Control of Nonaffine Nonlinear Discrete Time Systems using Reinforcement-learning-Based Linearly Parameterized Neural Networks

A nonaffine discrete-time system represented by the nonlinear autoregressive moving average with eXogenous input (NARMAX) representation with unknown nonlinear system dynamics is considered. An equivalent affinelike representation in terms of the tracking error dynamics is first obtained from the original nonaffine nonlinear discrete-time system so that reinforcement-learning-based near-optimal neural network (NN) controller can be developed. The control scheme consists of two linearly parameterized NNs. One NN is designated as the critic NN, which approximates a predefined long-term cost function, and an action NN is employed to derive a near-optimal control signal for the system to track a desired trajectory while minimizing the cost function simultaneously. The NN weights are tuned online. by using the standard Lyapunov approach, the stability of the closed-loop system is shown. The net result is a supervised actor-critic NN controller scheme which can be applied to a general nonaffine nonlinear discrete-time system without needing the affinelike representation. Simulation results demonstrate satisfactory performance of the controlle

Lyapunov based optimal control of a class of nonlinear systems

Optimal control of nonlinear systems is in fact difficult since it requires the solution to the Hamilton-Jacobi-Bellman (HJB) equation which has no closed-form solution. In contrast to offline and/or online iterative schemes for optimal control, this dissertation in the form of five papers focuses on the design of iteration free, online optimal adaptive controllers for nonlinear discrete and continuous-time systems whose dynamics are completely or partially unknown even when the states not measurable. Thus, in Paper I, motivated by homogeneous charge compression ignition (HCCI) engine dynamics, a neural network-based infinite horizon robust optimal controller is introduced for uncertain nonaffine nonlinear discrete-time systems. First, the nonaffine system is transformed into an affine-like representation while the resulting higher order terms are mitigated by using a robust term. The optimal adaptive controller for the affinelike system solves HJB equation and identifies the system dynamics provided a target set point is given. Since it is difficult to define the set point a priori in Paper II, an extremum seeking control loop is designed while maximizing an uncertain output function. On the other hand, Paper III focuses on the infinite horizon online optimal tracking control of known nonlinear continuous-time systems in strict feedback form by using state and output feedback by relaxing the initial admissible controller requirement. Paper IV applies the optimal controller from Paper III to an underactuated helicopter attitude and position tracking problem. In Paper V, the optimal control of nonlinear continuous-time systems in strict feedback form from Paper III is revisited by using state and output feedback when the internal dynamics are unknown. Closed-loop stability is demonstrated for all the controller designs developed in this dissertation by using Lyapunov analysis --Abstract, page iv

Neural network control of nonstrict feedback and nonaffine nonlinear discrete-time systems with application to engine control

In this dissertation, neural networks (NN) approximate unknown nonlinear functions in the system equations, unknown control inputs, and cost functions for two different classes of nonlinear discrete-time systems. Employing NN in closed-loop feedback systems requires that weight update algorithms be stable...Controllers are developed and applied to a nonlinear, discrete-time system of equations for a spark ignition engine model to reduce the cyclic dispersion of heat release --Abstract, page iv

A brief review of neural networks based learning and control and their applications for robots

As an imitation of the biological nervous systems, neural networks (NN), which are characterized with powerful learning ability, have been employed in a wide range of applications, such as control of complex nonlinear systems, optimization, system identification and patterns recognition etc. This article aims to bring a brief review of the state-of-art NN for the complex nonlinear systems. Recent progresses of NNs in both theoretical developments and practical applications are investigated and surveyed. Specifically, NN based robot learning and control applications were further reviewed, including NN based robot manipulator control, NN based human robot interaction and NN based behavior recognition and generation

Data-Driven Robust Control of Unknown MIMO Nonlinear System Subject to Input Saturations and Disturbances

This paper presented a new data-driven robust control scheme for unknown nonlinear systems in the presence of input saturation and external disturbances. According to the input and output data of the nonlinear system, a recurrent neural network (RNN) data-driven model is established to reconstruct the dynamics of the nonlinear system. An adaptive output-feedback controller is developed to approximate the unknown disturbances and a novel input saturation compensation method is used to attenuate the effect of the input saturation. Under the proposed adaptive control scheme, the uniformly ultimately bounded convergence of all the signals of the closed-loop nonlinear system is guaranteed via Lyapunov analysis. The simulation results are given to show the effectiveness of the proposed data-driven robust controller

Output-feedback online optimal control for a class of nonlinear systems

In this paper an output-feedback model-based reinforcement learning (MBRL) method for a class of second-order nonlinear systems is developed. The control technique uses exact model knowledge and integrates a dynamic state estimator within the model-based reinforcement learning framework to achieve output-feedback MBRL. Simulation results demonstrate the efficacy of the developed method