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This paper presents a robust adaptive optimal control strategy for wave energy converters (WECs). We first propose a new estimator in a simple form to address modeling uncertainties and formulate the control of WECs as an optimal control problem. Then a novel energy maximization control strategy is developed based on the concept of adaptive dynamic programming (ADP), where a critic neural network (NN) is used to approximate the time-dependent optimal cost value. To achieve guaranteed convergence, a recently proposed adaptive law based on the parameter estimation error is further tailored to online update the weights of critic NN. Consequently, the critic NN output, e.g. the costate, can be used to compute the optimal feedback control. The proposed robust ADP WEC control method is not only effective in handling dynamic uncertainties, but also computationally efficient with a very fast online convergence rate for the weights of the critic NN (less than 20 seconds for irregular sea waves as demonstrated in the simulations). These advantages significantly enhance the real-time applicability of the proposed method. Simulation results show that this approach is robust to model uncertainties and has significantly reduced computational costs for implementation. Index Terms-Wave energy converter, adaptive optimal control, adaptive dynamic programming, uncertainty estimator.

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In this paper, we address the energy maximization problem of wave energy converters (WEC) subject to nonlinearities and constraints, and present an efficient online control strategy based on the principle of adaptive dynamic programming (ADP) for solving the associated Hamilton-Jacobi-Bellman (HJB) equation. To solve the derived constrained nonlinear optimal control problem, a critic neural network (NN) is used to approximate the timedependant optimal cost value and then calculate the practical suboptimal causal control action. The proposed novel WEC control strategy leads to a simplified ADP framework without involving the widely used actor NN. The significantly improved computational efficacy of the proposed control makes it attractive for its practical implementation on a WEC to achieve a reduced unit cost of energy output, which is especially important when the dynamics of a WEC are complicated and need to be described accurately by a high-order model with nonlinearities and constraints. Simulation results are provided to show the efficacy of the proposed control method.

In this paper, the authors focus on the application of linear matrix inequality (LMI) in the stabilization of fractional-order chaotic systems and the strict mathematical description and proof of LMI. Based on the theory of the fractional-order interval system, the generalized Takagi-Sugeno fuzzy model is applied to a wide class of fractional-order chaotic systems with uncertain parameters. The sufficient stability condition for the fractional-order systems is presented as a set of LMI for the first time and the strict mathematical norms of LMI are given. Furthermore, a controller is developed to stabilize fractional-order chaotic systems, and may be applied to fractional-order systems with uncertainty. Finally, two representative examples of the three-dimensional fractional-order permanent magnet synchronous motor system and the four-dimensional fractional-order hyperchaotic system based on Chen’s system are provided to demonstrate the effectiveness of theoretical analysis.

In this study, a robust finite time Takagi-Sugeno fuzzy control method for hydro-turbine governing system (HTGS) is investigated. Firstly, the mathematical model of HTGS is introduced, and on the basis of Takagi-Sugeno (T-S) fuzzy rules, the T-S fuzzy model of HTGS is presented. Secondly, based on finite time stability theory, a novel finite time Takagi-Sugeno fuzzy control method is designed for the stability control of HTGS. Thirdly, the relatively loose sufficient stability condition is acquired, which could be transformed into a group of linear matrix inequalities (LMIs) via Schur complement as well as the strict mathematical derivation is given. Furthermore, the control method could resist random disturbances, which shows the good robustness. Simulation results indicate the designed finite time T-S fuzzy control scheme works well compared with the conventional method. The approach proposed in this paper is easy to implement and also provides reference for relevant hydropower systems.