A sliding sector approach to quantized feedback variable structure control

This paper is concerned with the quantized feedback quadratic stabilization problem for linear time-invariant systems. Sliding sector based quantized state feedback variable structure control schemes are established. The main benefit of the sliding sector technique is that it can avoid chattering caused by the utilization of variable structure control strategy. With the proposed discrete on-line adjustment of the quantization parameter, it is shown that the proposed sliding sector based sliding mode controllers can tackle state quantization and guarantee quadratic stability of the closed-loop system. Simulation results are given to verify the effectiveness of the proposed method.     

A new approach to quantized feedback control systems

This paper presents a new approach to the problems of analysis and synthesis for quantized feedback control systems. Both single- and multiple-input cases are considered, with complete results provided for stability and H_∞ performance analysis as well as controller synthesis for discrete-time state-feedback control systems with logarithmic quantizers. The most significant feature is the utilization of a quantization dependent Lyapunov function, leading to less conservative results, which is shown both theoretically and through numerical examples.     

A sector bound approach to feedback control of nonlinear systems with state quantization

This paper studies the feedback control problem of nonlinear systems in strict-feedback form with state quantizers, which are static and bounded by sectors. Through a novel set-valued map based recursive control design approach, the quantized control system is transformed into an interconnection of several input-to-state stable (ISS) subsystems. The ISS property of the closed-loop system is guaranteed by the recently developed cyclic-small-gain theorem. With an appropriately designed quantized controller, the output of the quantized control system can be steered to within a neighborhood of the origin with its size slightly larger than the quantization error near the origin.     

On the absolute stability approach to quantized feedback control

By exploring some geometric properties of the logarithmic quantizer and using the fact that the logarithmic quantizer is sector bounded and nondecreasing, this paper presents a new approach to the stability analysis of quantized feedback control systems. Our method is based on Tsypkin-type Lyapunov functions that have been widely used in absolute stability analysis problems. The results are expressed in linear matrix inequalities (LMIs) and are valid for both single-input and multiple-input discrete-time linear systems with a logarithmic quantizer. Both theoretical analysis and numerical examples show that the results in this paper are generally less conservative than those in the quadratic framework.     

一种新的量化反馈控制系统稳定性分析方法

针对一类量化反馈控制系统,在考虑量化范围和量化误差的情况下,建立该系统的动态数学模型.利用Lyapunov稳定性理论,结合线性矩阵不等式(LMI),给出了基于LMI和时变Lyapunov函数的渐近稳定性判据.假设量化器参数满足一定条件,则通过该判据能分析和判定量化反馈控制系统的渐近稳定性,并进一步设计相应的量化反馈控制律.与已有的方法相比,该方法更加有效且求解方便.数值仿真结果表明了该方法的有效性.     

A generalized sector‐bound approach to feedback stabilization of nonlinear control systems

This paper proposes and develops a generalized sector‐bound approach to feedback stabilization of nonlinear control systems described by state–space models. This approach is inherited from the methodology of the sector‐bounded or passive nonlinearities and influenced by the concept of absolute and quadratic stability. It aims not only to regionally stabilize the nonlinear dynamics asymptotically but also to maximize the estimated region of quadratic attraction and to ensure nominal performance at each equilibrium. More importantly, it has a close connection to gain scheduling and switching control. A path of equilibria is programmed on the basis of the assumption of centered‐ ε‐cover, which leads to a sequence of linear controllers that regionally stabilize the desired equilibrium asymptotically. Simulation results are worked out to illustrate our proposed design method. Copyright © 2012 John Wiley & Sons, Ltd.     

Linear programming approach to constrained feedback control

This paper deals with the problem of stabilizing linear discrete-time systems under state and control linear constraints using linear programming techniques. Linear state constraints describe a polyhedron in the state space so that the problem considered is to make such a polyhedron positively invariant while the control does not violate its constraints. For this, necessary and sufficient conditions are given for the existence of a solution of the problem in terms of polyhedron's vertices and directions. These conditions are described by a set of linear constraints and, following the approach introduced by Vassilaki et al. , they can be solved using linear programming techniques. The objective function proposed here turns out to be a natural one when describing the constraints in terms of polyhedron's vertices and directions.     

