This paper studies a number of quantized feedback design problems for linear systems. We consider the case where quantizers are static (memoryless). The common aim of these design problems is to stabilize the given system or to achieve certain performance with the coarsest quantization density. Our main discovery is that the classical sector bound approach is nonconservative for studying these design problems. Consequently, we are able to convert many quantized feedback design problems to well-known robust control problems with sector bound uncertainties. In particular, we derive the coarsest quantization densities for stabilization for multiple-input-multiple-output systems in both state feedback and output feedback cases; and we also derive conditions for quantized feedback control for quadratic cost and H/sub /spl infin// performances.

The sector bound approach to quantized feedback control | NOVA. The University of Newcastle's Digital Repository

In this paper, the adaptive neural network (NN) tracking control problem is addressed for robot manipulators subject to dead-zone input. The control objective is to design an adaptive NN controller to guarantee the stability of the systems and obtain good performance. Different from the existing results, which used NN to approximate the nonlinearities directly, NNs are employed to identify the originally designed virtual control signals with unknown nonlinear items in this paper. Moreover, a sequence of virtual control signals and real controller are designed. The adaptive backstepping control method and Lyapunov stability theory are used to prove the proposed controller can ensure all the signals in the systems are semiglobally uniformly ultimately bounded, and the output of the systems can track the reference signal closely. Finally, the proposed adaptive control strategy is applied to the Puma 560 robot manipulator to demonstrate its effectiveness.

Adaptive Neural Network Tracking Control for Robotic Manipulators With Dead Zone

This paper addresses the problem of adaptive tracking control for a class of strict-feedback nonlinear state constrained systems with input delay. To alleviate the major challenges caused by the appearances of full state constraints and input delay, an appropriate barrier Lyapunov function and an opportune backstepping design are used to avoid the constraint violation, and the Pade approximation and an intermediate variable are employed to eliminate the effect of the input delay. Neural networks are employed to estimate unknown functions in the design procedure. It is proven that the closed-loop signals are semiglobal uniformly ultimately bounded, and the tracking error converges to a compact set of the origin, as well as the states remain within a bounded interval. The simulation studies are given to illustrate the effectiveness of the proposed control strategy in this paper.

Neural Networks-Based Adaptive Control for Nonlinear State Constrained Systems With Input Delay

This paper addresses the trajectory tracking control problem of a class of nonstrict-feedback nonlinear systems with the actuator faults. The functional relationship in the affine form between the nonlinear functions with whole state and error variables is established by using the structure consistency of intermediate control signals and the variable-partition technique. The fuzzy control and adaptive backstepping schemes are applied to construct an improved fault-tolerant controller without requiring the specific knowledge of control gains and actuator faults, including both stuck constant value and loss of effectiveness. The proposed fault-tolerant controller ensures that all signals in the closed-loop system are semiglobally practically finite-time stable and the tracking error remains in a small neighborhood of the origin after a finite period of time. The developed control method is verified through two numerical examples.

Adaptive Fuzzy Finite-Time Control of Nonlinear Systems With Actuator Faults

An adaptive neural network (NN) event-triggered control scheme is proposed for nonlinear nonstrict-feedback multiagent systems (MASs) against input saturation, unknown disturbance, and sensor faults. Mean-value theorem and Nussbaum-type function are invoked to transform the structure of the input saturation and overcome the difficulty of unknown control directions, respectively. On the basis of the universal approximation property of NNs, a nonlinear disturbance observer is designed to estimate the unknown compounded disturbance composed of external disturbance and the residual term of input saturation. According to the measurement error defined by control signal, an event-triggered mechanism is developed to save network transmission resource and reduce the number of controller update. Then, an adaptive NN compensation control approach is proposed to tackle the problem of sensor faults via the dynamic surface control (DSC) technique. It is proved that all signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, simulation results demonstrate the effectiveness of the presented control strategy.

