Adaptive control for time-varying systems: congelation and interconnection

This thesis investigates the adaptive control problem for systems with time-varying parameters. Two concepts are developed and exploited throughout the thesis: the congelation of variables, and the active nodes. The thesis first revisits the classical adaptive schemes and explains the challenges brought by the presence of time-varying parameters. Then, the concept of congelation of variables is introduced and its use in combinations with passivity-based, immersion-and-invariant, and identification-based adaptive schemes are discussed. As the congelation of variables method introduces additional interconnection in the closed-loop system, a framework for small-gain-like control synthesis for interconnected systems is needed.\vspace{2ex} To this end, the thesis proceeds by introducing the notion of active nodes. This is instrumental to show that as long as a class of node systems that possess adjustable damping parameters, that is the active nodes, satisfy certain graph-theoretic conditions, the desired small-gain-like property for the overall system can be enforced via tuning these adjustable parameters. Such conditions for interconnected systems with quadratic, nonlinear, and linearly parametrized supply rates, respectively, are elaborated from the analysis and control synthesis perspectives. The placement and the computation/adaptation of the damping parameters are also discussed. Following the introduction of these two fundamental tools, the thesis proceeds by discussing state-feedback designs for a class of lower-triangular nonlinear systems. The backstepping technique and the congelation of variables method are combined for passivity-based, immersion-and-invariance, and identification-based schemes. The notion of active nodes is exploited to yield simple and systematic proofs. Based on the results established for lower-triangular systems, the thesis continues to investigate output-feedback adaptive control problems. An immersion-and-invariance scheme for single-input single-output linear systems and a passivity-based scheme for nonlinear systems in observer form are proposed. The proof and interpretation of these results are also based on the notion of active nodes. The simulation results show that the adaptive control schemes proposed in the thesis have superior performance when compared with the classical schemes in the presence of time-varying parameters. Finally, the thesis studies two applications of the theoretical results proposed. The servo control problem for serial elastic actuators, and the disease control problem for interconnected settlements. The discussions show that these problems can be solved efficiently using the framework provided by the thesis.Open Acces

Adaptive observer for state variables of a time-varying nonlinear system with unknown constant parameters and delayed measurements

Unknown constant parameters estimation problem for a nonlinear time-varying system with delayed measurements is considered. The objective of this work is to design an adaptive observer for a nonlinear time-varying system. The observer must provide asymptotic convergence of the unknown constant parameters estimates to their true values. The main idea behind the method is to perform the parametrization of initial dynamical system based on GPEBO (Generalized Parameter Estimation Based Observer) technology and to build a linear regression model. The identification of linear regression model unknown parameters is performed using least square method with forgetting factor. This work develops the previously published approach for the case of nonlinear time-varying systems with delayed measurements. New parameters estimation algorithm can be applied for technical tasks, such as technical condition control and automatic control systems design

System Identification and Control of Cavity Noise Reduction

This dissertation first presents indirect closed-loop system identification through residual whitening, then identifies the cavity noise system and applies controllers to reduce the noise. High speed air flow over the cavity produces a complex oscillatory flow-field and induces pressure oscillations within the cavity. The existence of cavities induces large pressure fluctuations which generate undesirable and loud noise. This may have an adverse effect on the objects, such as reducing the stability and performance of overall system, or damaging the sensitive instruments within the cavity. System identification is the process of building mathematical models of dynamical systems based on the available input and output data from the systems. The indirect system identification by residual whitening is used to improve the accuracy of the identification result, and the optimal properties of the Kalman filter could be enforced for a finite set of data through residual whitening. Linear Quadratic Gaussian (LQG) and deadbeat controllers are applied to obtain the desired system performance. Linear Quadratic Gaussian (LQG) control design is the technique of combining the linear quadratic regulator (LQR) and Kalman tilter together, namely, state feedback (LQR) and state estimation (Kalman filter). Deadbeat control design is to bring the output to zero, and both indirect and direct algorithms are applied. For the indirect method, one needs to calculate the finite difference model coefficient parameters first, then form the control parameters. In the recursive direct algorithms, however, one can compute the control parameters directly. When systems change with time, the system parameters become time-varying. An adaptive predictive control is needed for this situation. Since the system parameters are time-varying, the control parameters need to be updated in order to catch up with the systems\u27 changes. The classical recursive least-squares technique is used for the recursive deadbeat controller, and it could be operated for on-line application

Event sampled optimal adaptive regulation of linear and a class of nonlinear systems

