Haris E. Psillakis

NN-Based Adaptive Tracking Control of Uncertain Nonlinear Systems Disturbed by Unknown Covariance Noise

A class of uncertain nonlinear systems that are additionally driven by unknown covariance noise is considered. Based on the backstepping technique, adaptive neural control schemes are developed to solve the output tracking control problem of such systems. As it is proven by stability analysis, the proposed controller guarantees that all the error variables are bounded with desired probability in a compact set while the tracking error is mean-square semiglobally uniformly ultimately bounded (M-SGUUB). The tracking performance and the effectiveness of the proposed design are evaluated by simulation results.

Further Results on the Use of Nussbaum Gains in Adaptive Neural Network Control

In this note, the use of Nussbaum gains for adaptive neural network (NN) control is examined. Extending previous approaches that have been successfully applied to prove the forward completeness property (boundedness up to finite time), we address the boundedness for all time (up to infinity) problem. An example is constructed showing that this is not possible in general with the existing theoretical tools. To achieve boundedness for all time, a novel hysteresis-based deadzone scheme with resetting is introduced for the associated update laws. In this way, a unique, piecewise continuously differentiable solution is obtained while the error converges in finite time within some arbitrarily small region of the origin. Using the proposed modification, an adaptive NN tracking controller is designed for a class of multiple-input multiple-output nonlinear systems.

Adaptive Neural Tracking for a Class of SISO Uncertain and Stochastic Nonlinear Systems

Adaptive neural control schemes based on the backstepping technique are developed to solve the tracking control problem of a combined stochastic and uncertain nonlinear system. As shown by an extensive stability analysis the proposed control scheme ensures that all the error variables are bounded in probability while the mean square tracking error becomes semiglobally uniformly ultimately bounded in an arbitrarily small area around the origin. The effectiveness of the design approach is illustrated by simulation results.

Sampled-Data Adaptive NN Tracking Control of Uncertain Nonlinear Systems

In this paper, for a class of single-input-single-output (SISO) uncertain nonlinear systems, adaptive neural tracking controllers designed for digital computer implementation are proposed. The overall scheme can be considered as a sampled-data adaptive neural control system. As an intermediate result, it is proven that, for a sufficiently small sampling period, the emulated adaptive neural controller i.e., the discrete implementation of the continuous-time adaptive neural network controller ensures semiglobal uniformly ultimate boundedness of the closed-loop system. Then, based on the exact discrete-time model, a controller redesign is proposed that performs efficiently for sampling periods for which the emulation controller fails. The redesigned controller consists of two terms: the emulated control law and an extra robustness term designed to increase the order of the perturbation (with respect to the sampling period) in the Lyapunov difference. In all cases, high-order neural networks are employed to approximate the unknown nonlinearities. Using Lyapunov techniques, it is proven that, for a sufficiently small sampling period, the proposed redesigned controller ensures the (semiglobal) boundedness of all the signals in the closed-loop while the output of the system converges to a small neighborhood of the desired trajectory. Simulation results illustrate the superiority of the proposed scheme with respect to the emulation controller and verify the theoretical analysis.

An extension of the Georgiou–Smith example: Boundedness and attractivity in the presence of unmodelled dynamics via nonlinear PI control

In this paper, a nonlinear extension of the Georgiou-Smith system is considered and robustness results are proved for a class of nonlinear PI controllers with respect to fast parasitic first-order dynamics. More specifically, for a perturbed nonlinear system with sector bounded nonlinearity and unknown control direction, sufficient conditions for global boundedness and attractivity have been derived. It is shown that the closed loop system is globally bounded and attractive if (i) the unmodelled dynamics are sufficiently fast and (ii) the PI control gain has the Nussbaum function property. For the case of nominally unstable systems, the Nussbaum property of the control gain appears to be crucial. A simulation study confirms the theoretical results.

Integrator backstepping with the nonlinear PI method: An integral equation approach

Abstract In this paper we extend the nonlinear PI method within an integrator backstepping framework. The main idea of our approach is a novel selection of the virtual control laws through suitable nonlinear integral equations. Using the proposed methodology a new robust regulation control scheme is developed for time-varying strict feedback nonlinear systems with unknown control directions. A simulation study demonstrates the validity of our theoretical results.

Projection-Based Adaptive Neurocontrol With Switching Logic Deadzone Tuning

In this brief, an adaptive neural network (NN) controller is proposed for multiple-input-multiple-output (MIMO) nonlinear systems with triangular control structure and unknown control directions. Deadzones are employed in the projection-based NN weight learning laws and the Nussbaum parameter update laws with levels tuned by an innovative switching logic tuning mechanism. Detailed analysis using a family of Lyapunov-like integral functions and the function approximation capability of NNs proves that all the tracking errors are semiglobal uniform ultimate bounded in small neighborhoods of the origin while the closed-loop system variables (state vector, NN weights, Nussbaum parameters) and the control law remain bounded. A simulation study confirms the theoretical results and verifies the effectiveness of the proposed design.

Consensus in Networks of Agents With Unknown High-Frequency Gain Signs and Switching Topology

The agreement control problem of single and double-integrator agents with unknown and nonidentical control directions is addressed in this note under switching network topology. Distributed nonlinear PI control laws are proposed which ensure asymptotic consensus among the agents based on a new boundedness lemma and a generalized version of Barbaláts lemma for uniformly piecewise right continuous functions. Theoretical results are verified by simulation studies.

Further results on robustness of the nonlinear PI control method: The ignored actuator dynamics case

This note examines the robustness properties of the nonlinear PI control method for a simple system with unknown control directions and ignored order actuator dynamics. It is shown that global boundedness and regulation can be achieved for sector bounded nonlinearities if the actuator dynamics are sufficiently fast and the nonlinear PI control gain is chosen from a subclass of the Nussbaum function class. Simulations are also presented that demonstrate the validity of our analysis.

An Observer Approach for Deterministic Learning Using Patchy Neural Networks with Applications to Fuzzy Cognitive Networks

In this paper, a new methodology is proposed for deterministic learning with neural networks. Using an observer that employs the integral of the sign of the error term, asymptotic estimation of the respective nonlinear vector field is achieved. Patchy Neural Networks (PNNs) are introduced to identify the unknown nonlinearity from the observers output and the state measurements. The proposed scheme achieves learning with a single pass from the respective patches and does not need standard persistency of excitation conditions. Furthermore, the PNN weights are updated algebraically, reducing the computational load of learning significantly. Simulation results for a Duffing oscillator and a fuzzy cognitive network illustrate the effectiveness of the proposed approach.