Event-Triggered Control for Multiagent Systems With Sensor Faults and Input Saturation

This paper studies an output-based adaptive fault-tolerant control problem for nonlinear systems with nonstrict-feedback form. Neural networks are utilized to identify the unknown nonlinear characteristics in the system. An observer and a general fault model are constructed to estimate the unavailable states and describe the fault, respectively. Adaptive parameters are constructed to overcome the difficulties in the design process for nonstrict-feedback systems. Meanwhile, dynamic surface control technique is introduced to avoid the problem of “explosion of complexity”. Furthermore, based on adaptive backstepping control method, an output-based adaptive neural tracking control strategy is developed for the considered system against actuator fault, which can ensure that all the signals in the resulting closed-loop system are bounded, and the system output signal can be regulated to follow the response of the given reference signal with a small error. Finally, the simulation results are provided to validate the effectiveness of the control strategy proposed in this paper.

Observer-Based Adaptive Fault-Tolerant Tracking Control of Nonlinear Nonstrict-Feedback Systems

In this article, we investigate a distributed online constrained optimization problem with differential privacy where the network is modeled by an unbalanced digraph with a row-stochastic adjacency matrix. To address such a problem, a distributed differentially private algorithm without introducing a trusted third-party is proposed to preserve the privacy of the participating nodes. Under mild conditions, we show that the proposed algorithm attains an $O(\log T)$ expected regret bound for strongly convex local cost functions, where $T$ is the time horizon. Moreover, we remove the need for knowing the time horizon $T$ in advance by adopting doubling trick scheme, and derive an $O(\sqrt{T})$ expected regret bound for general convex local cost functions. Our results coincide with the best theoretical regrets that can be achieved in the state-of-the-art algorithms. Finally, simulation results are conducted to validate the efficiency of our proposed algorithm.

Privacy-Preserving Distributed Online Optimization Over Unbalanced Digraphs via Subgradient Rescaling

An integral sliding mode approach to distributed control of coupled networks with measurement Quantization

This study is concerned with the generalised ℋ 2 fault detection problem for a class of discrete-time switched systems with repeated scalar non-linearities. To reduce the overdesign of the quadratic framework, this study proposes a switching-sequence-dependent Lyapunov function approach to the fault detection filter design procedure. Sufficient conditions are obtained for the existence of admissible generalised ℋ 2 fault detection filter. Since these conditions involve matrix equalities, the cone complementarity linearisation procedure is employed to cast the non-convex feasibility problem into a sequential minimisation problem subject to linear matrix inequalities, which can be readily solved by using the standard numerical software. If these conditions are feasible, a desired fault detection filter can be easily constructed. Finally, a numerical example is given to illustrate the effectiveness of the proposed theory.

Fault detection of switched systems with repeated scalar non-linearities

To handle the common existing constraints, that is, limited energy supplies and limited communication bandwidth in multiagent systems (MASs), this article investigates the consensus problem in MASs with event-triggered communication (ETC) and state quantization. In order to compensate for the effect brought by mismatched disturbances, we also propose a novel multiple discontinuous sliding-mode surface, and the corresponding sliding-mode control law is constructed by considering the event-triggered and dynamic quantized mechanisms jointly. Under such a scheme, it is shown that the state trajectories of all the agents will be regulated to achieve consensus asymptotically and the Zeno behavior can be avoided completely. We further extend this work to self-triggered and periodic event-triggered cases. Particularly, in a periodic event-triggered approach, the new form of triggering conditions and upper bound of the sampling periods are provided explicitly. As a result, all agents can reach bounded consensus. Moreover, the upper bound of the consensus error can be arbitrarily adjusted by appropriately selecting parameters, and the periodic event-triggered case will be reduced to the event-triggered case when the bound approaches 0 (sampling periods approach 0 at the same time). A numerical example is illustrated to verify the effectiveness of the proposed algorithms.

Yongyang Xiong

Papers

Observer-Based Adaptive Fault-Tolerant Tracking Control of Nonlinear Nonstrict-Feedback Systems

Privacy-Preserving Distributed Online Optimization Over Unbalanced Digraphs via Subgradient Rescaling

An integral sliding mode approach to distributed control of coupled networks with measurement Quantization

Fault detection of switched systems with repeated scalar non-linearities

Event-Triggered Quantized Communication-Based Consensus in Multiagent Systems via Sliding Mode.