Systems with sector bound nonlinearities: A behavioral approach

The class of nonlinear dynamical systems obtained by interconnection of a linear, time-invariant dynamical system and a memoryless, time-invariant, sector-bound nonlinearity has been widely studied in literature. In this paper it is shown that many important results for this class of systems can be elegantly unified using behavioral theory of dynamical systems. Systems with slope-restricted nonlinearities are also considered.     

Non-fragile state feedback H-infinity control for discrete-time systems with quantized signals

This paper presents a study on the problem of non-fragile state feedback H-infinity controller design for linear discrete-time systems with quantized signals. The quantizers considered here are dynamic and time-varying. With the consideration of controller gain variations and quantized signals at the same time, a new non-fragile H-infinity control strategy is proposed with updating quantizer＇s parameters, such that the quantized closed-loop system is asymptotically stable and with a prescribed H-infinity performance bound. An example is presented to illustrate the effectiveness of the proposed control strategy.     

Robust adaptive output feedback control for uncertain nonlinear systems with quantized input

In this paper, we study the input quantization problem for a class of uncertain nonlinear systems. The quantizer adopted belongs to a class of sector‐bounded quantizers, which basically include all the currently available static quantizers. Different from the existing results, the quantized input signal, rather than the input signal itself, is used to design the state observers, which guarantees that the state estimation errors will eventually converge to zero. Because the resulting system may be discontinuous and non‐smooth, the existence of the solution in the classical sense is not guaranteed. To cope with this problem, we utilize the non‐smooth analysis techniques and consider the Filippov solutions. A robust way based on the sector bound property of the quantizers is used to handle the quantization errors such that certain restrictive conditions in the existing results are removed and the problem of output feedback control with input signal quantized by logarithmic (or hysteresis) quantizers is solved for the first time. The designed controller guarantees that all the closed‐loop signals are globally bounded and the tracking error exponentially converges towards a small region around zero, which is adjustable. Copyright © 2016 John Wiley & Sons, Ltd.     

Matched processors for quantized control: A practical parallel-processing approach

Deterministic ‘quantized control’ problems are investigated from a novel and often computationally feasible ‘matched processors’ (MPs) perspective. It is noted that a bank of independent MPs, each matched to an admissible decision sequence, can evaluate, given the state and remaining duration, the dynamic performance cost-to-go values corresponding to a suitably selected ‘small’ subset of all admissible decision sequences. By choosing the best admissible decision sequence in this subset and using its first decision at each stage a computationally feasible and generally sub-optimum MP control scheme is produced. This scheme is found to be ideally suited for very-large-scale integration. In particular, for processes that are linear in the state and performance criteria that are quadratic in the state, the cost-to-go reduces to a simple quadratic function of the given state which in turn results in an MP control scheme structure similar to offered VLSI-based digital computers. It is demonstrated that the proposed scheme performs quite well in two experimental examples.     

A gradient flow approach to decentralised output feedback optimal control

This paper visits the quadratic optimal control problem of decentralised control systems via static output feedback. A gradient flow approach is introduced as a tool to compute the optimal output feedback gain. Several nice properties are revealed concerning the convergence of the gain matrix along the trajectory of an ordinary differential equation obtained from the gradient of objective cost, i.e. the objective cost is decreasing along this trajectory. If the equilibrium points are isolated, the convergence can be guaranteed. A simulation example is given to illustrate the effectiveness of this approach.     

Off-line approach to dynamic output feedback robust model predictive control

This paper presents an off-line approach to the dynamic output feedback robust model predictive control (OFRMPC) for a system with both polytopic uncertainty and bounded disturbance. For the off-line optimization, a sequence of controller parameters and the corresponding regions of attraction are calculated for all combinations of the pre-specified estimated states and estimation error sets (EESs). These controller parameters and the corresponding regions of attraction are stored in a look-up table. On-line, the controller parameters are searched in this look-up table corresponding to real-time EES, and to the region of attraction with the closest containment of real-time estimated state. This method considerably reduces the on-line computational burden. Two numerical examples are given to illustrate the effectiveness of the approach.     

Robust quantized feedback stabilization of linear systems

This paper investigates the feedback stabilization problem for SISO linear uncertain control systems with saturating quantized measurements. In the fixed quantization sensitivity framework, we propose a time varying control law able to effectively account for the presence of saturation, which is often the main source of instability, designed using sliding mode techniques. Such controller is proved able to stabilize the plant both in the presence and in the absence of quantization.     

