Tansel Yucelen

Low-Frequency Learning and Fast Adaptation in Model Reference Adaptive Control

While adaptive control has been used in numerous applications to achieve system performance without excessive reliance on dynamical system models, the necessity of high-gain learning rates to achieve fast adaptation can be a serious limitation of adaptive controllers. This is due to the fact that fast adaptation using high-gain learning rates can cause high-frequency oscillations in the control response resulting in system instability. In this note, we present a new adaptive control architecture for nonlinear uncertain dynamical systems to address the problem of achieving fast adaptation using high-gain learning rates. The proposed framework involves a new and novel controller architecture involving a modification term in the update law. Specifically, this modification term filters out the high-frequency content contained in the update law while preserving asymptotic stability of the system error dynamics. This key feature of our framework allows for robust, fast adaptation in the face of high-gain learning rates. Furthermore, we show that transient and steady-state system performance is guaranteed with the proposed architecture. Two illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.

Derivative-Free Model Reference Adaptive Control

A derivative-free, delayed weight update law is developed for model reference adaptive control of continuous-time uncertain systems, without assuming the existence of constant ideal weights. Using a Lyapunov―Krasovskii functional it is proven that the error dynamics are uniformly ultimately bounded, without the need for modification terms in the adaptive law. Estimates for the ultimate bound and the exponential rate of convergence to the ultimate bound are provided. Also discussed are employing various modification terms for further improving performance and robustness of the adaptively controlled system. Examples illustrate that the proposed derivative-free model reference adaptive control law is advantageous for applications to systems that can undergo a sudden change in dynamics.

A Loop Recovery Method for Adaptive Control

This paper presents a new modification term for use in adaptive control to improve an already existing design. By employing this term in a conventional adaptive law, the loop transfer properties of a reference model associated with a non-adaptive control design can be preserved. Consequently, this term increases the level of confidence of adaptive flight control systems for purposes of increased flight safety. The results are illustrated on an unmanned combat aerial vehicle dynamic model. I. Introduction n this paper we present an improved method of adaptation that enhances robustness of adaptive control systems. The method is arrived at by examining the loop transfer properties of an adaptive system when linearized about a given flight condition. The design approach modifies a conventional adaptive law with the goal of preserving the loop transfer properties of a reference model associated with a non-adaptive control design. The aim is to achieve an adaptive system that preserves the stability margins of a non-adaptive design, while at the same time providing the benefits of adaptation to modeling error. I

Kalman Filter Modification in Adaptive Control

This paper presents a novel Kalman-filter-based approach for approximately enforcing a linear constraint in adaptive control. One application is that this leads to alternative forms for well-known modification terms such as e modification. It is shown that employing this approach does not increase the theoretical guaranteed ultimate bounds for the closed-loop error signals of an existing adaptive design. In addition, it leads to smaller tracking errors without incurring significant oscillations in the system response and without requiring high modification gain. Three novel modifications to classical adaptive laws are illustrated and tested on a model of wing rock dynamics.

Control of multiagent systems under persistent disturbances

This paper focuses on the consensus and formation problems of multiagent systems under unknown, persistent disturbances. Specifically, we propose a method that combines an existing consensus (or formation) algorithm with a new controller. The new controller has an integral action that produces a control input based on an error signal locally projected onto the column space of the graph Laplacian. This action allows agents to achieve a consensus or a predetermined formation objective under constant or time-varying disturbances.

Improving transient performance of adaptive control architectures using frequency-limited system error dynamics

Although adaptive control theory offers mathematical tools to achieve system performance without excessive reliance on dynamical system models, its applications to safety-critical systems can be limited due to poor transient performance and robustness. In this paper, we develop an adaptive control architecture to achieve stabilisation and command following of uncertain dynamical systems with improved transient performance. Our framework consists of a new reference system and an adaptive controller. The proposed reference system captures a desired closed-loop dynamical system behaviour modified by a mismatch term representing the high-frequency content between the uncertain dynamical system and this reference system, i.e., the system error. In particular, this mismatch term allows the frequency content of the system error dynamics to be limited, which is used to drive the adaptive controller. It is shown that this key feature of our framework yields fast adaptation without incurring high-frequency oscillations in the transient performance. We further show the effects of design parameters on the system performance, analyse closeness of the uncertain dynamical system to the unmodified (ideal) reference system, discuss robustness of the proposed approach with respect to time-varying uncertainties and disturbances, and make connections to gradient minimisation and classical control theory. A numerical example is provided to demonstrate the efficacy of the proposed architecture.

