Controller parameterization for SISO and MIMO plants with time delay

Controller parameterization is a very fundamental problem in control theory. It provides an elegant and efficient way towards solving the stabilizing and design problem, with which all stabilizing controllers are characterized and thus a constrained design procedure can be replaced by an unconstrained optimization. In this paper we deal with the problem of characterizing all stabilizing controllers for single-input/single-output (SISO) plants with time delay and multi-input/multi-output (MIMO) plants with multiple time delays. A new parameterization is derived on the basis of the definition of the internal stability. The new parameterization does not depend on the coprime factorization of the plant and has similar form to that of the Youla parameterization for stable plants. An important merit of the proposed parameterization is that it reflects the internal model control (IMC) structure and thus has a very simple relationship to the sensitivity function and complementary sensitivity function. Numerical examples are given to illustrate the proposed parameterization.     

Adaptive estimation of discrete-time systems with nonlinear parameterization

This paper concerns adaptive estimation of dynamic systems which are nonlinearly parameterized. A majority of adaptive algorithms employ a gradient approach to determine the direction of adjustment, which ensures stable estimation when parameters occur linearly. These algorithms, however, do not suffice for estimation in systems with nonlinear parameterization. We introduce in this paper a new algorithm for such systems and show that it leads to globally stable estimation by employing a different regression vector and selecting a suitable step size. Both concave/convex parameterizations as well as general nonlinear parameterizations are considered. Stable estimation in the presence of both nonlinear parameters and linear parameters which may appear multiplicatively is established. For the case of concave/convex parameterizations, parameter convergence is shown to result under certain conditions of persistent excitation.     

Adaptive regulation of cascade systems with nonlinear parameterization

This article provides a solution to the problem of global adaptive regulation, for a class of nonlinearly parameterized cascade systems including feedback linearizable and minimum‐phase systems with nonlinear parameterization. The solution is derived by using a novel parameter separation technique combined with a feedback domination design. We remove all the restrictive conditions previously imposed on the unknown parameters, such as linear parameterization or convex/concave parameterization conditions, which have been commonly assumed so far in the literature of nonlinear adaptive control. Copyright © 2002 John Wiley & Sons, Ltd.     

Adaptive control of nonlinear systems with nonlinear parameterization

An adaptive feedback regulation scheme is proposed for a class of single input nonlinear systems, with nonlinear parameterizations. A proof of local regulation is given. The results are validated through a simulation study.     

Lyapunov-based adaptive control of MIMO systems

The design of Model-Reference Adaptive Control for MIMO linear systems has not yet achieved, in spite of significant efforts, the completeness and simplicity of its SISO counterpart. One of the main obstacles has been the generalization of the SISO assumption that the sign of the high-frequency gain (HFG) is known. Here we overcome this obstacle and present a more complete MIMO analog to the well known Lyapunov-based SISO design which is significantly less restrictive than the existing analogs. Our algorithm makes use of a new control parametrization derived from a factorization of the HFG matrix K_p=SDU, where S is symmetric positive definite, D is diagonal, and U is unity upper triangular. Only the signs of the entries of D or, equivalently, the signs of the leading principal minors of K_p, are assumed to be known.     

多时滞线性系统的控制参数优化方法

采用控制参数化方法研究具有连续状态不等式约束和多重状态及控制时滞的线性系统优化控制问题．通过把时滞系统动态模型中的控制量表示成关于时间的分段常数函数,把每个控制参数看作决策变量,将多时滞系统的控制问题转化为数学规划问题．推导出在连续状态不等式约束条件下的目标函数和约束函数对于待求参数的梯度公式,并用序列二次规划算法求出其最优控制量．最后,将该优化算法应用于湿法炼锌净化过程中．仿真结果表明,锌粉的添加量可以有效地减少,从而避免了资源的浪费．     

Non-uniform sampled-data control of MIMO systems

In this paper, the problem of controlling MIMO plants where the pattern of measurements sampling and control actions delivering is not regular is tackled. Multirate control, time delay systems, missing data environments as well as limited computing and communication resources are on the grounds of these problems. There is an extensive literature on these topics. Different models are reviewed and, from the control viewpoint, model-based control design techniques are reported and new algorithms are proposed. Among the main challenges are the achievement of good performance and the avoidance of intersampling ripple. Both issues are considered and some results are discussed.     

Independent parameterization of two-degree-of-freedom compensatorsin general robust tracking systems

Consideration is given to a general robust tracking problem in which the controlled object is a linear multivariable system having measured variables that are not necessary coincident with the output variables to be controlled. A necessary and sufficient condition for the two-degree-of-freedom compensator to achieve a robust tracking system with internal stability is given. An existence condition is derived for such a compensator, and the class of all such compensators is parameterized, so that two specifications with respect to responses for reference commands and feedback properties can be satisfied independently by the two free parameters     

Limiting zeros of decouplable MIMO systems

For sufficiently rapid zero-order hold (ZOH) sampling, it is known that the zeros of single-input/single-output discrete-time systems expressed in the forward shift operator converge to values determined only by the degrees of the finite and infinite zeros of the underlying continuous-time system. In this paper, it is shown how this result can be generalized to multi-input/multi-output (MIMO) systems decouplable by static-state feedback (equivalently, having a diagonal interactor matrix). In the fast sampling limit, the authors show how invariant and infinite zero structure is mapped under ZOH sampling for discrete-time systems expressed in either the delta (forward difference) or forward shift operators     

