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Proceedings ArticleDOI

Optimal Control Approach to Robust Control of Nonlinear Systems Using Neural Network Based HJB solution

TL;DR: A Hamilton-Jacobi-Bellman (HJB) equation based optimal control algorithm for robust controller design, is proposed for a nonlinear system and is shown to be optimal with respect to a cost functional that includes maximum bound on system uncertainty.
Abstract: In this paper, a Hamilton-Jacobi-Bellman (HJB) equation based optimal control algorithm for robust controller design, is proposed for a nonlinear system. Utilizing the Lyapunov direct method, controller is shown to be optimal with respect to a cost functional that includes maximum bound on system uncertainty. Controller is continuous and requires the knowledge of the upper bound of system uncertainty. In the proposed algorithm, Neural Network (NN) is used to find approximate solution of HJB equation. Proposed algorithm has been applied on a nonlinear uncertain system.
Citations
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Journal ArticleDOI
TL;DR: It is shown that the robust control law with aperiodic information ensures input-to-state stability of the original system in the presence of mismatched uncertainty, and derived the event-triggering condition for a discrete-time uncertain system.
Abstract: This technical note proposes a procedure to control an uncertain discrete-time networked system using an aperiodic stabilizing input information. The system is primarily affected by the time-varying, norm bounded, mismatched parametric uncertainty. Aperiodic exchange of information is done due to bandwidth constraint of the communication network. An event-triggered based robust control strategy is adopted to reduce the effects of system uncertainty in such bandwidth constrained networks. In event-triggered control, the control input is computed and actuated at the system end only when a pre-specified event condition is violated. The robust control input is derived to stabilize the uncertain system by solving an optimal control problem based on a virtual nominal dynamics and a modified cost-functional. It is shown that the robust control law with aperiodic information ensures input-to-state stability (ISS) of the original system in the presence of mismatched uncertainty. Deriving the event-triggering condition for a discrete-time uncertain system and ensuring the stability of such system analytically are the key contributions of this technical note. A numerical example is given to prove the efficacy of the proposed event-based control algorithm over the conventional periodic one.

43 citations

References
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Journal ArticleDOI
TL;DR: A shoulder strap retainer having a base to be positioned on the exterior shoulder portion of a garment with securing means attached to the undersurface of the base for removably securing the base to the exterior shoulders portion of the garment.

1,709 citations


"Optimal Control Approach to Robust ..." refers background in this paper

  • ...It is well known that an NN can be used to approximate time-invariant functions on prescribed compact sets [5]....

    [...]

Journal ArticleDOI
TL;DR: In this article, a notion of quadratic stabilizability is defined and the Lyapunov function and the control are constructed using only the bounds ℛ,L.
Abstract: Consider an uncertain system (Σ) described by the equationx(t)=A(r(t))x(t)+B(s(t))u(t), wherex(t) ∈R n is the state,u(t) ∈R m is the control,r(t) ∈ ℛ ⊂R p represents the model parameter uncertainty, ands(t) ∈L ⊂R l represents the input connection parameter uncertainty. The matrix functionsA(·),B(·) are assumed to be continuous and the restraint sets ℛ,L are assumed to be compact. Within this framework, a notion of quadratic stabilizability is defined. It is important to note that this type of stabilization is robust in the following sense: The Lyapunov function and the control are constructed using only the bounds ℛ,L. Much of the previous literature has concentrated on a fundamental question: Under what conditions onA(·),B(·), ℛ,L can quadratic stabilizability be assured? In dealing with this question, previous authors have shown that, if (Σ) satisfies certain matching conditions, then quadratic stabilizability is indeed assured (e.g., Refs. 1–2). Given the fact that matching is only a sufficient condition for quadratic stabilizability, the objective here is to characterize the class of systems for which quadratic stabilizability can be guaranteed.

649 citations


"Optimal Control Approach to Robust ..." refers background in this paper

  • ...In general, it is possible to guarantee the existence of feedback controller for system with matched uncertainties [1],[7]....

    [...]

  • ...To tackle system uncertainty, few literatures [1],[3],[7] reported robust control design for certain class of uncertainties....

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Journal ArticleDOI
TL;DR: This paper states sufficient conditions that guarantee that the Galerkin approximation converges to the solution of the GHJB equation and that the resulting approximate control is stabilizing on the same region as the initial control.

580 citations

Book
01 Jan 1984
TL;DR: Practical control problems from various engineering disciplines have been drawn to illustrate the potential concepts and most of the theoretical results have been presented in a manner suitable for digital computer programming along with the necessary algorithms for numerical computations.
Abstract: From the Publisher: The book provides an integrated treatment of continuous-time and discrete-time systems for two courses at postgraduate level, or one course at undergraduate and one course at postgraduate level. It covers mainly two areas of modern control theory, namely: system theory, and multivariable and optimal control. The coverage of the former is quite exhaustive while that of latter is adequate with significant provision of the necessary topics that enables a research student to comprehend various technical papers. The stress is on the interdisciplinary nature of the subject. Practical control problems from various engineering disciplines have been drawn to illustrate the potential concepts. Most of the theoretical results have been presented in a manner suitable for digital computer programming along with the necessary algorithms for numerical computations.

204 citations

Journal ArticleDOI
Y.H. Chen1
TL;DR: The general design approach for robust controllers of uncertain dynamical systems is considered, and the design approach can be used to construct various classes of controllers which render the systems practically stable.
Abstract: The general design approach for robust controllers of uncertain dynamical systems is considered. The design approach, utilizing only the bound of uncertainty, can be used to construct various classes of controllers which render the systems practically stable. No statistical information of the uncertainty is required, and the system performance is described in a deterministic manner. >

73 citations