In this paper, a new nonlinear control synthesis technique (θ - D approximation) is presented. This approach achieves suboptimal solutions to nonlinear optimal control problems in the sense that it solves the Hamilton-Jacobi-Bellman (HJB) equation approximately by adding perturbations to the cost function. By manipulating the perturbation terms both semi-globally asymptotic stability and suboptimality properties can be obtained. The convergence and stability proofs are given. This method overcomes the large control for large initial states problem that occurs in some other Taylor expansion based methods. It does not need time-consuming online computations like the state dependent Riccati equation (SDRE) technique. A vector problem is investigated to demonstrate the effectiveness of this new technique.
M. Xin and S. N. Balakrishnan, "A New Method for Suboptimal Control of a Class of Nonlinear Systems," Proceedings of the 41st IEEE Conference on Decision and Control, 2002, Institute of Electrical and Electronics Engineers (IEEE), Jan 2002.
The definitive version is available at http://dx.doi.org/10.1109/CDC.2002.1184258
41st IEEE Conference on Decision and Control, 2002
Mechanical and Aerospace Engineering
Keywords and Phrases
Hamilton-Jacobi-Bellman Equation; Jacobian Matrices; Taylor Expansion Based Methods; Asymptotic Stability; Cost Function; Flow Instability; Nonlinear Control Synthesis Technique; Nonlinear Control Systems; Nonlinear Systems; Semiglobally Asymptotic Stability; Stability Proofs; Suboptimal Control; Suboptimality Properties
International Standard Serial Number (ISSN)
Article - Conference proceedings
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