Shinn-Horng Chen

Optimal control of Takagi-Sugeno fuzzy-model-based systems representing dynamic ship positioning systems

Orthogonal function approach (OFA) and the hybrid Taguchi-genetic algorithm (HTGA) are used to solve quadratic finite-horizon optimal controller design problems in both a fuzzy parallel distributed compensation (PDC) controller and a non-PDC controller (linear state feedback controller) for Takagi-Sugeno (TS) fuzzy-model-based control systems for dynamic ship positioning systems (TS-DSPS). Based on the OFA, an algorithm requiring only algebraic computation is used to solve dynamic equations for TS-fuzzy-model-based feedback and is then integrated with HTGA to design quadratic finite-horizon optimal controllers for TS-DSPS under the criterion of minimizing a quadratic finite-horizon integral performance index, which is also converted to algebraic form by the OFA. Integration of OFA and HTGA in the proposed approach enables use of simple algebraic computation and is well adapted to the computer implementation. Therefore, it facilitates design tasks of quadratic finite-horizon optimal controllers for the TS-DSPS. The applicability of the proposed approach is demonstrated in the example of a moored tanker designed using quadratic finite-horizon optimal controllers.

Design of robust-optimal output feedback controllers for linear uncertain systems using LMI-based approach and genetic algorithm

This paper considers the robust-optimal design problems of output feedback controllers for linear systems with both time-varying elemental (structured) and norm-bounded (unstructured) parameter uncertainties. Two new sufficient conditions are proposed in terms of linear-matrix-inequalities (LMIs) for ensuring that the linear output feedback systems with both time-varying elemental and norm-bounded parameter uncertainties are asymptotically stable, where the mixed quadratically-coupled parameter uncertainties are directly considered in the problem formulation. A numerical example is given to show that the presented sufficient conditions are less conservative than existing ones reported recently. Then, by integrating the hybrid Taguchi-genetic algorithm (HTGA) and the proposed LMI-based sufficient conditions, a new integrative approach is presented to find the output feedback controllers of the linear systems with both time-varying elemental and norm-bounded parameter uncertainties such that the control objective of minimizing a quadratic integral performance criterion subject to the stability robustness constraint is achieved. A design example of the robust-optimal output feedback controller for the AFTI/F-16 aircraft control system with the time-varying elemental parameter uncertainties is given to demonstrate the applicability of the proposed new integrative approach.

Regional eigenvalue-clustering robustness of linear uncertain multivariable output feedback PID control systems

Abstract This paper proposes a time domain approach to deal with the regional eigenvalue-clustering robustness analysis problem of linear uncertain multivariable output feedback proportional-integral–derivative (PID) control systems. The robust regional eigenvalue-clustering analysis problem of linear uncertain multivariable output feedback PID control systems is converted to the regional eigenvalue-clustering robustness analysis problem of linear uncertain singular systems with static output feedback controller. Based on some essential properties of matrix measures, a new sufficient condition is proposed for ensuring that the closed-loop singular system with both structured and mixed quadratically-coupled parameter uncertainties is regular and impulse-free, and has all its finite eigenvalues retained inside the same specified region as the nominal closed-loop singular system does. Two numerical examples are given to illustrate the application of the presented sufficient condition.

Stability robustness of linear output feedback systems with both time-varying structured and unstructured parameter uncertainties as well as delayed perturbations

This paper investigates the stability robustness of linear output feedback systems with both time-varying structured (elemental) and unstructured (norm-bounded) parameter uncertainties as well as delayed perturbations by directly considering the mixed quadratically coupled uncertainties in the problem formulation. Based on the Lyapunov approach and some essential properties of matrix measures, two new sufficient conditions are proposed for ensuring that the linear output feedback systems with delayed perturbations as well as both time-varying structured and unstructured parameter uncertainties are asymptotically stable. The corresponding stable region, that is obtained by using the proposed sufficient conditions, in the parameter space is not necessarily symmetric with respect to the origin of the parameter space. Two numerical examples are given to illustrate the application of the presented sufficient conditions, and for the case of only considering both the delayed perturbations and time-varying structured parameter uncertainties, it can be shown that the results proposed in this paper are better than the existing one reported in the literature.