In networked control systems (NCS), wherein a communication network is used to close the feedback loop, the transmission of feedback signals and execution of the controller is currently carried out at periodic sampling instants. Thus, this scheme requires a significant computational power and network bandwidth. In contrast, the event-based aperiodic sampling and control, which is introduced recently, appears to relieve the computational burden and high network resource utilization. Therefore, in this dissertation, a suite of novel event sampled adaptive regulation schemes in both discrete and continuous time domain for uncertain linear and nonlinear systems are designed. Event sampled Q-learning and adaptive/neuro dynamic programming (ADP) schemes without value and policy iterations are utilized for the linear and nonlinear systems, respectively, in both the time domains. Neural networks (NN) are employed as approximators for nonlinear systems and, hence, the universal approximation property of NN in the event-sampled framework is introduced. The tuning of the parameters and the NN weights are carried out in an aperiodic manner at the event sampled instants leading to a further saving in computation when compared to traditional NN based control. The adaptive regulator when applied on a linear NCS with time-varying network delays and packet losses shows a 30% and 56% reduction in computation and network bandwidth usage, respectively. In case of nonlinear NCS with event sampled ADP based regulator, a reduction of 27% and 66% is observed when compared to periodic sampled schemes. The sampling and transmission instants are determined through adaptive event sampling conditions derived using Lyapunov technique by viewing the closed-loop event sampled linear and nonlinear systems as switched and/or impulsive dynamical systems. --Abstract, page iii

An Iterative Learning Control Design Method for Nonlinear Discrete-Time Systems with Unknown Iteration-Varying Parameters and Control Direction

An iterative learning control (ILC) scheme is designed for a class of nonlinear discrete-time dynamical systems with unknown iteration-varying parameters and control direction. The iteration-varying parameters are described by a high-order internal model (HOIM) such that the unknown parameters in the current iteration are a linear combination of the counterparts in the previous certain iterations. Under the framework of ILC, the learning convergence condition is derived through rigorous analysis. It is shown that the adaptive ILC law can achieve perfect tracking of system state in presence of iteration-varying parameters and unknown control direction. The effectiveness of the proposed control scheme is verified by simulations

Synthesis and control of generalised dynamically substructured systems

The experimental technique for testing engineering systems via the method of dynamic substructuring is receiving significant global interest, for example in the fields of large-scale structural, aerospace, and automotive system testing. Dynamically substructured systems (DSSs) enable full-size, critical components of a complete system to be physically tested in real-time, within a laboratory environment, while the remainder of the system is modelled numerically. The intention is that the combined physical-numerical DSS behaves as if it were the complete (or emulated) system.In an ideal mechanical DSS, for example, perfect synchronization of displacements and forces at the interfaces between the numerical and physical components (or substructures) is required. Hence, a key design feature of successful DSS systems is the high fidelity of the control action. Equally, a DSS controller must be able to cope with non-linear, time-varying, and uncertain parameters within the physical substructure dynamics.The main purpose of this paper is to present a generalized DSS framework, together with associated linear and adaptive control strategies, that are specifically tailored to achieve high synchronization performance. The initial studies of this problem, as described in an earlier paper by Stoten and Hyde, are therefore continued by generalizing both the DSS dynamics and the control strategies to include (a) a number of newly defined modes of operation and (b) multivariable dynamics. In addition, comparative implementation and simulation studies are included, based upon the DSS testing of a mechanical system (a planar quasi-motorcycle rig), which was specifically designed to highlight the main features of this research. The comparative studies show that excellent DSS control can be achieved, especially with the addition of an adaptive component to the controller, despite significant changes to the physical substructure dynamics

Adaptive Stochastic Systems: Estimation, Filtering, And Noise Attenuation

This dissertation investigates problems arising in identification and control of stochastic systems. When the parameters determining the underlying systems are unknown and/or time varying, estimation and adaptive filter- ing are invoked to to identify parameters or to track time-varying systems. We begin by considering linear systems whose coefficients evolve as a slowly- varying Markov Chain. We propose three families of constant step-size (or gain size) algorithms for estimating and tracking the coefficient parameter: Least-Mean Squares (LMS), Sign-Regressor (SR), and Sign-Error (SE) algorithms. The analysis is carried out in a multi-scale framework considering the relative size of the gain (rate of adaptation) to the transition rate of the Markovian system parameter. Mean-square error bounds are established, and weak convergence methods are employed to show the convergence of suitably interpolated sequences of estimates to solutions of systems of ordinary and stochastic differential equations with regime switching. Next we consider problems in noise attenuation in systems with unmodeled dynamics and stochastic signal errors. A robust two-phase design procedure is developed which first estimates the signal in a simplified form, and then applies a control to tune out the noise. Worst-case error bounds are derived in terms of the unmodeled dynamics and variances of the disturbance and measurement errors

Projection Operator: A Step Towards Certification of Adaptive Controllers

One of the major barriers to wider use of adaptive controllers in commercial aviation is the lack of appropriate certification procedures. In order to be certified by the Federal Aviation Administration (FAA), an aircraft controller is expected to meet a set of guidelines on functionality and reliability while not negatively impacting other systems or safety of aircraft operations. Due to their inherent time-variant and non-linear behavior, adaptive controllers cannot be certified via the metrics used for linear conventional controllers, such as gain and phase margin. Projection Operator is a robustness augmentation technique that bounds the output of a non-linear adaptive controller while conforming to the Lyapunov stability rules. It can also be used to limit the control authority of the adaptive component so that the said control authority can be arbitrarily close to that of a linear controller. In this paper we will present the results of applying the Projection Operator to a Model-Reference Adaptive Controller (MRAC), varying the amount of control authority, and comparing controller s performance and stability characteristics with those of a linear controller. We will also show how adjusting Projection Operator parameters can make it easier for the controller to satisfy the certification guidelines by enabling a tradeoff between controller s performance and robustness