Benjamin C. Gruenwald

On transient performance improvement of adaptive control architectures

While adaptive control theory has been used in numerous applications to achieve given system stabilisation or command following criteria without excessive reliance on mathematical models, the ability to obtain a predictable transient performance is still an important problem – especially for applications to safety-critical systems and when there is no a-priori knowledge on upper bounds of existing system uncertainties. To address this problem, we present a new approach to improve the transient performance of adaptive control architectures. In particular, our approach is predicated on a novel controller architecture, which involves added terms in the update law entitled artificial basis functions. These terms are constructed through a gradient optimisation procedure to minimise the system error between an uncertain dynamical system and a given reference model during the learning phase of an adaptive controller. We provide a detailed stability analysis of the proposed approach, discuss the practical aspects of its implementation, and illustrate its efficacy on a numerical example.

A set-theoretic model reference adaptive control architecture for disturbance rejection and uncertainty suppression with strict performance guarantees

ABSTRACT Research in adaptive control algorithms for safety-critical applications is primarily motivated by the fact that these algorithms have the capability to suppress the effects of adverse conditions resulting from exogenous disturbances, imperfect dynamical system modelling, degraded modes of operation, and changes in system dynamics. Although government and industry agree on the potential of these algorithms in providing safety and reducing vehicle development costs, a major issue is the inability to achieve a-priori, user-defined performance guarantees with adaptive control algorithms. In this paper, a new model reference adaptive control architecture for uncertain dynamical systems is presented to address disturbance rejection and uncertainty suppression. The proposed framework is predicated on a set-theoretic adaptive controller construction using generalised restricted potential functions.The key feature of this framework allows the system error bound between the state of an uncertain dynamical system and the state of a reference model, which captures a desired closed-loop system performance, to be less than a-priori, user-defined worst-case performance bound, and hence, it has the capability to enforce strict performance guarantees. Examples are provided to demonstrate the efficacy of the proposed set-theoretic model reference adaptive control architecture.

Computing actuator bandwidth limits for model reference adaptive control

ABSTRACT Although model reference adaptive control theory has been used in numerous applications to achieve system performance without excessive reliance on dynamical system models, the presence of actuator dynamics can seriously limit the stability and the achievable performance of adaptive controllers. In this paper, a linear matrix inequalities-based hedging approach is developed and evaluated for model reference adaptive control of uncertain dynamical systems in the presence of actuator dynamics. The hedging method modifies the ideal reference model dynamics in order to allow correct adaptation that is not affected by the presence of actuator dynamics. Specifically, we first generalise the hedging approach to cover a variety of cases in which actuator output and the control effectiveness matrix of the uncertain dynamical system are known and unknown. We then show the stability of the closed-loop dynamical system using Lyapunov-based stability analysis tools and propose a linear matrix inequality-based framework for the computation of the minimum allowable actuator bandwidth limits such that the closed-loop dynamical system remains stable. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.

An LMI-Based Hedging Approach to Model Reference Adaptive Control With Actuator Dynamics

Although model reference adaptive control has been used in numerous applications to achieve system performance without excessive reliance on dynamical system models, the presence of actuator dynamics can seriously limit the stability and the achievable performance of adaptive controllers. In this paper, an linear matrix inequalities-based hedging approach is developed and evaluated for model reference adaptive control of uncertain dynamical systems in the presence of actuator dynamics. The hedging method modifies the ideal reference model dynamics in order to allow correct adaptation that does not get affected due to the presence of actuator dynamics. Specifically, we first generalize the hedging approach to cover cases in which actuator output and is known and unknown. We next show the stability of the closed-loop dynamical system using tools from Lyapunov stability and linear matrix inequalities. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed linear matrix-inequalities-based hedging approach to model reference adaptive control.Copyright

A Direct Uncertainty Minimization Framework in Model Reference Adaptive Control

This paper considers stabilization and command following of uncertain dynamical systems and presents a new adaptive control approach with improved system performance. The proposed framework consists of a novel architecture involving modification terms in the adaptive controller and the update law. Specifically, these terms are activated when the system error between an uncertain dynamical system and a given reference model, which captures a desired closed-loop dynamical system behavior, is nonzero and vanishes as the system reaches its steady-state. This key feature of our framework allows to suppress the effect of system uncertainty on the transient system response through a gradient minimization procedure, and hence, leads to improved system performance. We further show that by automatically adjusting the design parameter of the added terms in response to system variations, we can enforce system error to approximately stay in a priori given, userdefined error performance bounds. Several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.