Adaptive and robust controls of uncertain systems with nonlinear parameterization

Two classes of partially known systems are considered in this note; both of them have a fractional parameterization of the unknowns. The first class consists of nonlinear systems whose uncertainties are bounded by a function of fractional parameterization, and the second class compromises those systems whose unknown dynamics can directly, but nonlinearly, be parameterized. It is shown that adaptive robust control can be extended to accommodate nonlinearly parameterized bounding functions and that, with the aid of a robust auxiliary system, new adaptation laws and a simple adaptive control can be designed for the unknowns in the fractional parameterization. Practical stability (in terms of uniform boundedness and ultimate boundedness) is shown; global for adaptive robust control and semiglobal for the new adaptive control.     

Adaptive output tracking of inherently nonlinear systems with nonlinear parameterization

We address the problem of output tracking for a class of nonlinearly parameterized systems with unstabilizable linearization. To achieve practical output tracking globally in the case when both the bound of reference signals and the bound of unknown time-varying parameters are not known a priori, we present a robust adaptive control method that is based on the idea of universal control combined with the new adaptive feedback design method developed recently for controlling uncertain systems with nonlinear parameterization. Continuous adaptive tracking controllers are explicitly constructed in this paper. The proposed adaptive tracking controllers use only the information of a prescribed reference signal but not its derivatives, nor its bound.     

A state-space approach to parameterization of stabilizingcontrollers for nonlinear systems

A state-space approach to the Youla parameterization of stabilizing controllers for linear and nonlinear systems is suggested. The stabilizing controllers (or a class of stabilizing controllers for nonlinear systems) are characterized as fractional transformations of stable parameters. The main idea behind this approach is to decompose the output feedback stabilization problem into state feedback and state estimation problems. The parameterized output feedback controllers have separation structures. This machinery allows the parameterization of stabilizing controllers to be conducted directly in state space without using coprime factorization     

A hybrid parameterization of linear single input single output systems

We obtain a parameterization of the set of finite dimensional linear dynamical systems of unbounded McMillan degree. In this parameterization a given system is represented in a nonunique way. However, a certain notion of order is available, thereby providing a graded parameterization. An important feature is that each graded space is diffeomorphic to a Euclidean space. In view of this fact we hope that many of the local results in identification (valid only if the parameter space is Euclidean) an actually be generalized globally. Moreover we show that the topology induced on the space of all plants by this space is finer than the graph topology.     

Control parameterization and robustness of feedback systems: anasymptotic analysis

The problem of robust design is regarded as a parameterization problem, and the choice of parameters to satisfy with respect to a class of bounded perturbations is considered. Application areas for the general results derived include multivariate root-locus robustness, design based on simplified or reduced plant models, and singular perturbation analysis. The results are based on asymptotic analysis of feedback structures and a proof of the existence of parameter ranges for robust stability     

Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization

This paper investigates the adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization. By using the parameter separation lemma in [Lin, W., & Qian, C. (2002a). Adaptive control of nonlinearly parameterized systems: A nonsmooth feedback framework. IEEE Transactions on Automatic Control, 47, 757-774.] and some flexible algebraic techniques, and choosing an appropriate Lyapunov function, a smooth adaptive state-feedback controller is designed, which guarantees that the closed-loop system has an almost surely unique solution for any initial state, the equilibrium of interest is globally stable in probability, and the state can be regulated to the origin almost surely.     

Adaptive pole placement control of MIMO systems

An adaptive pole-assignment controller design for an MIMO (multi-input-multi-output) system is with unknown observability indexes or with an overparameterized system model is presented. The controller design algorithm and stability issues are addressed     

Approximation-based control of nonlinear MIMO time-delay systems

Approximation-based control is presented for a class of multi-input multi-output (MIMO) nonlinear systems in block-triangular form with unknown state delays. Neural networks (NNs) are utilized to approximate and compensate for unknown functions in the system dynamics, including the unknown bounds of the functions of delayed states. The use of a separation technique removes the need for any assumption on the function of delayed states, and allows the handling of multiple delays in each function of delayed states. By combining the use of Lyapunov-Krasovskii functionals and adaptive NN backstepping, the proposed control guarantees that all closed-loop signals remain bounded, while the outputs converge to a neighborhood of the desired trajectories. Simulation results demonstrate the effectiveness of the proposed scheme.     

Decentralised fixed modes of networked MIMO systems

In this paper, decentralised fixed modes (DFMs) of a networked system are studied. The network topology is directed and weighted and the nodes are higher-dimensional linear time-invariant (LTI) dynamical systems. The effects of the network topology, the node-system dynamics, the external control inputs, and the inner interactions on the existence of DFMs for the whole networked system are investigated. A necessary and sufficient condition for networked multi-input/multi-output (MIMO) systems in a general topology to possess no DFMs is derived. For networked single-input/single-output (SISO) LTI systems in general as well as some typical topologies, some specific conditions for having no DFMs are established. It is shown that the existence of DFMs is an integrated result of the aforementioned relevant factors which cannot be decoupled into individual DFMs of the node-systems and the properties solely determined by the network topology.