcome measure was the Action Research Arm Test (ARAT). Impairment measures included the upper limb Fugl— Meyer Assessment (FMA), tests of motor control (tracking accuracy), and isometric force. Results. Compliance was excellent and there were no adverse events. Statistically significant improvements were measured (P ≤ .05) in FMA motor score, unassisted tracking for 3 out of 4 trajectories, and in isometric force over 5 out of 6 directions. Changes in ARAT were not statistically significant. Conclusion. This study has demonstrated the feasibility of using ILC mediated by FES for upper limb stroke rehabilitation.

Norm-Optimal Iterative Learning Control Applied to Gantry Robots for Automation Applications

This paper is concerned with the practical implementation of the norm-optimal iterative learning control (NOILC) algorithm. Here, the complexity of this algorithm is first considered with respect to real-time control applications, and a new modified version, fast norm-optimal ILC (F-NOILC), is derived for this application, which potentially allows implementation with a sampling rate three times faster that the original algorithm. A performance index is used to assess the experimental results obtained from applying F-NOILC to an industrial gantry robot system and, in particular, the effects of varying the parameters in the cost function, which is at the heart of the norm-optimal approach

Stability and control of differential linear repetitive processes using an LMI setting

This paper considers differential linear repetitive processes which are a distinct class of two-dimensional continuous-discrete linear systems of both physical and systems theoretic interest. The substantial new results are on the application of linear-matrix-inequality-based tools to stability analysis and controller design for these processes, where the class of control laws used has a well defined physical basis. It is also shown that these tools extend naturally to cases when there is uncertainty in the state-space model of the underlying dynamics.

A Cascade MPC Control Structure for a PMSM With Speed Ripple Minimization

This paper addresses the problem of reducing the impact of periodic disturbances arising from the current sensor offset error on the speed control of a permanent-magnet synchronous motor. The new results are based on a cascade model predictive control scheme with an embedded disturbance model. Supporting experimental results, where the per-unit model is used to improve numerical conditioning, are also given.