Journal ArticleDOI
Backstepping design with local optimality matching
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The recursive construction of a cost functional and the corresponding solution to the Hamilton-Jacobi-Isaacs equation employs a new concept of nonlinear Cholesky factorization, and shows that the backstepping design procedure can be tuned to yield the optimal control law.Abstract:
In nonlinear H/sup /spl infin//-optimal control design for strict-feedback nonlinear systems, our objective is to construct globally stabilizing control laws to match the optimal control law up to any desired order, and to be inverse optimal with respect to some computable cost functional. Our recursive construction of a cost functional and the corresponding solution to the Hamilton-Jacobi-Isaacs equation employs a new concept of nonlinear Cholesky factorization. When the value function for the system has a nonlinear Cholesky factorization, we show that the backstepping design procedure can be tuned to yield the optimal control law.read more
Citations
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Journal ArticleDOI
Brief paper: Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization
Xue-Jun Xie,Jie Tian +1 more
TL;DR: This paper investigates the adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization by using the parameter separation lemma in Lin, W., & Qian, C. (2002a), and some flexible algebraic techniques.
Journal ArticleDOI
Practical Output-Feedback Risk-Sensitive Control for Stochastic Nonlinear Systems with Stable Zero-Dynamics
Yun-Gang Liu,Ji-Feng Zhang +1 more
TL;DR: This paper addresses the design problem of practical output-feedingback controls for stochastic strict-feedback nonlinear systems in observer canonical form with stable zero-dynamics under long-term average tracking risk-sensitive cost criteria by using the integrator backstepping methodology.
Journal ArticleDOI
Adaptive neural tracking control for a class of stochastic nonlinear systems
TL;DR: In this article, the radial basis function neural networks are used to approximate the nonlinearities, and adaptive backstepping technique is employed to construct controllers for a class of single-input single-output strict-feedback stochastic nonlinear systems whose output is an known linear function.
Journal ArticleDOI
State-feedback stabilization for high-order stochastic nonlinear systems with stochastic inverse dynamics
Xue-Jun Xie,Jie Tian +1 more
TL;DR: In this paper, a smooth state-feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on [0, ∞], the equilibrium at the origin of the closedloop system is globally asymptotically stable in probability, and the states can be regulated to the origin almost surely.
Journal ArticleDOI
Locally optimal and robust backstepping design
TL;DR: For a class of nonlinear systems, a robust backstepping design achieves both local optimality and global inverse optimality.
References
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Book
Nonlinear Control Systems
Alberto Isidori,M. Thoma,Eduardo D. Sontag,B. W. Dickinson,A. Fettweis,J. L. Massey,J. W. Modestino +6 more
TL;DR: In this paper, a systematic feedback design theory for solving the problems of asymptotic tracking and disturbance rejection for linear distributed parameter systems is presented, which is intended to support the development of flight controllers for increasing the high angle of attack or high agility capabilities of existing and future generations of aircraft.
Book
Nonlinear and adaptive control design
TL;DR: In this paper, the focus is on adaptive nonlinear control results introduced with the new recursive design methodology -adaptive backstepping, and basic tools for nonadaptive BackStepping design with state and output feedbacks.
Journal ArticleDOI
Systematic design of adaptive controllers for feedback linearizable systems
TL;DR: A systematic procedure for the design of adaptive regulation and tracking schemes for a class of feedback linearizable nonlinear systems is developed, which substantially enlarges the class of non linear systems with unknown parameters for which global stabilization can be achieved.
Proceedings ArticleDOI
Systematic Design of Adaptive Controllers for Feedback Linearizable Systems
TL;DR: In this paper, a systematic procedure is developed for the design of adaptive regulation and tracking schemes for a class of feedback linearizable nonlinear systems, which are transformable into the so-called pure-feedback form.