In this paper, the direct adaptive neural control is proposed for a class of uncertain nonaffine nonlinear systems with unknown nonsymmetric input saturation. Based on the implicit function theorem and mean value theorem, both state feedback and output feedback direct adaptive controls are developed using neural networks (NNs) and a disturbance observer. A compounded disturbance is defined to take into account of the effect of the unknown external disturbance, the unknown nonsymmetric input saturation, and the approximation error of NN. Then, a disturbance observer is developed to estimate the unknown compounded disturbance, and it is established that the estimate error converges to a compact set if appropriate observer design parameters are chosen. Both state feedback and output feedback direct adaptive controls can guarantee semiglobal uniform boundedness of the closed-loop system signals as rigorously proved by Lyapunov analysis. Numerical simulation results are presented to illustrate the effectiveness of the proposed direct adaptive neural control techniques.

Direct Adaptive Neural Control for a Class of Uncertain Nonaffine Nonlinear Systems Based on Disturbance Observer

Most current model reference adaptive control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element is radial basis function networks (RBFNs), with RBF centers preallocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become noneffective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semiglobal in nature. This paper investigates a Gaussian process-based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. The GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed-loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning.

https://dspace.mit.edu/bitstream/handle/1721.1/77931/TNN12.pdf?sequence=1

Bayesian Nonparametric Adaptive Control Using Gaussian Processes

Presents an approach and a systematic design methodology to adaptive motion control based on neural networks (NNs) for high-performance robot manipulators, for which stability conditions and performance evaluation are given. The neurocontroller includes a linear combination of a set of off-line trained NNs, and an update law of the linear combination coefficients to adjust robot dynamics and payload uncertain parameters. A procedure is presented to select the learning conditions for each NN in the bank. The proposed scheme, based on fixed NNs, is computationally more efficient than the case of using the learning capabilities of the neural network to be adapted, as that used in feedback architectures that need to propagate back control errors through the model to adjust the neurocontroller. A practical stability result for the neurocontrol system is given. That is, we prove that the control error converges asymptotically to a neighborhood of zero, whose size is evaluated and depends on the approximation error of the NN bank and the design parameters of the controller. In addition, a robust adaptive controller to NN learning errors is proposed, using a sign or saturation switching function in the control law, which leads to global asymptotic stability and zero convergence of control errors. Simulation results showing the practical feasibility and performance of the proposed approach to robotics are given.

Neural networks for advanced control of robot manipulators

In recent years, neural networks have fulfilled the promise of providing model-free learning controllers for nonlinear systems; however, it is very difficult to guarantee the stability and robustness of neural network control systems. This paper proposes an adaptive neurocontroller for robot manipulators based on the radial basis function network (RBFN). The RBFN is a branch of neural networks and is mathematically tractable. Therefore, we adopt the RBFN to approximate nonlinear robot dynamics. The RBFN generates control input signals based on the Lyapunov stability that is often used in the conventional control schemes. A saturation function is also chosen as an auxiliary controller to guarantee the stability and robustness of the control system under the external disturbances and modeling uncertainties.

An adaptive neurocontroller using RBFN for robot manipulators

In this paper, we investigate the adaptive exponential synchronization in both the mean square and the almost sure senses for an array of $ {N}$ identical Markovian stochastic coupled neural networks of neutral-type with time-varying delay and random coupling strength. The generalized Lyapunov theorem of the exponential stability in the mean square for the neutral stochastic Markov system with the time-varying delay is first established. The time-varying delay in the system is assumed to be a bounded measurable function. Then, sufficient conditions to guarantee the exponential synchronization in the mean square for the underlying system are developed under an adaptive feedback controller, which are given in terms of the $\mathcal {M}$ -matrix and the algebraic inequalities. Under the same conditions, the almost sure exponential synchronization is also presented. A numerical example is given to show the effectiveness and potential of the proposed theoretical results.

Exponential Synchronization for Markovian Stochastic Coupled Neural Networks of Neutral-Type via Adaptive Feedback Control

In this paper, an approach to model reference adaptive control based on neural networks is proposed and analyzed for a class of first-order continuous-time nonlinear dynamical systems. The controller structure can employ either a radial basis function network or a feedforward neural network to compensate adaptively the nonlinearities in the plant. A stable controller-parameter adjustment mechanism, which is determined using the Lyapunov theory, is constructed using a /spl sigma/-modification-type updating law. The evaluation of control error in terms of the neural network learning error is performed. That is, the control error converges asymptotically to a neighborhood of zero, whose size is evaluated and depends on the approximation error of the neural network. In the design and analysis of neural network-based control systems, it is important to take into account the neural network learning error and its influence on the control error of the plant. Simulation results showing the feasibility and performance of the proposed approach are given.

Neural network-based model reference adaptive control system

Addresses the problem of generating autonomously an optimal control action sequence for ship steering control based on adaptive critic designs. The principal objective is to autonomously design an optimal controller that steers the center of the ship through a number of gates in a particular order using a minimum amount of time. In general, the steering of mobile vehicles depends on the interactions between a vehicle and its supporting medium. Nautical ships present particularly long time delays in response to rudder movements (control actions). Planning for the future encounters with gates should be part of the current control decision, since the ship's position and orientation as it moves through one gate greatly affect the ease of navigation through successive gates. The proposed adaptive critic design-based controller learns to guide the ship through a set of gates autonomously. The simulation results show the performance of the proposed approach.

H.D. Patino

Papers

Neural network-based model reference adaptive control system

Adaptive critic designs for self-learning ship steering control