This book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.

Adaptive Control

This paper is concerned with the synchronization control problem for a class of discrete time-delay complex dynamical networks under a dynamic event-triggered mechanism. For the efficiency of energy utilization, we make the first attempt to introduce a dynamic event-triggering strategy into the design of synchronization controllers for complex dynamical networks. A new discrete-time version of the dynamic event-triggering mechanism is proposed in terms of the absolute errors between control input updates. By constructing an appropriate Lyapunov functional, the dynamics of each network node combined with the introduced event-triggering mechanism are first analyzed, and a sufficient condition is then provided under which the synchronization error dynamics is exponentially ultimately bounded. Subsequently, a set of the desired synchronization controllers is designed by solving a matrix inequality. Finally, a simulation example is provided to verify the effectiveness of the proposed dynamic event-triggered synchronization control scheme.

Synchronization Control for A Class of Discrete Time-Delay Complex Dynamical Networks: A Dynamic Event-Triggered Approach

In this paper, the problem of robust fault tolerant control for a class of singular systems subject to both time-varying state-dependent nonlinear perturbation and actuator saturation is investigated. A sufficient condition for the existence of a fixed-gain controller is first proposed which guarantees the regularity, impulse-free and stability of the closed-loop system under all possible faults. An optimization problem with LMI constraints is formulated to determine the largest contractively invariant ellipsoid. An adaptive fault tolerant controller is then developed to compensate for the failure effects on the system by estimating the fault and updating the design parameter matrices online. Both of these two controllers are in the form of a saturation avoidance feedback with the advantage of relatively small actuator capacities compared with the high gain counterpart. An example is included to illustrate the proposed procedures and their effectiveness.

Fault tolerant control for singular systems with actuator saturation and nonlinear perturbationFault tolerant control for singular systems with actuator saturation and nonlinear perturbation.

In the framework of the networked control systems (NCSs), the components are connected with each other over a shared band-limited network. The merits of NCSs include easy extensibility, resource sh...

A survey on sliding mode control for networked control systems

In this paper, an adaptive neural network (NN) control problem is investigated for discrete-time nonlinear systems with input saturation. Radial-basis-function (RBF) NNs, including critic NNs and action NNs, are employed to approximate the utility functions and system uncertainties, respectively. In the previous works, a gradient descent scheme is applied to update weight vectors, which may lead to local optimal problem. To circumvent this problem, a multigradient recursive (MGR) reinforcement learning scheme is proposed, which utilizes both the current gradient and the past gradients. As a consequence, the MGR scheme not only eliminates the local optimal problem but also guarantees faster convergence rate than the gradient descent scheme. Moreover, the constraint of actuator input saturation is considered. The closed-loop system stability is developed by using the Lyapunov stability theory, and it is proved that all the signals in the closed-loop system are semiglobal uniformly ultimately bounded (SGUUB). Finally, the effectiveness of the proposed approach is further validated via some simulation results.

Adaptive Reinforcement Learning Neural Network Control for Uncertain Nonlinear System With Input Saturation

Output tracking of uncertain fractional-order nonlinear systems via a novel fractional-order sliding mode approach

This technical note studies the robust output tracking controller design for a class of uncertain discrete-time systems subject to actuator saturation. To achieve this capability, a new controller is proposed by robustifying the discrete-time composite nonlinear feedback (DCNF) control law. Since, the proposed controller may be saturated; a precise analysis is done to show its robust performance in spite of presence of actuator saturation and time-varying external disturbances. Additionally, a theorem is given and proved which guarantees the disturbance attenuation via the proposed control law for three different cases of the saturation function and it is shown that even if the control signal is saturated, the proposed controller achieves steady-state error of order $O(T)$ for state regulation. Finally, computer simulations are performed for a practical system and the applicability of the proposed controller is shown.

Design of Robust Controller for a Class of Uncertain Discrete-Time Systems Subject to Actuator Saturation

This paper is concerned with a robust observer-based control of nonlinear one-sided Lipschitz systems in the presence of time delay, model uncertainties, and unknown energy-bounded exogenous distur...

Observer-based H∞ finite-time controller for time-delay nonlinear one-sided Lipschitz systems with exogenous disturbances:

This paper considers the problem of delay-independent stabilization of linear fractional order (FO) systems with state delay. As in most practical systems in which the value of delay is not exactly...

Delay-independent sliding mode control of time-delay linear fractional order systems:

This paper considers the problem of passivity-based sliding mode control of uncertain nonlinear systems. For this purpose, two cases are studied. In the first case, it is assumed that only the matched uncertainties exist in the system dynamics. In this case, the passivity-based control approach is used to design an appropriate sliding manifold with a flexible structure such that the asymptotic stability of the reduced-order model (i.e., the motion equations on the proposed sliding manifold) is guaranteed. In the second case, both matched and unmatched uncertainties are considered in the system dynamics and thus the reduced-order model has uncertain terms. In this case, the modified Lyapunov redesign technique is combined with the passivity-based control method for design of robust sliding manifold. The function that is basically used in the classical Lyapunov redesign method is the signum function, which is not differentiable. Since, for evaluating the derivative of the sliding manifold its equation must be differentiable, a new additional continuous control term is suggested. In addition, the robust practical stabilization of the motion equations is guaranteed without considering any limitation on the upper bound of the unmatched uncertainties. Finally, computer simulations are performed for a practical example (flexible spacecraft) and also a numerical example to demonstrate the ability of the proposed controller in robust stabilization of uncertain nonlinear dynamical systems.

Tahereh Binazadeh

Papers

Output tracking of uncertain fractional-order nonlinear systems via a novel fractional-order sliding mode approach

Design of Robust Controller for a Class of Uncertain Discrete-Time Systems Subject to Actuator Saturation

Observer-based H∞ finite-time controller for time-delay nonlinear one-sided Lipschitz systems with exogenous disturbances:

Delay-independent sliding mode control of time-delay linear fractional order systems:

Flexible Structure Control of Unmatched Uncertain Nonlinear Systems via Passivity-based Sliding Mode Technique