Browsing by Author "Lin, Li-Gang"

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A Guidance Law Design Using the Combination of ISMC and SDRE Schemes
(2013)
Liang, Yew-Wen
;
Chen, Jun-Yu
;
Lin, Li-Gang
;
電控工程研究所
;
Institute of Electrical and Control Engineering
This paper studies the design of a robust guidance law for missiles in the presence of uncertainties, which may include inaccurate prediction of target maneuver. Under the design, the closed-loop guidance system is shown to be robust to the uncertainties. Additionally, the scheme presented possesses the flexibility of allowing the engineer to select a desired guidance law for the nominal system (i.e., system without uncertainty) so that the state response of the overall uncertain guidance system is close to that of the selected nominal closed-loop guidance system. The simulation results demonstrate the benefits of the presented scheme.
Analysis of SDC matrices for successfully implementing the SDRE scheme
(2013-10-01)
Liang, Yew-Wen
;
Lin, Li-Gang
;
電控工程研究所
;
Institute of Electrical and Control Engineering
The state-dependent Riccati equation (SORE) approach for stabilization of nonlinear affine systems was recently reported to be effective in many practical applications; however, there is no guideline on the construction of state-dependent coefficient (SDC) matrix when the SDRE solvability condition is violated, which may result in the SDRE scheme being terminated. In this study, we present several easy checking conditions so that the SORE scheme can be successfully implemented. Additionally, when the presented checking conditions are satisfied, the sets of all feasible SDC matrices and their structures are explicitly depicted for the planar system. (C) 2013 Elsevier Ltd. All rights reserved.
Analytical representation of the state-dependent coefficients in the SDRE/SDDRE scheme for multivariable systems
(2015-09-01)
Lin, Li-Gang
;
Vandewalle, Joos
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Liang, Yew-Wen
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電控工程研究所
;
Institute of Electrical and Control Engineering
Recently, the easy-to-implement state-dependent Riccati equation (SDRE) strategy has been shown effective for numerous practical applications. Since being similar to SDRE, the newly emerged state-dependent differential Riccati equation (SDDRE) approach shares most of the benefits of SORE, and exhibits interesting potential from both the analytical and practical viewpoints. By generalizing previous works to the general-order nonlinear time-variant systems, we try to resolve several problems related to the design flexibility (the infinitely many candidates of the state-dependent coefficient matrix), since they appear at the beginning of the implementation of both schemes. Finally, we demonstrate the proposed scheme via examples. (C) 2015 Elsevier Ltd. All rights reserved.
CONTROL FOR A CLASS OF SECOND-ORDER SYSTEMS VIA A STATE-DEPENDENT RICCATI EQUATION APPROACH
(2018-01-01)
Lin, Li-Gang
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Liang, Yew-Wen
;
Cheng, Li-Jen
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電控工程研究所
;
Institute of Electrical and Control Engineering
This study investigates the state-dependent Riccati equation (SDRE) controller for a class of second-order nonlinear systems. By fully exploiting the design degree of freedom (DOF) arising from the nonunique state-dependent coefficient (SDC) matrices, we explicitly calculate the ranges of control input via the SDRE scheme. Moreover, when a permissible control input is determined, we also explicitly parameterize the SDC matrices that result in the designated control value, in terms of system states and parameters, so the engineer can easily implement the scheme. Notably, this is the first analytical result that explores the range of control input using the design DOF of SDC matrices. In addition, by applying the analytical results, it is shown that the second order systems are always globally stabilizable, without any supplementary assumptions on weighting matrices (as extended from existing SDRE global results), and the corresponding stabilizing SDC matrices are also explicitly presented. Finally, illustrative examples clearly demonstrate the benefits of the analytical results.
Convex Quadratic Equation
(2020-09-01)
Lin, Li-Gang
;
Liang, Yew-Wen
;
Hsieh, Wen-Yuan
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電控工程研究所
;
Institute of Electrical and Control Engineering
Two main results (A) and (B) are presented in algebraic closed forms. (A) Regarding the convex quadratic equation, an analytical equivalent solvability condition and parameterization of all solutions are formulated, for the first time in the literature and in a unified framework. The philosophy is based on the matrix algebra, while facilitated by a novel equivalence/coordinate transformation (with respect to the much more challenging case of rank-deficient Hessian matrix). In addition, the parameter-solution bijection is verified. From the perspective via (A), a major application is re-examined that accounts for the other main result (B), which deals with both the infinite and finite-time horizon nonlinear optimal control. By virtue of (A), the underlying convex quadratic equations associated with the Hamilton-Jacobi equation, Hamilton-Jacobi inequality, and Hamilton-Jacobi-Bellman equation are explicitly solved, respectively. Therefore, the long quest for the constituent of the optimal controller, gradient of the associated value function, can be captured in each solution set. Moving forward, a preliminary to exactly locate the optimality using the state-dependent (resp., differential) Riccati equation scheme is prepared for the remaining symmetry condition.
Study of Reliable Control Via an Integral-Type Sliding Mode Control Scheme
(2012-08-01)
Liang, Yew-Wen
;
Ting, Li-Wei
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Lin, Li-Gang
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電機工程學系
;
Department of Electrical and Computer Engineering
This paper studies the active reliable control issues for a class of second-order nonlinear uncertain systems using an integral-type sliding mode control (ISMC) strategy. The proposed ISMC reliable scheme is shown to be able to tolerate some of the actuators' faults whenever the fault detection and diagnosis information is available. The presented scheme also maintains the main advantages of the ISMC designs, including robustness, rapid response, and ease of implementation. When the uncertainties and the output of the faulty actuators are matched regarding the nominal healthy subsystem, the state trajectories of the nominal healthy subsystem and the uncertain faulty system are identical. As a result, the engineers may adopt an optimal strategy for the nominal system, creating a desired trajectory for that of the uncertain faulty system to follow. Simulation results demonstrate the benefits of the proposed scheme.