Sufficient stability bounds for slowly varying direct-form recursive linear filters and their applications in adaptive IIR filters

Journal ArticleAbstract-This correspondence derives a sufficient time-varying bound on the maximum variation of the coefficients of an exponentially stable time-varying direct-form homogeneous linear recursive filter. The stability bound is less conservative than all previously derived bounds for time-varying IIR systems. The bound is then applied to control the step size of output-error adaptive IIR filters to achieve bounded-input bounded-output (BIBO) stability of the adaptive filter. Experimental results that demonstrate the good stability characteristics of the resulting algorithms are included. This correspondence also contains comparisons with other competing output-error adaptive IIR filters. The results indicate that the stabilized method possesses better convergence behavior than other competing techniques

Passification-based adaptive control: Uncertain input and output delays

For a class of uncertain systems we analyze passification-based adaptive controller in the presence of small, unavoidable input and output time-varying delays as may be present in controller implementation. We derive upper bounds for time delays such that in some domain of initial conditions the states of the closed-loop system tend to zero, whereas an adaptive controller gain tends to a constant value. The results are semi-global, that is the domain of initial conditions is bounded but can be made arbitrary large by tuning an appropriate controller parameter. For the first time, we apply an adaptive controller to linear uncertain networked control systems, where sensors, controllers, and actuators exchange their information through communication networks. The efficiency of the results is demonstrated by the example of adaptive network-based control of an aircraft

Applications of statistics in the spectral analysis of time-varying systems

Recent advances in the theory of evolutionary spectral analysis of time-varying systems has led to a resurgence in the popularity of frequency domain analysis techniques. Policies for adaptive control of time-varying systems based on state-space and Liaponov techniques require an accurate measurement of the system phase variables. Under inherently noisy conditions, access to the complete system state is seldom possible, and frequency domain analysis requirinq only input/output measurements has an obvious appeal. The sampling properties of short-term spectral estimates are of central importance both in system tracking and in choosing suitable control policies. Goodman (1957) developed some of the sampling properties associated with spectral estimates of complex bivariate Gaussian processes. Akaike (1962-66) extended Goodman's results to multi input/output linear systems with 'Gaussian input forcing functions. Both these authors considered the case where the data sequences were stationary. This thesis reviews and extends the research of these two authors with respect to single input/output linear systems. It is shown that the sampling distributions associated with spectral estimates of stationary open-loop systems are approximately valid for a restricted class of non-stationary systems. Two examples of non-stationary systems are investigated and an adaptive control technique using input compensation in the frequency domain is developed on a hydraulic fatigue loading rig. It is shown that statistical tests developed earlier can successfully identify system variations when estimates are measured in a noisy environment. The sampling distributions associated with spectral estimates of closed-loop systems are developed and the results are applied to the modelling and tracking of the human operator response in a trackinq task situation, for various input signals. With regard to future research, it remains to extend the results for closed-loop systems to the time-varying multi input/output case. In its full complexity this problem remains intractable but by considering uncorrelated Gaussian inputs it reduces to determining the distributions associated with multi-variate complex Gaussian sequences

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

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 Output Feedback Control of Nonlinear Systems

Adaptive output feedback control of classes of nonlinear systems and related problems are investigated. The classes of systems that are studied include Lipschitz nonlinear systems, large-scale interconnected nonlinear systems with quadratically bounded interconnections, nonlinear systems containing product terms of unmeasured states and unknown parameters, and mechanical systems with unknown time-varying parameters and disturbances. Solutions and their bounds of relevant algebraic and differential matrix equations in systems and control theory are also studied. For analysis and synthesis of controllers, methods from Lyapunov theory, Algebraic Riccati Equations (AREs), Linear Matrix Inequalities (LMIs), and local polynomial approximations are extensively used. Findings and Conclusions: A stable output feedback controller can be designed for Lipschitz nonlinear systems if sufficient conditions related to distances to uncontrollability and unobservability of pairs of system matrices are satisfied. Stable linear decentralized output feedback controllers can be designed for large-scale systems if certain sufficient conditions are satisfied; these conditions can be formulated either as existence of positive definite solutions to AREs or as a feasibility problem of an LMI. By casting the dynamics of a nonlinear system, which contains products of unmeasurable states and unknown parameters, into a modified form, a stable adaptive output feedback controller can be constructed using a parameter dependent Lyapunov function; the procedure for casting the system dynamics into a modified form is constructive and is always possible. A stable adaptive controller for mechanical systems with unknown time-varying parameters and disturbances can be designed using local polynomial approximation; the time-varying parameters and disturbances are estimated by a modified least-squares algorithm using a new resetting strategy, which is a consequence of keeping the estimates continuous at the beginning of each time interval of local polynomial approximation. For all the problems that are investigated, simulation and experimental results are given to verify and validate the proposed methods.Department of Biochemistry and Molecular Biolog

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

Passification-based decentralized adaptive synchronization of dynamical networks with time-varying delays

This paper is aimed at application of the passification based adaptive control to decentralized synchronization of dynamical networks. We consider Lurie type systems with hyper-minimum-phase linear parts and two types of nonlinearities: Lipschitz and matched. The network is assumed to have both instant and delayed time-varying interconnections. Agent model may also include delays. Based on the speed-gradient method decentralized adaptive controllers are derived, i.e. each controller measures only the output of the node it controls. Synchronization conditions for disturbance free networks and ultimate boundedness conditions for networks with disturbances are formulated. The proofs are based on Passification lemma in combination with Lyapunov–Krasovskii functionals technique. Numerical examples for the networks of 4 and 100 interconnected Chua systems are presented to demonstrate the efficiency of the proposed approach