State feedback H∞ control for quantized discrete‐time systems

This paper is concerned with the quantized state feedback H_∞ control problem for discrete‐time linear time‐invariant systems. The quantizer considered here is dynamic and composed of an adjustable “zoom” parameter and a static quantizer. Static quantizer ranges are with practical significance and fully considered here. A quantized H_∞ controller design strategy is proposed with taking quantizer errors into account, where an iterative linear matrix inequality (LMI) based optimization algorithm is developed to minimize static quantizer ranges with meeting H_∞ performance requirement for quantized closed‐loop systems. An example is presented to illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A new approach to dynamic feedback linearization control of aninduction motor

A new approach to dynamic feedback linearization control of an induction motor is given, Previously, it has been shown that the dynamic model of an induction motor, consisting of speed, stator currents, and rotor flux, is dynamically feedback linearizable. However, the controller and transformation were valid only as long as the motor torque was nonzero and the methodology required switching between two computationally complex transformations. Here it is shown that by considering the direct-quadrature model of the induction motor, a single dynamic feedback linearizing transformation exists and is valid (essentially) as long as the (magnitude of the) rotor flux is nonzero. Furthermore, the resulting control computations are well within the capabilities of contemporary microprocessor technology     

An ILMI approach to robust static output feedback sliding mode control

This paper proposes a systematic methodology for designing robust static output feedback sliding mode control (SOFSMC) for a class of systems with mismatched uncertainties. This methodology consists of two parts: one is a new sufficient and necessary condition for the existence problem in terms of two matrix inequalities; the other is a direct solving method using the iterative linear matrix inequality (ILMI) technique. The main advantages of this method are that only original system parameters are involved without any extra coordinate changes, and that appealing to solving the static output feedback stabilization (SOFS) problem is no longer required. In addition, the ILMI algorithm includes an optimal part to avoid high control efforts. A numerical example also demonstrates the efficacy of the proposed approach.     

A transverse local feedback linearization approach to human head movement control

In the mid-nineteenth century, Donders had proposed that for every human head rotating away from the primary pointing direction, the rotational vectors in the direction of the corresponding axes of rotation, is restricted to lie on a surface. Donders'' intuition was that under such a restriction, the head orientation would be a function of its pointing direction. In this paper, we revisit Donders'' Law and show that indeed the proposed intuition is true for a restricted class of head-orientations satisfying a class of quadratic Donders'' surfaces, if the head points to a suitable neighborhood of the frontal pointing direction. Moreover, on a suitably chosen subspace of the 3D rotation group ${rm SO}(3)$, we describe a head movement dynamical system with input control signals that are the three external torques on the head provided by muscles. Three output signals are also suitably chosen as follows. Two of the output signals are coordinates of the frontal pointing direction. The third signal measures deviation of the state vector from the Donders'' surface. We claim that the square system is locally feedback linearizable on the subspace chosen, and the linear dynamics is decomposed into parts, transverse and tangential to the Donders'' surface. We demonstrate our approach by synthesizing a tracking and path-following controller. Additionally, for different choices of the Donders'' surface parameters, head gaits are visualized by simulating different movement patterns of the head-top vector, as the head-pointing vector rotates around a circle.     

Energy-based approach to the output feedback control of wind energy systems

Wind energy systems can be classified into constant speed and variable speed ones. In constant speed schemes, the generator is directly connected to the electric grid. On the other hand, variable speed operation can be accomplished interposing a static converter in the energy flow between the generator and the grid, permitting a high control flexibility. The main control objectives are the maximization of the conversion efficiency and the elimination of torque oscillations propagated through the drive train. It is assumed in this paper that the most flexible part of the system lies on the turbine, constraining the control solutions to generator speed feedback. The control task is addressed from a passivity-based control viewpoint. The drive train dynamics is modelled as a port-controlled Hamiltonian system with dissipation. Then, stabilization of the desired operating point is achieved through energy shaping and damping injection. Depending on the damping matrix assignment, different control solutions are recovered. Finally, a dynamic feedback controller which preserves the system structure is proposed to improve the system performance without measuring the wind velocity.