Stabilization of Continuous-Time Adaptive Control Systems with Possible Input Saturation through a Controllable Modified Estimation Model

This paper presents an indirect adaptive control scheme for linear continuous-time systems. The estimated plant model is controllable and then the adaptive scheme is free from singularities. Such singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That property is achieved by ensuring that the absolute value of its determinant does not lie below a positive threshold. An alternative modification scheme based on the achievement of a modified diagonally dominant Sylvester matrix of the parameter estimates is also proposed. This diagonal dominance is achieved through estimates modification as a way to guarantee the controllability of the modified estimated model when a controllability measure of the estimation model without modification fails. In both schemes, the use of a hysteresis switching function for the modification of the estimates is not required to ensure the controllability of the modified estimated model. Both schemes ensure that chattering due to switches associated with the modification is not present. The results are extended to the first-order case when the input is subject to saturation being modeled as a sigmoid function. In this case, a hysteresis-type switching law is used to implement the estimates modification

Robust controllers design for unknown error and exosystem: a hybid optimization and output regulation approach

This thesis addresses the problem of robustness in control in two main topics: linear output regulation when no knowledge is assumed of the modes of the exosystem, and hybrid gradient-free optimization. A framework is presented for the solution of the first problem, in which asymptotic regulation is achieved in case of a persistence of excitation condition. The stability properties of the closed-loop system are proved under a small-gain argument with no minimum phase assumption. The second part of the thesis addresses, and proposes, a solution to the gradientfree optimization problem, solved by a discrete-time direct search algorithm. The algorithm is shown to convergence to the set of minima of a particular class of non convex functions. It is, then, applied considering it coupled with a continuous-time dynamical system. A hybrid controller is developed in order to guarantee convergence to the set of minima and stability of the interconnection of the two systems. Almost global asymptotic is proven for the proposed hybrid controller. Shown to not be robust to any bounded measurement noise, a robust solution is also proposed. The aim of this thesis is to lay the ground for a solution of the output regulation problem in case the error is unknown, but a proxy optimization function is available. A controller embedding the characteristics of the two proposed approaches, as a main solution to the aforementioned problem, will be the focus of future studies

Adaptive control of time-invariant systems with discrete delays subject to multiestimation

This paper deals with a robustly stable adaptive pole-placement-based controller for time-delay linear systems with unknown point delays within known intervals of sufficiently small lengths under unmodeled dynamics and bounded disturbances. A multiestimation scheme is used to improve the identification error and then to deal with possible errors between the true basic delays compared to that used in the regressor of the adaptive scheme. Each estimation scheme possess a relative dead zone for each estimation scheme which freezes the adaptation for small sizes of the adaptation error compared with the estimated size of the contribution of the uncertainties to the filtered output. All the estimation schemes run in parallel but only that, which is currently in operation, parameterizes the adaptive controller to generate the plant input at each time. A supervisory scheme chooses in real time the appropriate estimator subject to a minimum residence time which is the tool to ensure closed-loop stability under switching between the estimators in the estimation scheme. The dead zone adaptation mechanism prevents the closed-loop system against potential instability caused by uncertainties

Robust Adaptive Stabilization of Linear Time-Invariant Dynamic Systems by Using Fractional-Order Holds and Multirate Sampling Controls

This paper presents a strategy for designing a robust discrete-time adaptive controller for stabilizing linear time-invariant (LTI) continuous-time dynamic systems. Such systems may be unstable and noninversely stable in the worst case. A reduced-order model is considered to design the adaptive controller. The control design is based on the discretization of the system with the use of a multirate sampling device with fast-sampled control signal. A suitable on-line adaptation of the multirate gains guarantees the stability of the inverse of the discretized estimated model, which is used to parameterize the adaptive controller. A dead zone is included in the parameters estimation algorithm for robustness purposes under the presence of unmodeled dynamics in the controlled dynamic system. The adaptive controller guarantees the boundedness of the system measured signal for all time. Some examples illustrate the efficacy of this control strategy

Evolving Ensemble Fuzzy Classifier

The concept of ensemble learning offers a promising avenue in learning from data streams under complex environments because it addresses the bias and variance dilemma better than its single model counterpart and features a reconfigurable structure, which is well suited to the given context. While various extensions of ensemble learning for mining non-stationary data streams can be found in the literature, most of them are crafted under a static base classifier and revisits preceding samples in the sliding window for a retraining step. This feature causes computationally prohibitive complexity and is not flexible enough to cope with rapidly changing environments. Their complexities are often demanding because it involves a large collection of offline classifiers due to the absence of structural complexities reduction mechanisms and lack of an online feature selection mechanism. A novel evolving ensemble classifier, namely Parsimonious Ensemble pENsemble, is proposed in this paper. pENsemble differs from existing architectures in the fact that it is built upon an evolving classifier from data streams, termed Parsimonious Classifier pClass. pENsemble is equipped by an ensemble pruning mechanism, which estimates a localized generalization error of a base classifier. A dynamic online feature selection scenario is integrated into the pENsemble. This method allows for dynamic selection and deselection of input features on the fly. pENsemble adopts a dynamic ensemble structure to output a final classification decision where it features a novel drift detection scenario to grow the ensemble structure. The efficacy of the pENsemble has been numerically demonstrated through rigorous numerical studies with dynamic and evolving data streams where it delivers the most encouraging performance in attaining a tradeoff between accuracy and complexity.Comment: this paper has been published by IEEE Transactions on Fuzzy System

Synchronous response modelling and control of an annular momentum control device

Research on the synchronous response modelling and control of an advanced Annular Momentun Control Device (AMCD) used to control the attitude of a spacecraft is described. For the flexible rotor AMCD, two sources of synchronous vibrations were identified. One source, which corresponds to the mass unbalance problem of rigid rotors suspended in conventional bearings, is caused by measurement errors of the rotor center of mass position. The other sources of synchronous vibrations is misalignment between the hub and flywheel masses of the AMCD. Four different control algorithms were examined. These were lead-lag compensators that mimic conventional bearing dynamics, tracking notch filters used in the feedback loop, tracking differential-notch filters, and model-based compensators. The tracking differential-notch filters were shown to have a number of advantages over more conventional approaches for both rigid-body rotor applications and flexible rotor applications such as the AMCD. Hardware implementation schemes for the tracking differential-notch filter were investigated. A simple design was developed that can be implemented with analog multipliers and low bandwidth, digital hardware

ROBUST STABILITY AND PERFORMANCE VIA FIXED-ORDER DYNAMIC COMPENSATION

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57855/1/RobustStabilitySicon1989.pd