Design of Robust Adaptive Controllers for Nonlinear Systems with Dynamic Uncertainties

A general class of uncertain nonlinear systems with uncertain input unmodeled dynamics is considered. The system structure includes a core nominal subsystem of triangular structure with additive uncertain nonlinear functions and coupled with a set of uncertain nonlinear appended dynamics as well as uncertain dynamic input nonlinearities. The dynamic input nonlinearities include an uncertain non-affine function and a dynamic perturbation through an uncertain input unmodeled dynamics subsystem. The input unmodeled dynamics subsystem is coupled with the entire system state including the unmeasured state of the uncertain nonlinear appended dynamics coupled with the nominal triangular system. The control design is based on dual controller/observer dynamic high-gain scaling with an additional dynamic scaling based on a singular-perturbation-like redesign to address the non-affine and uncertain nature of the input appearance into the system dynamics. The proposed approach yields a global robust adaptive output-feedback control design that is robust to the dynamic input uncertainties and to uncertain nonlinear functions allowed throughout the system structure.

A small-gain approach to inverse optimal adaptive control of nonlinear systems with unmodeled dynamics

This paper presents the design of a robust direct model reference adaptive control (DMRAC) algorithm with focus on the satisfaction of an almost strictly positive real (ASPR) condition in the presence of plant uncertainty represented as either variations in plant parameters or unmodelled dynamics in the form of additive or multiplicative norm bounded perturbations in the transfer function. Both the time and frequency domain design conditions for a feedforward compensator have been developed utilizing the robust stability analysis and optimization methods. Illustrative examples are presented to validate the algorithm's use and applicability to control systems with parametric uncertainty or unmodelled dynamics.

Design of an adaptive controller for complex dynamic systems is a big challenge faced by the researchers. In this paper, we propose a novel method for the design of an error- based robust adaptive controller to make the system response reasonably fast with no overshoot. Here the control action is designed by introducing the notion of ‘error-based adaptive controller’ (EB-AC). In the design of this feedback adaptive controller, parameters of the controller are designed as a function of the system error. For example, the position feedback parameter K p (e, t), which controls the bandwidth of the system as well as the dynamic response, is a function of the system error e(t). In the design of the position feedback parameter K p (e, t), for large error K p (e, t) is kept large, thus increasing the bandwidth of the system which yields a fast response, whereas for decreasing errors, K p (e, t) is continuously decreased to a small value. Thus, during the dynamic response of the system, the bandwidth of the system is continuously controlled by the system error e(t). Similarly, the velocity feedback parameter K v (e, t) which controls the damping of the system is kept very small for large errors, and continuously increased to a large value for decreasing value of error. Hence, in the design of the proposed adaptive controller, the position feedback K p (e, t) and the velocity feedback K v (e, t) are formulated as a function of the system error, and this approach for formulating the adaptive controller yields a very fast response with no overshoot. In this paper, we present an error-based robust adaptive control design methodology for a linear system.

The present paper utilizes covariance matrix adaptation (CMA), an evolution strategy, in conjunction with H∞-based robust control law to design a stable adaptive fuzzy controller for a class of non-linear systems. The objective of the design is to develop a self-adaptive optimal/near optimal fuzzy controller, with guaranteed stability and satisfactory robust transient performance. The global search capability of CMA and H∞-based tuning, that provide a fast adaptation utilizing local search method, is employed in tandem with this proposed design methodology. The hybrid control strategy is implemented for benchmark simulation case study, and the results demonstrate the usefulness of the proposed approach.

A robust adaptive backstepping controller design method is proposed for a nonlinear system with uncertainty and unknown parameters based on the CMAC neural network. The CMAC neural network was used not only to approach the arbitrary model uncertainties but also to eliminate the bad effects of the uncertainties with robust terms in the controller and virtual controllers. Novel update and control laws are proposed to guarantee that all the signals in the closed-loop control system are uniformly ultimately bounded in a Lyapunov sense. Simulation experimental showed the tracking control of the nonlinear system is achieved and this method is effectual.

Distributed adaptive output feedback containment control for time-delay nonlinear multiagent systems

This paper is concerned with the parameter estimation and adaptive control problem for a sort of strict‐feedback nonlinear systems with unknown parameters. In order to deal with the nonlinear functions, we develop a kind of least‐squares estimator in the parameter estimation part. With such an estimator, we design the state‐feedback control law and analyze the properties of the closed‐loop system. To be concrete, the parameter estimator can guarantee the boundedness of parameter estimate error. At the same time, the adaptive control law is proposed to make the system states converge to zero and the equilibrium stable globally under some common assumptions. Finally, simulations are given to demonstrate the theoretical results.

Adaptive fuzzy finite-time tracking control of nonlinear systems with unmodeled dynamics

For general uncertain nonlinear time-delay systems, a domination design approach to robust adaptive controller based on Lyapunov-Razumikhin function is provided. To deal with the obstacle brought by the Lyapunov-Razumikhin function with the Razumikhin condition, a new parameter variable is introduced into the adaptive controller design instead of the conventional parameter variable. Based on Lyapunov-Razumikhin stability theory, it is shown that the proposed robust adaptive controller can guarantee the global uniform ultimate boundedness of all the signals in the resulting closed-loop dynamical system. In addition, it is also shown that the proposed design scheme can be applied to recursive design for the robust adaptive stabilizing controller of general uncertain nonlinear time-delay systems with triangular structure.

<div class="htmlview paragraph">In this paper, a robust adaptive optimal tracking control design for the air-path system of diesel engines with uncertain parameters and external driver commands is proposed.</div> <div class="htmlview paragraph">First, an optimal controller based on the analytic solution of a performance index is derived. It achieves tracking of suitable references (corresponding to low emissions and fuel consumption) for both the air-fuel ratio and the fraction of the recirculated exhaust gas. Then, a fuzzy estimation algorithm is used to identify the plant parameters and consequently to adapt the controller online.</div> <div class="htmlview paragraph">The simulated diesel engine is a medium duty Caterpillar 3126B with six cylinders, equipped with a variable geometry turbocharger and an exhaust gas recirculation valve. The proposed controller design is based on the reduced third order mean value model and implemented as a closed-form nonlinear model predictive control law on the full order model. The resulting controllers, with and without adaptation, are assessed through simulations with a SIL architecture using dSpace simulator. The adaptive controller, in particular, exhibits good control performance, with zero tracking offset with also ensuring global stability and tracking of output references.</div>

This paper presents an adaptive multi-dimensional Taylor network (MTN) control approach for a class of nonlinear systems with unknown parameters. MTN is employed to identify unknown nonlinear characteristics existing in the system, and then a novel adaptive MTN tracking control method is proposed, via backstepping technique. In the controller design, double adaptive laws are designed and appropriate Lyapunov functions are chosen to overcome the difficulties caused by the unknown parameters. The designed controller can guarantee that all the variables in the closed-loop systems are bounded and the tracking error can be arbitrarily small. Finally, simulation results are presented to verify the effectiveness of the proposed approach.

Optimal design of adaptive tracking controllers for non-linear systems

A new approach is given for the design of adaptive robust control in the frequency domain. Starting with an initial model of a stable plant and a robust stabilizing controller, the new (windsurfer) approach allows the bandwidth of the closed‐loop system to be increased progressively through an iterative control‐relevant system identification and control design procedure. The method deals with both undermodelling and measurement noise issues. Encouraging results are obtained in the simulations that illustrate the new idea.

Implicit function based adaptive control of non-canonical form discrete-time nonlinear systems