Mathematical control of complex systems 2013

Mathematical control of complex systems have already become an ideal research area for control engineers, mathematicians, computer scientists, and biologists to understand, manage, analyze, and interpret functional information/dynamical behaviours from real-world complex dynamical systems, such as communication systems, process control, environmental systems, intelligent manufacturing systems, transportation systems, and structural systems. This special issue aims to bring together the latest/innovative knowledge and advances in mathematics for handling complex systems. Topics include, but are not limited to the following: control systems theory (behavioural systems, networked control systems, delay systems, distributed systems, infinite-dimensional systems, and positive systems); networked control (channel capacity constraints, control over communication networks, distributed filtering and control, information theory and control, and sensor networks); and stochastic systems (nonlinear filtering, nonparametric methods, particle filtering, partial identification, stochastic control, stochastic realization, system identification)

Model based control strategies for a class of nonlinear mechanical sub-systems

This paper presents a comparison between various control strategies for a class of mechanical actuators common in heavy-duty industry. Typical actuator components are hydraulic or pneumatic elements with static non-linearities, which are commonly referred to as Hammerstein systems. Such static non-linearities may vary in time as a function of the load and hence classical inverse-model based control strategies may deliver sub-optimal performance. This paper investigates the ability of advanced model based control strategies to satisfy a tolerance interval for position error values, overshoot and settling time specifications. Due to the presence of static non-linearity requiring changing direction of movement, control effort is also evaluated in terms of zero crossing frequency (up-down or left-right movement). Simulation and experimental data from a lab setup suggest that sliding mode control is able to improve global performance parameters

Neural Network-based Finite-time Control of Nonlinear Systems with Unknown Dead-zones: Application to Quadrotors

Over the years, researchers have addressed several control problems of various classes of nonlinear systems. This article considers a class of uncertain strict feedback nonlinear system with unknown external disturbances and asymmetric input dead-zone. Designing a tracking controller for such system is very complex and challenging. This article aims to design a finite-time adaptive neural network backstepping tracking control for the nonlinear system under consideration. In addition,  all unknown disturbances and nonlinear functions are lumped together and approximated by radial basis function neural network (RBFNN). Moreover, no prior  information about the boundedness of the dead-zone parameters is required in the controller design. With the aid of a Lyapunov candidate function, it has been shown that the tracking errors converge near the origin in finite-time. Simulation results testify that the proposed control approach can force the output to follow the reference trajectory in a short time despite the presence of  asymmetric input dead-zone and external disturbances. At last, in order to highlight the effectiveness of the proposed control method, it is applied to a quadrotor unmanned aerial vehicle (UAV)

Adaptive Control of Systems with Quantization and Time Delays

This thesis addresses problems relating to tracking control of nonlinear systems in the presence of quantization and time delays. Motivated by the importance in areas such as networked control systems (NCSs) and digital systems, where the use of a communication network in NCS introduces several constraints to the control system, such as the occurrence of quantization and time delays. Quantization and time delays are of both practical and theoretical importance, and the study of systems where these issues arises is thus of great importance. If the system also has parameters that vary or are uncertain, this will make the control problem more complicated. Adaptive control is one tool to handle such system uncertainty. In this thesis, adaptive backstepping control schemes are proposed to handle uncertainties in the system, and to reduce the effects of quantization. Different control problems are considered where quantization is introduced in the control loop, either at the input, the state or both the input and the state. The quantization introduces difficulties in the controller design and stability analysis due to the limited information and nonlinear characteristics, such as discontinuous phenomena. In the thesis, it is analytically shown how the choice of quantization level affects the tracking performance, and how the stability of the closed-loop system equilibrium can be achieved by choosing proper design parameters. In addition, a predictor feedback control scheme is proposed to compensate for a time delay in the system, where the inputs are quantized at the same time. Experiments on a 2-degrees of freedom (DOF) helicopter system demonstrate the different developed control schemes.publishedVersio

Estimator-based adaptive neural network control of leader-follower high-order nonlinear multiagent systems with actuator faults

The problem of distributed cooperative control for networked multiagent systems is investigated in this paper. Each agent is modeled as an uncertain nonlinear high-order system incorporating with model uncertainty, unknown external disturbance, and actuator fault. The communication network between followers can be an undirected or a directed graph, and only some of the follower agents can obtain the commands from the leader. To develop the distributed cooperative control algorithm, a prefilter is designed, which can derive the state-space representation to a newly constructed plant. Then, a set of distributed adaptive neural network controllers are designed by making certain modifications on traditional backstepping techniques with the aid of adaptive control, neural network control, and a second-order sliding mode estimator. Rigorous proving procedures are provided,which show that uniform ultimate boundedness of all the tracking errors can be achieved in a networked multiagent system. Finally, a numerical simulation is carried out to evaluate the theoretical results

Quantized control of non-Lipschitz nonlinear systems: a novel control framework with prescribed transient performance and lower design complexity

A novel control design framework is proposed for a class of non-Lipschitz nonlinear systems with quantized states, meanwhile prescribed transient performance and lower control design complexity could be guaranteed. Firstly, different from all existing control methods for systems with state quantization, global stability of strict-feedback nonlinear systems is achieved without requiring the condition that the nonlinearities of the system model satisfy global Lipschitz continuity. Secondly, a novel barrier function-free prescribed performance control (BFPPC) method is proposed, which can guarantee prescribed transient performance under quantized states. Thirdly, a new \textit{W}-function-based control scheme is designed such that virtual control signals are not required to be differentiated repeatedly and the controller could be designed in a simple way, which guarantees global stability and lower design complexity compared with traditional dynamic surface control (DSC). Simulation results demonstrate the effectiveness of our method

Adaptive quantized control of uncertain nonlinear rigid body systems

This paper investigates the attitude tracking control problem for uncertain nonlinear rigid body systems, where both inputs and states are quantized. It is common in networked control systems that sensor and control signals are quantized before they are transmitted via a communication network. An adaptive backstepping control algorithm is developed for a class of uncertain multiple-input multiple-output (MIMO) systems where a class of sector bounded quantizers is considered. It is shown that all the closed-loop signals are ensured uniformly bounded and tracking is achieved. Further, the tracking errors are shown to converge towards a compact set containing the origin and the set can be made small by the choice of the quantization parameters and the control parameters. For illustration of the proposed control scheme, experiments were conducted on a 2 degrees-of-freedom (DOF) helicopter system.publishedVersio

Adaptive Active Anti-vibration Control for a Three-dimensional Helicopter Flexible Slung-load System with Input Saturations and Backlash

This study investigates active anti-vibration control for a three-dimensional helicopter flexible slung-load system (HFSLS) subject to input saturations and backlash. The first target of the study is to establish a model for a three-dimensional HFSLS. The second target is to develop an adaptive control law for a HFSLS by analyzing its ability to compensate for the effects of input saturations, input backlash, and external disturbances, while achieving the goal of vibration reduction. Simulation results of the numerical show that the proposed adaptive active control technology is effective in solving the oscillation suppression problem for the three-dimensional HFSLS with input saturations and backlash.</p