Ehsan Arabi

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.

A generalization to set-theoretic model reference adaptive control architecture for enforcing user-defined time-varying performance bounds

It is a challenge to achieve user-defined performance guarantees while utilizing model reference adaptive control laws in the feedback loop. To this end, we recently introduced a set-theoretic model reference adaptive control framework. The key feature of this approach allows the distance between the state of an uncertain dynamical system and the state of a reference model (i.e., the system error) to be less than a user-defined constant performance bound. In this paper, the set-theoretic model reference adaptive control framework is generalized to enforce user-defined time-varying performance bounds on the system error, which gives user the flexibility to control the closed-loop system performance as desired on different time intervals (e.g., transient time interval and steady-state time interval). For this purpose, an architecture is proposed for adaptive command following, where two numerical examples are provided to illustrate the efficacy of the proposed contribution.

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.

Model Reference Neuroadaptive Control Revisited: How to Keep the System Trajectories on a Given Compact Set

We revisit the design of model reference neuroadaptive control laws. This class of control laws have the capability to approximate any system uncertainty with an unknown structure and parameters on a compact set using neural networks. Yet, a challenge in their design is to keep the controlled system trajectories on this compact set for satisfying the universal function approximation property. Motivated by this challenge, a new model reference neuroadaptive control architecture is proposed to keep the controlled system trajectories within a-priori, user-defined compact set while addressing disturbance rejection and system uncertainty suppression. The presented architecture is illustrated by a numerical example.

Mitigating the effects of sensor uncertainties in networked multiagent systems

Networked multiagent systems consist of interacting agents that locally exchange information, energy, or matter. Since they do not in general have a centralized entity to monitor the activity of each agent, resilient distributed control system design for networked multiagent systems is essential in providing high system performance, reliability, and operation in the presence of system uncertainties. An important class of such system uncertainties that can significantly deteriorate the achievable closed-loop system performance is sensor uncertainties, which can arise due to low sensor quality, sensor failure, sensor bias, or detrimental environmental conditions. This paper presents a novel distributed adaptive control architecture for networked multiagent systems to mitigate the effect of sensor uncertainties. Specifically, we consider agents having high-order, linear dynamics with agent interactions corrupted by unknown exogenous disturbances. We show that the proposed adaptive control architecture guarantees asymptotic stability of the closed-loop dynamical system when the exogenous disturbances are time-invariant and uniform ultimate boundedness when the exogenous disturbances are time-varying. A numerical example is provided to illustrate the efficacy of the proposed distributed adaptive control architecture.

Set-theoretic model reference adaptive control with time-varying performance bounds

ABSTRACT One of the fundamental problems in model reference adaptive control design is the ability of the controlled system to achieve not only stability but also a user-defined performance in the presence of exogenous disturbances and system uncertainties. To this end, we recently proposed a set-theoretic model reference adaptive control framework, which guarantees the norm of the system error to be less than a user-defined constant performance bound. The contribution of this paper is to generalise the set-theoretic model reference adaptive control framework for enforcing user-defined time-varying performance bounds on the system error, which gives the control designer a flexibility to control the closed-loop system performance as desired on different time intervals (e.g. transient time interval and steady-state time interval). Two adaptive command following control architectures are proposed and their stability and performance properties are rigorously established using system-theoretic methods.

Mitigating the Effects of Sensor Uncertainties in Networked Multi-Agent Systems

Networked multi-agent systems consist of interacting agents that locally exchange information, energy, or matter. Since these systems do not in general have a centralized architecture to monitor the activity of each agent, resilient distributed control system design for networked multi-agent systems is essential in providing high system performance, reliability, and operation in the presence of system uncertainties. An important class of such system uncertainties that can significantly deteriorate the achievable closed-loop system performance is sensor uncertainties, which can arise due to low sensor quality, sensor failure, sensor bias, or detrimental environmental conditions. This paper presents a novel distributed adaptive control architecture for networked multi-agent systems with undirected communication graph topologies to mitigate the effect of sensor uncertainties. Specifically, we consider agents having identical high-order, linear dynamics with agent interactions corrupted by unknown exogenous disturbances. We show that the proposed adaptive control architecture guarantees asymptotic stability of the closed-loop dynamical system when the exogenous disturbances are time-invariant and uniform ultimate boundedness when the exogenous disturbances are time-varying. Two numerical examples are provided to illustrate the efficacy of the proposed distributed adaptive control architecture. [DOI: 10.1115/1.4035092]

Decentralised adaptive architectures for control of large-scale active–passive modular systems with stability and performance guarantees

ABSTRACT Decentralised control of large-scale active–passive modular systems is considered in this paper. The considered class of large-scale systems consist of physically interconnected and generally heterogeneous modules, where local control signals can only be applied to a subset of these modules (i.e. active modules) and the rest do not admit any control signals (i.e. passive modules). Specifically, based on a set-theoretic model reference adaptive control approach predicated on restricted potential functions, we design and analyse decentralised command following control laws for each active module such that they can effectively perform their tasks in the presence of unknown physical interconnections between modules and module-level system uncertainties. The key feature of our framework allows the system error trajectories of the active modules to be contained within a-priori, user-defined compact sets. Thus, they are guaranteed to achieve strict performance guarantees, where this is of paramount importance for practical applications. In addition to our theoretical findings and research contributions, the efficacy of the proposed decentralised adaptive control architecture is demonstrated in an illustrative numerical example.

Set-Theoretic Model Reference Adaptive Control of a Generic Transport Model

This paper illustrates an application of a recently developed set-theoretic model reference adaptive control architecture on a generic transport model developed by NASA. The settheoretic model reference adaptive control allows the system error bound between the state of an uncertain dynamical system and the state of a given reference model to be less than a-priori, user-defined worst-case performance bound. Thus, it has the capability to enforce strict performance guarantees to the adaptively controlled uncertain dynamical systems. Specifically, after designing set-theoretic adaptive controllers for both longitudinal and lateral-directional dynamics here, the efficacy of this architecture is illustrated on the NASA generic transport model.