Liapunov redesign of model reference adaptive control systems

Parks, P. C.

doi:10.1109/tac.1966.1098361

Cited by 433 publications

(108 citation statements)

References 5 publications

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“…It is therefore necessary to consider the problem of adaptation in the context of optimal control, although adaptation is a difficult topic of research [2], [6], [26], [35], [48], [97]- [100].. The adaptation included in this paper is a gradient method with a modification to Lyapunov theory similar to that reported in [78,20,51,52]. The gradient method (40) is also similar to earlier attempts to describe neural learning mechanisms, cf.…”

Section: Discussionmentioning

confidence: 99%

Optimal coordination and control of posture and movements

Johansson

Fransson

Magnusson

2009

Journal of Physiology-Paris

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This paper presents a theoretical model of stability and coordination of posture and locomotion, together with algorithms for continuous-time quadratic optimization of motion control. Explicit solutions to the Hamilton-Jacobi equation for optimal control of rigid-body motion are obtained by solving an algebraic matrix equation. The stability is investigated with Lyapunov function theory and it is shown that global asymptotic stability holds. It is also shown how optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters. The solution describes motion strategies of minimum effort and variance. The proposed optimal control is formulated to be suitable as a posture and movement model for experimental validation and verification. The combination of adaptive and optimal control makes this algorithm a candidate for coordination and control of functional neuromuscular stimulation as well as of prostheses. Validation examples with experimental data are provided.

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Section: Discussionmentioning

confidence: 99%

Optimal coordination and control of posture and movements

Johansson

Fransson

Magnusson

2009

Journal of Physiology-Paris

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“…By defining the minimum approximation error (13) the error equation (10) can be written as follows: (14) In this paper, we use FLSs of the form (3) for approximation. They are linear in their parameters and we have (15) where and are the parameter vectors of the FLSs and , respectively, and is the vector of fuzzy basis functions (4). The parameter vectors and consist of the centers (the center of a fuzzy set is the point at which the membership function achieves its maximum value) of fuzzy sets in the consequent part of fuzzy If-Then rules that construct the FLSs and , respectively.…”

Section: A Self-tuning Fuzzy Controllermentioning

confidence: 99%

“…The goal of parameter adjustment is to make and , and consequently, make a good estimate of , and . We use the Lyapunov redesign approach [15], [17] in which the adaptive law is chosen such that to make a Lyapunov function decrease along the trajectories of the adaptive system.…”

Section: B Adaptive Lawmentioning

confidence: 99%

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Hybrid adaptive fuzzy identification and control of nonlinear systems

Hojati

Gazor

2002

IEEE Trans. Fuzzy Syst.

203

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Abstract-In this paper, we present a combined direct and indirect adaptive control scheme for adjusting an adaptive fuzzy controller, and an adaptive fuzzy identification model parameters. First, using adaptive fuzzy building blocks, with a common set of parameters, we design and study an adaptive controller and an adaptive identification model that have been proposed for a general class of the uncertain structure nonlinear dynamic systems. We then propose a hybrid adaptive (HA) law for adjusting the parameters. The HA law utilizes two types of errors in the adaptive system, the tracking error and the modeling error. Performance analysis using a Lyapunov synthesis approach proves the superiority of the HA law over the direct adaptive (DA) method in terms of faster and improved tracking and parameter convergence. Furthermore, this is achieved at a negligible increasing in the implementation cost and the computational complexity. We prove a theorem that shows the properties of this hybrid adaptive fuzzy control system, i.e., bounds for the integral of the squared errors, and the conditions under which these errors converge asymptotically to zero are obtained. Finally, we apply the hybrid adaptive fuzzy controller to control a chaotic system, and the inverted pendulum system. The simulation results demonstrate and confirm the theoretical results.

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“…In [2], the linear quadratic regulator method has been considered. In addition [2], pseudo inverse method [3], feedback linearization [4] , the Lyapunov method [5], sliding mode control [6] are all considered, in [10] a reconfigurable controller design via output feedback in the case of post order fault is represented. [11] considers a modified approach that guarantees the stability of the closed-loop system by using an appropriate Lyapunov equation -all examples of approaches for designing reconfigurable control.…”

Section: Introductionmentioning

confidence: 99%

Reconfigurable Controller Design in Descriptor Systems Obtained from Second Order Dynamic Systems via State Feedback Eigenstructure Assignment

Valadbeygi

Pourgharibshahi

2012

International Journal of Advanced Robotic Systems

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this paper proposes a new method for designing a reconfigurable controller for descriptor systems which is obtained from the second order dynamics of a robot control situation. Using mathematical tools the equations of robot control situation have been translated to descriptor systems, thus, after this change the controller has been designed for control performances. The proposed reconfigurable controller can recover the nominal closed-loop performances after fault occurrence in the system. The dynamics of descriptor systems contain infinite and finite elements, so a complete response of descriptor systems can be represented by an eigenstructure which involves finite and infinite elements. In this paper eigenstructure assignment is used to design a reconfigurable controller in general such that the reconfigured system can recover the complete response of a nominal system as much as possible. Finally, an example represents the effectiveness of the new method.

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Liapunov redesign of model reference adaptive control systems

Cited by 433 publications

References 5 publications

Optimal coordination and control of posture and movements

Optimal coordination and control of posture and movements

Hybrid adaptive fuzzy identification and control of nonlinear systems

Reconfigurable Controller Design in Descriptor Systems Obtained from Second Order Dynamic Systems via State Feedback Eigenstructure Assignment

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