Homogeneous Feedback Control of Nonlinear Systems Based on Control <scp>L</scp>yapunov Functions

In the present work, a novel method is devised for controlling an uncertain wheeled mobile robot (WMR) in a desired path. To achieve this objective, an optimal and robust control system with adaptive gains is combined to benefit from the advantages of both methods. In fact, applying this controller not only controls a nonlinear system robustly against uncertainties and external disturbances, but also optimizes a quadratic cost function. Also, since the upper bound of uncertainty is determined by an adaptive law, it does not need to be adjusted manually. To ensure the designed controller's finite time stability, Lyapunov theory is used. Finally, to illustrate the effectiveness of the proposed control method, a case study involving a WMR is presented. By comparing the results of this approach with those of an adaptive sliding mode control (ASMC), it is shown that the proposed controller uses less control effort, relative to the ASMC controller, to stabilize the uncertain WMR in the presence of external disturbances.

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“…ð Þ that can stabilize the Equation 4. Based on the CLF approach, Sontag proposed the following formula [41,52]:…”

Section: Considering a Radially-unbounded And Positive Definite Candidate Lyapunov Functionmentioning

confidence: 99%

“…In general, its major weakness is that it can only be applied to a specific class of nonlinear systems [40]. Among the existing optimal control approaches, the control Lyapunov function (CLF) has been extensively used in many robotic systems [41]. The CLF, which solves the HJB equation, optimizes certain performance criteria.…”

Section: Introductionmentioning

confidence: 99%

Trajectory tracking control of a wheeled mobile robot in the presence of matched uncertainties via a composite control approach

Shafei

Bahrami

2020

Asian Journal of Control

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“…In contrast to linear systems, the designing of an optimal controller for a nonlinear system is a difficult task and requires the numerical solution of a nonlinear two-point boundary value problem (Faris et al, 2009). From the existing optimal control approaches for nonlinear systems, the control Lyapunov function (CLF) has been extensively used in many robotic systems (Pukdeboon and Kumam, 2015; Zhang et al, 2013). The CLF, which solves the Hamilton–Jacobi–Bellman (HJB) equation, is able to optimize certain performance criteria.…”

Section: Introductionmentioning

confidence: 99%

Design of adaptive optimal robust control for two-flexible-link manipulators in the presence of matched uncertainties

Shafei

Bahrami

Talebi

2020

Journal of Vibration and Control

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This study uses a comprehensive control approach to deal with the trajectory tracking problem of a two-flexible-link manipulator subjected to model uncertainties. Because the control inputs of two-flexible-link manipulators are less than their state variables, the proposed controller should be able to tackle the stated challenge. Practically speaking, there is only a single control signal for each joint, which can be used to suppress link deflections and control joint trajectories. To achieve this objective, a novel optimal robust control scheme, with an updated gain under the adaptive law, has been developed in this work for the first time. In this regard, a nonsingular terminal sliding mode control approach is used as the robust controller and a control Lyapunov function is used as the optimal control law, to benefit from the advantages of both methods. To systematically deal with system uncertainties, an adaptive law is used to update the gain of nonsingular terminal sliding mode control. The advantage of this approach over the existing methods is that it not only can robustly and stably control an uncertain nonlinear system against external disturbances but also can optimally solve a quadratic cost function (e.g. minimization of control effort). The Lyapunov stability theory has been applied to verify the stability of the proposed approach. Moreover, to show the superiority of this method, the computer simulation results of the proposed method have been compared with those of an adaptive sliding mode control scheme. This comparison shows that the presented approach is capable of optimizing the control inputs while achieving the stability of the examined two-flexible-link manipulator in the presence of model uncertainties and external disturbances.

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“…Sontag (1983) introduced the universal formula, which was a milestone in feedback stabilization. Zhang et al (2014) proposed a CLF-based method for the design of stabilizing homogeneous controllers. Formulation of CLF leading to the design of an optimal feedback controller for typical classes of systems have been discussed in literature (Freeman and Kokotovic, 1995; Freeman and Primbs, 1996; Galloway, 2015; Shamma and Cloutier, 2003; Yang and Lee, 2012).…”

Section: Introductionmentioning

confidence: 99%

Inverse optimal control of a class of affine nonlinear systems

Prasanna

Jacob

Nandakumar

2019

Transactions of the Institute of Measurement and Control

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This paper proposes a systematic formulation of inverse optimal control (IOC) law based on a rather straightforward reduction of control Lyapunov function (CLF), applicable to a class of second-order nonlinear systems affine in the input. This method exploits the additional design degrees of freedom resulting from the non-uniqueness of the state dependent coefficient (SDC) formulation, which is widely used in pseudo-linear control techniques. The applicability of the proposed approach necessitates an apparently effortless SDC formulation satisfying an SDC matrix criterion in terms of the structure and characteristics of the state matrix, [Formula: see text]. Subsequently, a sufficient condition for the global asymptotic stability (g.a.s) of the closed-loop system is established. The SDC formulations conforming to the sufficient condition ensure the existence and determination of a smooth radially unbounded polynomial CLF of the form [Formula: see text], while offering a benevolent choice for the gain matrix [Formula: see text], in the CLF. The direct relationship between the gain matrix [Formula: see text] and state weighing matrix [Formula: see text] ensures optimization of an equivalent [Formula: see text]. This feature enables one to rightfully choose the gain matrix [Formula: see text] as per the performance requisites of the system. Finally, the application of the proposed methodology for the speed control of a permanent magnet synchronous motor validates the efficacy and design flexibility of the methodology.

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Homogeneous Feedback Control of Nonlinear Systems Based on Control Lyapunov Functions

Cited by 4 publications

References 27 publications

Trajectory tracking control of a wheeled mobile robot in the presence of matched uncertainties via a composite control approach

Trajectory tracking control of a wheeled mobile robot in the presence of matched uncertainties via a composite control approach

Design of adaptive optimal robust control for two-flexible-link manipulators in the presence of matched uncertainties

Inverse optimal control of a class of affine nonlinear systems

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