Experimentally validated continuous-time repetitive control of non-minimum phase plants with a prescribed degree of stability

This paper considers the application of continuous-time repetitive control to non-minimum phase plants in a continuous-time model predictive control setting. In particular, it is shown how some critical performance problems associated with repetitive control of such plants can be avoided by use of predictive control with a prescribed degree of stability. The results developed are first illustrated by simulation studies and then through experimental tests on a non-minimum phase electro-mechanical system

Constrained optimal control theory for differential linear repetitive processes

Differential repetitive processes are a distinct class of continuous-discrete two-dimensional linear systems of both systems theoretic and applications interest. These processes complete a series of sweeps termed passes through a set of dynamics defined over a finite duration known as the pass length, and once the end is reached the process is reset to its starting position before the next pass begins. Moreover the output or pass profile produced on each pass explicitly contributes to the dynamics of the next one. Applications areas include iterative learning control and iterative solution algorithms, for classes of dynamic nonlinear optimal control problems based on the maximum principle, and the modeling of numerous industrial processes such as metal rolling, long-wall cutting, etc. In this paper we develop substantial new results on optimal control of these processes in the presence of constraints where the cost function and constraints are motivated by practical application of iterative learning control to robotic manipulators and other electromechanical systems. The analysis is based on generalizing the well-known maximum and $\epsilon$-maximum principles to the

Robust L2–L∞ control of uncertain differential linear repetitive processes

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdFor two-dimensional (2-D) systems, information propagates in two independent directions. 2-D systems are known to have both system-theoretical and applications interest, and the so-called linear repetitive processes (LRPs) are a distinct class of 2-D discrete linear systems. This paper is concerned with the problem of L2–L∞ (energy to peak) control for uncertain differential LRPs, where the parameter uncertainties are assumed to be norm-bounded. For an unstable LRP, our attention is focused on the design of an L2–L∞ static state feedback controller and an L2–L∞ dynamic output feedback controller, both of which guarantee the corresponding closed-loop LRPs to be stable along the pass and have a prescribed L2–L∞ performance. Sufficient conditions for the existence of such L2–L∞ controllers are proposed in terms of linear matrix inequalities (LMIs). The desired L2–L∞ dynamic output feedback controller can be found by solving a convex optimization problem. A numerical example is provided to demonstrate the effectiveness of the proposed controller design procedures.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

Fuzzy PD-Type Iterative Learning Control of a Single Pneumatic Muscle Actuator

Pneumatic muscles actuator (PMA) is widely used in the field of rehabilitation robot for its good flexibility, light weight and high power/mass ratio as compared to traditional actuator. In this paper, a fuzzy logic-based PD-type iterative learning controller (ILC) is proposed to control the PMA to track a predefined trajectory more precisely during repetitive movements. In order to optimize the parameters of the learning law, fuzzy logic control is introduced into ILC to achieve smaller errors and faster convergence. A simulation experiment was first conducted by taking the PMA model fitted by support vector machine (SVM) as controlled target, which showed that the proposed method achieved a better tracking performance than traditional PD-type ILC. A satisfactory control effect was also obtained when fuzzy PD-type ILC was applied to actual PMA control experiment. Result showed that it takes 25 iterations for the maximum error of trajectory converges to a minimum of about 0.2

Development of new learning control approaches

Ph.DDOCTOR OF PHILOSOPH

Unconstrained receding-horizon control of nonlinear systems

It is well known that unconstrained infinite-horizon optimal control may be used to construct a stabilizing controller for a nonlinear system. We show that similar stabilization results may be achieved using unconstrained finite horizon optimal control. The key idea is to approximate the tail of the infinite horizon cost-to-go using, as terminal cost, an appropriate control Lyapunov function. Roughly speaking, the terminal control Lyapunov function (CLF) should provide an (incremental) upper bound on the cost. In this fashion, important stability characteristics may be retained without the use of terminal constraints such as those employed by a number of other researchers. The absence of constraints allows a significant speedup in computation. Furthermore, it is shown that in order to guarantee stability, it suffices to satisfy an improvement property, thereby relaxing the requirement that truly optimal trajectories be found. We provide a complete analysis of the stability and region of attraction/operation properties of receding horizon control strategies that utilize finite horizon approximations in the proposed class. It is shown that the guaranteed region of operation contains that of the CLF controller and may be made as large as desired by increasing the optimization horizon (restricted, of course, to the infinite horizon domain). Moreover, it is easily seen that both CLF and infinite-horizon optimal control approaches are limiting cases of our receding horizon strategy. The key results are illustrated using a familiar example, the inverted pendulum, where significant improvements in guaranteed region of operation and cost are noted

