Optimal Control of Unknown Nonlinear System From Inputoutput Data

Optimal control designers usually require a plant model to design a controller. The problem is the controller\u27s performance heavily depends on the accuracy of the plant model. However, in many situations, it is very time-consuming to implement the system identification procedure and an accurate structure of a plant model is very difficult to obtain. On the other hand, neuro-fuzzy models with product inference engine, singleton fuzzifier, center average defuzzifier, and Gaussian membership functions can be easily trained by many well-established learning algorithms based on given input-output data pairs. Therefore, this kind of model is used in the current optimal controller design. Two approaches of designing optimal controllers of unknown nonlinear systems based on neuro-fuzzy models are presented in the thesis. The first approach first utilizes neuro-fuzzy models to approximate the unknown nonlinear systems, and then the feasible-direction algorithm is used to achieve the numerical solution of the Euler-Lagrange equations of the formulated optimal control problem. This algorithm uses the steepest descent to find the search direction and then apply a one-dimensional search routine to find the best step length. Finally several nonlinear optimal control problems are simulated and the results show that the performance of the proposed approach is quite similar to that of optimal control to the system represented by an explicit mathematical model. However, due to the limitation of the feasible-direction algorithm, this method cannot be applied to highly nonlinear and dimensional plants. Therefore, another approach that can overcome these drawbacks is proposed. This method utilizes Takagi-Sugeno (TS) fuzzy models to design the optimal controller. TS fuzzy models are first derived from the direct linearization of the neuro-fuzzy models, which is close to the local linearization of the nonlinear dynamic systems. The operating points are chosen so that the TS fuzzy model is a good approximation of the neuro-fuzzy model. Based on the TS fuzzy model, the optimal control is implemented for a nonlinear two-link flexible robot and a rigid asymmetric spacecraft, thus providing the possibility of implementing the well-established optimal control method on unknown nonlinear dynamic systems

Adaptive dynamic programming with eligibility traces and complexity reduction of high-dimensional systems

This dissertation investigates the application of a variety of computational intelligence techniques, particularly clustering and adaptive dynamic programming (ADP) designs especially heuristic dynamic programming (HDP) and dual heuristic programming (DHP). Moreover, a one-step temporal-difference (TD(0)) and n-step TD (TD(λ)) with their gradients are utilized as learning algorithms to train and online-adapt the families of ADP. The dissertation is organized into seven papers. The first paper demonstrates the robustness of model order reduction (MOR) for simulating complex dynamical systems. Agglomerative hierarchical clustering based on performance evaluation is introduced for MOR. This method computes the reduced order denominator of the transfer function by clustering system poles in a hierarchical dendrogram. Several numerical examples of reducing techniques are taken from the literature to compare with our work. In the second paper, a HDP is combined with the Dyna algorithm for path planning. The third paper uses DHP with an eligibility trace parameter (λ) to track a reference trajectory under uncertainties for a nonholonomic mobile robot by using a first-order Sugeno fuzzy neural network structure for the critic and actor networks. In the fourth and fifth papers, a stability analysis for a model-free action-dependent HDP(λ) is demonstrated with batch- and online-implementation learning, respectively. The sixth work combines two different gradient prediction levels of critic networks. In this work, we provide a convergence proofs. The seventh paper develops a two-hybrid recurrent fuzzy neural network structures for both critic and actor networks. They use a novel n-step gradient temporal-difference (gradient of TD(λ)) of an advanced ADP algorithm called value-gradient learning (VGL(λ)), and convergence proofs are given. Furthermore, the seventh paper is the first to combine the single network adaptive critic with VGL(λ). --Abstract, page iv

Decentralized Optimal Control With Application In Power System

An output-feedback decentralized optimal controller is proposed for power systems with renewable energy penetration. Renewable energy source is modeled similar to the classical generator model and is equipped with the unified power flow controller (UPFC). The transient performance of power system is considered and stability of the dynamical states are investigated. An offline decentralized optimal controller is designed that utilizes only the local states. The network comprises conventional synchronous generators as well as renewable sources with inverter equipped with UPFC. Subsequently, the optimal decentralized controller is compared to the initial stabilizing controller used to obtain the optimal controller. An online decentralized optimal controller is designed for discrete-time system. Two neuro networks are utilized to estimate value function and optimal control strategy. Furthermore, a novel observer-based decentralized optimal controller is developed on small scale discrete-time power system. The system is trained followed by least square rules and successive approximation. Simulation results on IEEE 14-, 30-, and 118-bus power system benchmarks shows satisfactory performance of the online decentralized controller. And also, simulation results demonstrate great performance of the observer and the optimal controller compare to the centralized optimal controller