We consider the iterative learning control problem from an adaptive control viewpoint. It is shown that many standard adaptive designs can be modified in a straightforward manner to give a solution to either the feedback or feedforward ILC problem. In particular we show that many of the common assumptions of nonlinear iterative learning control can be relaxed: eg. we relax the common linear growth asssumption on the nonlinearities and handle systems of arbitrary relative degree. Furthermore it is shown that these new ILC designs have the power to solve a new ILC problem: the learning of unseen trajectories (generalisation) . It is shown that generally a linear rate of convergence of the MSE can be achieved, and some simple robustness analyses are given. For linear plants we show that a linear rate of MSE convergence can be achieved for non-minimum phase plants. 1 Introduction The purpose of this paper is to consider the Iterative Learning Control (ILC) problem from an adaptive control...

Abstract — In our recent work, an adaptive composite control technique was suggested for nonlinear adaptive control with statistical learning methods. While this original work was restricted to a simple class of nonlinear SISO systems that were linear in the inputs, in this paper we present a more general treatment of learning a composite controller for the class of nonlinear systems characterized by the form ˙x = f(x)+g(x)u. We will first examine such systems in the first order SISO framework, and present a stability proof including a parameter projection method that is needed to avoid potential singularities during adaptation. Second, we generalize our adaptive controller to higher order SISO systems, and discuss the application to MIMO problems. We evaluate our theoretical control framework in numerical simulations to illustrate the effectiveness of the proposed learning adaptive controller for rapid convergence and high accuracy of control. I.

This paper presents the design of an optimal neurocontroller that replaces the conventional automatic voltage regulator (AVR) and the turbine governor for a turbogenerator connected to the power grid. The neurocontroller design uses a novel technique based on the adaptive critic designs (ACDs), specifically on heuristic dynamic programming (HDP) and dual heuristic programming (DHP). Results show that both neurocontrollers are robust, but that DHP outperforms HDP or conventional controllers, especially when the system conditions and configuration change. This paper also shows how to design optimal neurocontrollers for nonlinear systems, such as turbogenerators, without having to do continually online training of the neural networks, thus avoiding risks of instability.

OF DISSERTATION A SYNTHESIS OF REINFORCEMENT LEARNING AND ROBUST CONTROL THEORY The pursuit of control algorithms with improved performance drives the entire control research community as well as large parts of the mathematics, engineering, and artificial intelligence research communities. A fundamental limitation on achieving control performance is the conflicting requirement of maintaining system stability. In general, the more aggressive is the controller, the better the control performance but also the closer to system instability.

Abstract—This paper surveys how some “intelligence ” can be incorporated in sliding-mode controllers (SMCs) by the use of computational intelligence methodologies in order to alleviate the wellknown problems met in practical implementations of SMCs. The use of variable-structure system theory in design and stability analysis of fuzzy controllers is also discussed by drawing parallels between fuzzy control and SMCs. An overview of the research and applications reported in the literature in this respect is presented. Index Terms—Computational intelligence, sliding-mode control, soft computing.

In this paper, the recently proposed neural network adaptive robust control (NNARC) design are general-ized to synthesize performance oriented control laws for a class of nonlinear systems transformable to the semi-strict feedback forms through the incorporation of backstepping design techniques. All unknown but re-peatable nonlinearities in system are approximated by outputs of multi-layer neural networks to achieve a bet-ter model compensation and an improved performance. Through the use of discontinuous projections with fic-titious bounds, a controlled on-line training of all NN weights is achieved. Robust control terms can then be constructed to attenuate various model uncertainties ef-fectively for a guaranteed output tracking transient per-formance and a guaranteed final tracking accuracy. 1

We consider the adaptive tracking problem for a chain of integrators, where the uncertainty is static and functional. The uncertainty is specified by L or weighted L norm bounds. We analyse a standard Lyapunov based adaptive design which utilizes a function approximator to induce a parametric uncertainty, on which the adaptive design is completed. Performance is measured by a modified LQ cost functional, penalising both the tracking error transient and the control effort. With such a cost functional, it is shown that a standard control design has divergent performance when the resolution of a `mono-resolution' approximator is increased. The class of `mono-resolution' approximators includes models popular in applications. A general construction of a class of approximators and their associated controllers which have a uniformly bounded performance independent of the resolution of the approximator is given.

We consider systems satisfying a matching condition which are functionally known up to weighted L 2 and L 1 measures of uncertainty. A modified LQ measure of control and state transient performance is given, and the performance of a class of approximate model based adaptive controllers is studied. An upper performance bound is derived in terms of the uncertainty models (stability and the state transient bounds require only the L 2 uncertainty model; control effort bounds require both L 2 and L 1 uncertainty models), and various structural properties of the model basis. Sufficient conditions are given to ensure that the performance is bounded independent of the model basis size. M.French@ecs.soton.ac.uk, Department of Electronics and Computer Science, University of Southampton, UK. y szepes@sol.cc.u-szeged.hu, Research Group on Artificial Intelligence, Hungarian Academy of Sciences -- JATE, Szeged, Hungary z E.Rogers@ecs.soton.ac.uk, Department of Electronics and Compute...

In this paper we derive a condition for robust local stability of multilayer recurrent neural networks with two hidden layers. The stability condition follows from linking theory about linearization, robustness analysis of linear systems under nonlinear perturbation and matrix inequalities. A characterization of the basin of attraction of the origin is given in terms of the level set of a quadratic Lyapunov function. In a similar way like for NL q theory, local stability is imposed around the origin and the apparent basin of attraction is made large by applying the criterion, while the proven basin of attraction is relatively small due to conservatism of the criterion. Modifying dynamic backpropagation by the new stability condition is discussed and illustrated by simulation examples.

This paper presents a new method to estimate the region of stability of an asymptotically stable equilibrium point of an autonomous nonlinear system using a neural network. In contrast to model-based analytical methods, this approach uses empirical data from the system to train the neural network. The neural network results are compared with estimates obtained by previously proposed methods for some sample two dimensional problems and for an inverted pendulum. 1. Introduction The problem of estimating the region of stability for the stable equilibrium of autonomous nonlinear systems is fundamental in the theory of dynamic systems, and has been studied for many years [15] [5]. In applications, knowledge of regions of stability is essential for the safe operation of many complex dynamic systems, such as power systems and nuclear reactors [14]. Despite many years of theoretical attention to this problem, and its clear practical importance, the existing methods for estimating stability r...