Controlled switching in Kalman filtering and iterative learning controls

“Switching is not an uncommon phenomenon in practical systems and processes, for examples, power switches opening and closing, transmissions lifting from low gear to high gear, and air planes crossing different layers in air. Switching can be a disaster to a system since frequent switching between two asymptotically stable subsystems may result in unstable dynamics. On the contrary, switching can be a benefit to a system since controlled switching is sometimes imposed by the designers to achieve desired performance. This encourages the study of system dynamics and performance when undesired switching occurs or controlled switching is imposed. In this research, the controlled switching is applied to an estimation process and a multivariable Iterative Learning Control (ILC) system, and system stability as well as system performance under switching are investigated. The first article develops a controlled switching strategy for the estimation of a temporal shift in a Laser Tracker (LT). For some reason, the shift cannot be measured at all time. Therefore, a model-based predictor is adopted for estimation when the measurement is not available, and a Kalman Filter (KF) is used to update the estimate when the measurement is available. With the proposed method, the estimation uncertainty is always bounded within two predefined boundaries. The second article develops a controlled switching method for multivariable ILC systems where only partial outputs are measured at a time. Zero tracking error cannot be achieved for such systems using standard ILC due to incomplete knowledge of the outputs. With the developed controlled switching, all the outputs are measured in a sequential order, and, with each currently-measured output, the standard ILC is executed. Conditions under which zero convergent tracking error is accomplished with the proposed method are investigated. The proposed method is finally applied to solving a multi-agent coordination problem”--Abstract, page iv

Real-Time Progressive Learning: Mutually Reinforcing Learning and Control with Neural-Network-Based Selective Memory

Memory, as the basis of learning, determines the storage, update and forgetting of the knowledge and further determines the efficiency of learning. Featured with a mechanism of memory, a radial basis function neural network (RBFNN) based learning control scheme named real-time progressive learning (RTPL) is proposed to learn the unknown dynamics of the system with guaranteed stability and closed-loop performance. Instead of the stochastic gradient descent (SGD) update law in adaptive neural control (ANC), RTPL adopts the selective memory recursive least squares (SMRLS) algorithm to update the weights of the RBFNN. Through SMRLS, the approximation capabilities of the RBFNN are uniformly distributed over the feature space and thus the passive knowledge forgetting phenomenon of SGD method is suppressed. Subsequently, RTPL achieves the following merits over the classical ANC: 1) guaranteed learning capability under low-level persistent excitation (PE), 2) improved learning performance (learning speed, accuracy and generalization capability), and 3) low gain requirement ensuring robustness of RTPL in practical applications. Moreover, the RTPL based learning and control will gradually reinforce each other during the task execution, making it appropriate for long-term learning control tasks. As an example, RTPL is used to address the tracking control problem of a class of nonlinear systems with RBFNN being an adaptive feedforward controller. Corresponding theoretical analysis and simulation studies demonstrate the effectiveness of RTPL.Comment: 16 pages, 15 figure

Contributions to distributed MPC: coalitional and learning approaches

A growing number of works and applications are consolidating the research area of distributed control with partial and varying communication topologies. In this context, many of the works included in this thesis focus on the so-called coalitional MPC. This approach is characterized by the dynamic formation of groups of cooperative MPC agents (referred to as coalitions) and seeks to provide a performance close to the centralized one with lighter computations and communication demands. The thesis includes a literature review of existing distributed control methods that boost scalability and flexibility by exploiting the degree of interaction between local controllers. Likewise, we present a hierarchical coalitional MPC for traffic freeways and new methods to address the agents' clustering problem, which, given its combinatoria! nature, becomes a key issue for the real-time implementation of this type of controller. Additionally, new theoretical results to provide this clustering strategy with robust and stability guarantees to track changing targets are included. Further works of this thesis focus on the application of learning techniques in distributed and decentralized MPC schemes, thus paving the way for a future extension to the coalitional framework. In this regard, we have focused on the use of neural networks to aid distributed negotiations, and on the development of a multi­ agent learning MPC based on a collaborative data collection