Guaranteed Model Reference Adaptive Control Performance in the Presence of Actuator Failures

For achieving strict closed-loop system performance guarantees in the presence of exogenous disturbances and system uncertainties, a new model reference adaptive control framework was recently proposed. Specifically, this framework was predicated on a settheoretic adaptive controller construction using generalized restricted potential functions, where its key feature was to keep the distance between the trajectories of an uncertain dynamical system and a given reference model to be less than a-priori, user-defined worstcase closed-loop system performance bound. The contribution of this paper is to generalize this framework to address disturbance rejection and system uncertainty suppression in the presence of actuator failures. A system-theoretical analysis is provided to show the strict closed-loop system performance guarantees of the proposed architecture to effectively handle actuator failures and its efficacy is demonstrated in an illustrative numerical example.

A decentralized adaptive control architecture for large-scale active-passive modular systems

Decentralized control of large-scale active-passive modular systems is considered. These systems consist of physically interconnected and generally heterogeneous modules, where local control signals can be only applied to a subset of these modules (i.e., active modules) and the rest are not subject to any control signals (i.e., passive modules). Using a set-theoretic adaptive control approach predicated on restricted potential functions, we design decentralized command following control architectures for each active module such that they can effectively perform their tasks with strict performance guarantees in the presence of unknown physical interconnections between modules and module-level system uncertainties. The efficacy of the proposed framework is demonstrated in an illustrative numerical example.

On model reference adaptive control for uncertain dynamical systems with unmodeled dynamics

On model reference adaptive control for uncertain dynamical systems, it is well know that there exists a fundamental stability limit, where the closed-loop dynamical system subject to this class of control laws remains stable either if there does not exist significant unmodeled dynamics or the effect of system uncertainties is negligible. Specifically, this implies that model reference adaptive controllers cannot tolerate large system uncertainties even when unmodeled dynamics satisfy a set of conditions. Motivated from this standpoint, this paper proposes a model reference adaptive control approach to relax this fundamental stability limit, where an adaptive control signal is augmented with an adaptive robustifying term. The key feature of our framework allows the closed-loop dynamical system to remain stable in the presence of large system uncertainties when the unmodeled dynamics satisfy a set of conditions. An illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.

Application of a Novel Scalability Notion in Adaptive Control to Various Adaptive Control Frameworks

In adaptive control theory it is a well-known phenomena that nonidentical command profiles entail nonidentical closed-loop responses of these adaptive systems. While adaptive controllers provide a viable methodology to control uncertain dynamical systems, this lack of predictability is a significant disadvantage, in particular in terms of certification of such control methods. Consequently, achieving predictable closed-loop responses of adaptively-controlled systems is of grand practical interest. For this purpose, we recently introduced a method to scale the learning rates of the adaptive weight update laws in order to achieve predictable closed-loop performances for nonidentical, but scalable command profiles. This paper applies the proposed methodology to a model of the longitudinal motion of a Boeing 747 aircraft and simulations for diverse adaptive control schemes illustrate the efficiacy of the proposed scalability notion, which may be a further step towards validation and verification of these adaptive control frameworks.

Adaptive control for a class of uncertain nonlinear dynamical systems in the presence of high-order actuator dynamics

Adaptive control is a powerful design methodology to achieve closed-loop system stability in the face of uncertainties resulting from modeling inaccuracies, degraded modes of operation, and changes in system dynamics. Yet, it is well known that the presence of actuator dynamics can seriously limit closed-loop system stability of any adaptive control framework. To address the problem of adaptive control design in the presence of actuator dynamics, we recently introduced a linear matrix inequalities-based adaptive control framework. The key feature of this approach is to reveal the fundamental stability interplay between the parameters of a given actuator dynamics model and the allowable uncertainties in the feedback loop. The contribution of this paper is to generalize our recent work for a class of uncertain nonlinear dynamical systems. Specifically, for a given high-order, linear time-invariant actuator dynamics model, we utilize tools and methods from Lyapunov stability and linear matrix inequalities for the computation of closed-loop system stability limits of adaptive control laws. An illustrative numerical example is also provided to demonstrate the efficacy and the practicality of the proposed design architecture.