Regularity and controllability robustness of TS fuzzy descriptor systems with structured parametric uncertainties

The problem of robust global regularity and controllability is considered in Takagi–Sugeno (TS) fuzzy descriptor control systems with structured parametric uncertainties. Sufficient conditions are proposed to ensure both global regularity and controllability in these uncertain systems. The conditions also provide the explicit relationships of bounds on parametric uncertainties to achieve regularity and controllability. One numerical and two engineering examples are given to illustrate the applications of the proposed sufficient conditions.

Algebraic Criterion for Robust Controllability of Continuous Linear Time-Delay Systems with Parametric Uncertainties

The robust controllability problem for the continuous linear time-delay systems with structured parametric uncertainties is studied in this paper. A new sufficient algebraic criterion for the robust controllability of uncertain linear time-delay systems is established. The proposed sufficient condition can provide the explicit relationship of the bounds on system uncertainties for guaranteeing the controllability property. Three numerical examples are given to illustrate the application of the proposed sufficient algebraic criterion and to compare the results with those obtained from the approaches in the literature.

Design of robust-stable and quadratic finite-horizon optimal controllers with low trajectory sensitivity for uncertain active suspension systems

This paper presents a design method for designing the robust-stable and quadratic-finite-horizon-optimal controllers of uncertain active suspension systems. The method integrates a robust stabilisability condition, the orthogonal functions approach (OFA) and the hybrid Taguchi-genetic algorithm (HTGA). Using the integrative computational method, a robust-stable and quadratic-finite-horizon-optimal controller with low-trajectory sensitivity can be obtained such that (i) the active suspension system with elemental parametric uncertainties is stabilised and (ii) a quadratic-finite-horizon-integral performance index including a quadratic trajectory sensitivity term for the nominal active suspension system is minimised. The robust stabilisability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the OFA, an algebraic algorithm only involving the algebraic computation is derived for solving the nominal active suspension feedback dynamic equations. By using the OFA and the LMI-based robust stabilisability condition, the dynamic optimisation problem for the robust-stable and quadratic-finite-horizon-optimal controller design of the linear uncertain active suspension system is transformed into a static-constrained-optimisation problem represented by the algebraic equations with constraint of LMI-based robust stabilisability condition; thus greatly simplifies the design problem. Then, for the static-constrained-optimisation problem, the HTGA is employed to find the robust-stable and quadratic-finite-horizon-optimal controllers of the linear uncertain active suspension systems. A design example is given to demonstrate the applicability of the proposed integrative computational approach.

Robust controllability of linear interval systems with multiple control delays

The robust controllability problem for linear interval systems with multiple control delays is studied in this article. The rank preservation problem is converted to the nonsingularity analysis problem of the minors of the matrix in discussion. Based on some essential properties of matrix measures, a new sufficient algebraically elegant criterion for the robust controllability of linear interval systems with multiple control delays is established. A numerical example is given to illustrate the application of the proposed sufficient algebraic criterion.

Application of Improved Differential Evolution Approach on Parameter Identification of Chen and Lü Chaotic Systems

In this paper, a Taguchi-sliding-level differential evolution algorithm (TSLDEA) is proposed to use for finding the actual parameters of Chen and Lü chaotic systems. The TSLDEA, a powerful global numerical optimization method, combines the differential evolution algorithm (DEA) with the Taguchi-sliding-level (TSL) method. The TSL method is fused in the crossover operation of a DEA. Then, the systematic reasoning ability of the TSL method is incorporated in the crossover operation of a DEA to select the better offspring to achieve the crossover, and consequently enhance the DEA. Therefore, the TSLDEA can be more robust, statistically sound, and quickly convergent. Two illustrative examples of parameter identification of Chen and Lü chaotic systems are given to demonstrate the applicability of the proposed TSLDEA.

Robust controllability of TS fuzzy descriptor systems with structured parametric uncertainties

The robust completely controllability problem for the Takagi-Sugeno (TS) fuzzy descriptor systems is studied in this paper. The proposed sufficient condition can provide the explicit relationship of the bounds on parameter uncertainties for preserving the assumed properties.