Adaptive Loop Transfer Recovery

DAPTIVE control is an attractive approach in nonlinear systems theory due to its ability to cope with system uncertainties and failures. Adaptive controllers can be classified as either indirect or direct. This paper focuses on improving the robustness of a direct adaptive control design. The method is arrived at by examining the loop transfer properties of an adaptive system when linearized about an equilibrium condition. The design approach modifiesanadaptivelawwiththegoalofpreservingthelooptransfer propertiesofareferencemodelassociatedwithanonadaptivecontrol design. The aim is to achieve an adaptive system that preserves the stability margins of a nonadaptive design, while at the same time providing the benefits of adaptation to modeling error. Many modification terms are reported in the literature [1–11]. Included among these, � modification [1] adds a pure damping term to the adaptive law, whereas e modification [2] adds a variable damping term that depends on the error signal. These terms are introduced to ensure that the adapted weights remain bounded. Backgroundlearning[3–5]usescurrentandpastdataconcurrentlyin the adaptation process. It allows the adaptation law to continually train in the background based on past data, while still being responsivetodynamicchangesbasedonthecurrentdata.Inthisway, background learning incorporates long-term learning. Q modification [6–8] is similar in spirit to background learning in its intent to improve adaptation performance by using a moving window of the integrated system uncertainty. There is an optimal control theory based modification term that improves adaptation in the presence of large adaptive gain [9]. More recently, a Kalman filter modification approach[10]hasbeenintroducedasamodificationterminadaptive control.Kalman filtermodificationleadstoalternativeformsforwell

Consensus protocols for networked multi-agent systems with a uniformly continuous quasi-resetting architecture

The consensus problem appears frequently in coordination of multiagent systems in science and engineering, and involves the agreement of networked agents upon certain quantities of interest. In this paper, we focus on a new consensus protocol for networked multiagent systems using a resetting control architecture. Specifically, the control protocol consists of a delayed feedback, quasi-resetting control law such that controller resettings occur when the relative state measurements between an agent and its neighboring agents are zero. In contrast to standard impulsive resetting controllers, the proposed resetting is uniformly continuous, and hence, our approach does not require any well-posedness assumptions imposed by impulsive resetting controllers. In addition, using a Lyapunov-Krasovskii functional, it is shown that the multiagent system reaches asymptotic state equipartitioning, where the system steady-state is uniformly distributed over the system initial conditions. Finally, we develop L∞ transient performance guarantees while accounting for system overshoot and excessive control effort.

Decentralized Consensus Control of a Rigid-Body Spacecraft Formation with Communication Delay

The decentralized consensus control of a formation of rigid-body spacecraft is studied in the framework of geometric mechanics while accounting for a constant communication time delay between spacecraft. The relative position and attitude (relative pose) are represented on the Lie group SE(3) and the communication topology is modeled as a digraph. The consensus problem is converted into a local stabilization problem of the error dynamics associated with the Lie algebra se(3) in the form of linear time-invariant delay differential equations with a single discrete delay in the case of a circular orbit, whereas it is in the form of linear time-periodic delay differential equations in the case of an elliptic orbit, in which the stability may be assessed using infinite-dimensional Floquet theory. The proposed technique is applied to the consensus control of four spacecraft in the vicinity of a Molniya orbit.

Control of multivehicle systems in the presence of uncertain dynamics

In this paper, we present a cooperative control architecture for high-order multivehicle systems having non-identical nonlinear uncertain dynamics. The proposed methodology consists of a local cooperative controller and a vehicle-level controller for each vehicle. The former controller receives the relative output measurements of the neighbouring vehicles in order to solve a containment problem formulated on a leader–follower framework. Specifically, the leaders generate trajectories in which the vehicles (followers) converge to the convex hull formed by those of the leaders. For a special case with one leader, this controller synchronises the output of the vehicles with the output of the leader. The latter controller receives the internal-state measurements for suppressing the nonlinear uncertain dynamics of the vehicle by using a decentralised adaptive control approach. The interaction topology between vehicles is described by undirected graphs and extensions to directed graphs are further discussed. The stability and convergence properties of the proposed cooperative control architecture are analysed by using the results from linear algebra and the Lyapunov theory. Several numerical examples are provided to demonstrate the efficacy of the proposed cooperative control architecture.