Direct adaptive control in a state-space setting

For single-input single-output linear time-invariant discrete-time systems, a simple procedure is given for directly determining the controller parameters in adaptive pole placement. The given system is not required to be minimum phase. The only assumption on the system model is that the minimal order of the system is known a priori. The controller parameters are estimated using a standard recursive least squares algorithm. If an expanded regression vector is sufficiently exciting (as opposed to persistently exciting), the closed-loop system is exponentially stable with the closed-loop poles located close to the desired poles in the limit.

This paper analyzes a direct adaptive pole placement control for linear stable minimum-phase systems with input magnitude and rate constraints. The key feature is the derivation of a governing equation relating the prediction error to the "input discrepancy" between the adaptive control and corresponding non-adaptive one, independent of how parameter estimates were obtained. With the governing equation, one is able to establish the input matching property of the adaptive constrained control, i.e., asymptotic convergence to zero of the "input discrepancy".

SummaryAt the present time, there is a great deal of interest in the adaptive control of systems with rapidly varying parameters. Such problems arise in different forms and in many disciplines including finance, sociology, biology, and engineering. In general, these problems are intractable mathematically and the time variations have to be classified in some form to obtain rigorous results. In this paper, we consider the adaptive identification and control of linear systems with periodically varying parameters (referred to as linear time‐varying periodic (LTP) systems). The class of systems with known periodic parameters has been investigated widely since the pioneering work of Floquet and lends itself to rigorous mathematical analysis. However, very little was known until the early years of the last decade concerning the adaptive control of such systems. The problem was introduced by Xu and explored in detail by Narendra and Zhiling in 2006 and 2009, respectively. In 2012, a new method was introduced in adaptive control by Han and Narendra and is referred to as second‐level adaptation. In this paper, the adaptive identification and control of LTP systems using second‐level adaptation is discussed.

Estimation and Direct Adaptive Control of Delay-Differential Systems

Estimation and direct adaptive control of delay-differential systems

Many traditional fault tolerant flight control systems augment a baseline controller with an algorithm to detect and then isolate faults. Often, this entails estimating a new system dynamics model and automatic synthesis of new controller parameters. An alternate approach to fault tolerant control can be utilized if the basel ine controller is a direct adaptive control system. For failure modes that do not require control reconfiguration, this baseline adaptive controller demonstrates fault tolerance. This paper details the general formulation of a direct adaptive controller based on dynamic inversion with neural network adaptation. The implementation of this controller on several vehicles is also presented. In order to show the broad applicability of this approach, these vehicles are chosen from a wide range of categories, namely a tailless fighter, a reusable launch vehicle technology demonstrator, a helicopter, a ducted fan, and an acrobatic airplane. Results for nominal and fault cases for these vehicles are provided. Through this summary of fault tolerance results for each vehicle, direct adaptive control is shown to be well -suited to providing both nominal and fault tolerant control for vehicles from a wide range of categories.

This paper shows that stable direct adaptive control of an LTI plant is possible using knowledge of only the plant order. The approach is based on periodic control, which relocates system zeros. No prior knowledge of the plant high-frequency gain or relative degree is used, and persistent excitation is not required. More importantly, no assumption or knowledge is required as to whether the plant is minimum or nonminimum phase. >

Globally stable direct adaptive backstepping NN control for uncertain nonlinear strict-feedback systems

Robust Adaptive Control

A parameterization for a linear system is presented to design a direct model reference adaptive pole placement controller. This parameterized model is one of the structured nonminimal models. The exponentially weighted least-squares algorithm is employed to estimate the control parameters. The direct adaptive controller has the exponential weighting properties by the proposed method of selecting the characteristic polynomials of the sensitivity function filters in connection with the reference model.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An adaptive integral plus states neural control of aerobic continuous stirred tank reactor

The force tracking error is dependent on both the position tracking error and the estimated parameter error so that, in constrained adaptive robot control, the convergence of the estimated parameter error becomes more important than in unconstrained adaptive robot control. However, in the direct adaptive controller, the parameter adaptation is driven only by the tracking error in the joint motion, while in the indirect adaptive controller, the parameter estimation is driven only by the prediction error in the joint torque. Based on this observation a new combined direct and indirect adaptive controller driven by both the tracking error and the prediction error is developed for constrained robots with inertia parameter uncertainty. Stability of the combined adaptive controllers is established in the Lyapunov sense. The combined control improves both position and force tracking performance compared with direct adaptive control. The computer simulations are presented to demonstrate the proposed schemes.

Optimal performance of discrete-time control systems based on network-induced delay

In this paper, we develop a Direct Model Reference Adaptive Tracking Controller for linear systems with unknown delays, sometimes known as retarded equations. This controller can also reject bounded disturbances of known wave form but unknown amplitude, e.g. steps or sinusoids. We prove that the controller produces global asymptotic tracking with bounded controller gains when the delay-free open-loop plant is almost strictly positive real (equivalently, is minimum phase and has CB positive definite) and the internal delay terms satisfy a linear matrix inequality. The adaptive controller has no knowledge of the delay. An illustrative example is provided.

This paper is focused on adaptively controlling a linear infinite-dimensional system to track a finite-dimensional reference model. Given a linear continuous-time infinite-dimensional plant on a Hilbert space with disturbances of known waveform but unknown amplitude and phase, we show that there exists a stabilizing direct model reference adaptive control law with the properties of certain disturbance rejection and robustness. The plant is described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states. The central result will show that all errors will converge to a prescribed neighborhood of zero in an infinite-dimensional Hilbert space. The result will not require the use of the standard Barbalat's lemma which requires certain signals to be uniformly continuous. This result is used to determine conditions under which a linear infinite-dimensional system can be directly adaptively controlled to follow a reference model. In particular, we examine conditions for a set of ideal trajectories to exist for the tracking problem. Our results are applied to adaptive control of general linear diffusion systems described by self-adjoint operators with compact resolvent.