Adaptive control of linear time-varying plants: a new modelreference controller structure

The problem of developing a control law which can force the output of a linear time-varying plant to track the output of a stable linear time-invariant reference model is discussed. It is shown that the standard model reference controller, used for linear time-invariant plants, cannot guarantee zero tracking error in general when the plant is time-varying. A new model reference controller is proposed which guarantees stability and zero tracking error for a general class of linear time-varying plants with known parameters. When the time-varying plant parameters are unknown but vary slowly with time, it is shown that the new controller can be combined with a suitable adaptive law so that all the signals in the closed loop remain bounded for any bounded initial conditions and the tracking error is small in the mean. The assumption of slow parameter variations in the adaptive case can be relaxed if some information about the frequency or the form of the fast varying parameters is available a priori. Such information can be incorporated in an appropriately designed adaptive law so that stability and improved tracking performance is guaranteed for a class of plants with fast varying parameters     

Hierarchically supervised control of linear plants with unpredictable mode-switch dynamics

A mode-switch process is defined allowing a linear, piecewise time-invariant plant to switch, from time to time, from the actual configuration to another one of a given family of linear, time-invariant plants. When and where switching occurs is not a priori known. It is required to find a stabilizing controller yielding an output response with some desired transient specifications. The solution proposed is given by the connection of multiple families of linear controllers with a hierarchically supervised switching scheme.     

Stability and robustness properties of a simple adaptive controller

A low-order adaptive tracking controller is proposed for linear time-invariant plants with a relative degree not exceeding two. The order of the plant is not required to be known a priori. The algorithm is robustly stable with respect to small linear time-invariant plant perturbations and bounded disturbances. The robustness is achieved by using a projection of the parameter estimates in the control law. An additional a priori information needed to design the controller is bounds on the plant parameters. In the absence of plant perturbations and disturbances, perfect tracking is obtained     

一种自适应鲁棒控制方法及其闭环稳定性分析

研究了含有未建模动态的慢时变系统的自适应镇定问题.考虑的对象具有非最小相 位、含未建模动态和大范围时变参数等不良特性,且存在未知但有界外部扰动.这类对象很难 用时不变鲁棒控制器或传统自适应控制器进行镇定.利用l1优化设计结合参数估计的投影算 法,提出了一种自适应鲁棒控制策略.基于l1优化设计的连续性和投影算法的收敛性,证明了 这种控制策略能够持续适应慢时变对象并且保持闭环系统一致稳定性.鲁棒性分析表明这种 控制策略具有良好的鲁棒镇定性.     

A new indirect adaptive control scheme for time-varying plants

Structures are developed for the control and estimation parts of the indirect adaptive scheme which are more appropriate for time-varying plants. In contrast to the usual pointwise schemes, the new controller structure can meet the control objective exactly for a wide class of plants with smooth but otherwise unrestricted parameter variations. On the other hand, the possibly available knowledge of the form or frequency of variation of the fast parameters is included in the new estimator structure so that, for successful estimation, the overall plant is not restricted to varying slowly with time. The new estimator and control law are combined using the certainty equivalence principle to develop an indirect adaptive control scheme meeting the control objective for plants with time-varying parameters whose fast varying parts are of known form and unknown parts are slow in the mean     

ARTIFICIAL INTELLIGENCE AND GRAPH THEORY TOOLS FOR DESCRIBING SWITCHED LINEAR CONTROL SYSTEMS

This paper develops a representation of multi-model based controllers using artificial intelligence techniques. These techniques will be graph theory, neural networks, genetic algorithms, and fuzzy logic. Thus, graph theory is used to describe in a formal and concise way the switching mechanism between the various plant parameterizations of the switched system. Moreover, the interpretation of multi-model controllers in an artificial intelligence frame will allow the application of each specific technique to the design of improved multi-model based controllers. The obtained artificial intelligence-based multi-model controllers are compared with classic single model-based ones. It is shown through simulation examples that a transient response improvement can be achieved by using multi-estimation based techniques. Furthermore, a method for synthesizing multi-model-based neural network controllers from already designed single model-based ones is presented, extending the applicability of this kind of technique to a more general type of controller. Also, some applications of genetic algorithms and fuzzy logic to multi-model controller design are proposed. In particular, the mutation operation from genetic algorithms inspires a robustness test, which consists of a random modification of the estimates which is used to select the one leading to the better identification performance towards parameterizing online the adaptive controller. Such a test is useful for plants operating in a noisy environment. The proposed robustness test improves the selection of the plant model used to parameterize the adaptive controller in comparison to classic multi-model schemes where the controller parameterization choice is basically taken based on the identification accuracy of each model. Moreover, the fuzzy logic approach suggests new ideas to the design of multi-estimation structures, which can be applied to a broad variety of adaptive controllers such as robotic manipulator controller design.     

Intelligent Control of Discrete Linear Systems Based on a Supervised Adaptive Multiestimation Scheme

A pole-placement based adaptive controller synthesised from a multiestimation scheme is designed for linear plants. A higher level switching structure between the various estimation schemes is used to supervise the reparameterisation of the adaptive controller in real time. The basic usefulness of the proposed scheme is to improve the transient response so that the closed-loop stability is guaranteed. The switching process is subject to a minimum dwelling or residence time within which the supervisor is not allowed to switch between the multiple estimation schemes. The high level supervision is based on the multiestimation identification scheme. The residence time condition guarantees the closed-loop stability. The above higher level switching structure is on-line supervised by a closed-loop tracking error based algorithm. This second supervision on-line tunes the free design parameters which appear as time varying weights in the loss function of the above switching structure. Thus, the closed-loop behaviour, compared to the constant parameter case one, is improved when the design parameter is not tightly initialised. Both supervisors are hierarchically organised in the sense that they act on the system at different rates. Furthermore, a projection algorithm has been considered in the estimation scheme in order to include a possible a priori knowledge of the estimates parameter vector value in the estimation algorithm.     

The digital adaptive control of a linear process modulated by random noise

A procedure for the design of a digital controller to compensate a certain class of linear time-varying processes is presented. The process time variation may be rapid compared to the input signals and is assumed to be caused by modulation of a plant with known parameters by a number of correlated random disturbances. Correlated additive noise may also be present. Plant identification is performed using state variable estimation techniques, while correlation of the random disturbances allows future plant behavior to be predicted. The adaptive controller is designed to optimize the predicted plant behavior over the near future, with controller redesign taking place as new information becomes available from the estimator. Test signals are not required if the plant statistics are known.     

An indirect adaptive controller with a self-excitation capability

An indirect adaptive pole placement controller is presented which stabilizes and asymptotically regulates any discrete-time single-input, single-output linear time-invariant plant which is of known order n , is controllable, and observable, and has unknown parameters. To avoid singular points in the algorithm, the adaptive controller solves the pole-placement design equation asymptotically with time rather than trying to solve it exactly at each time instant. The stability of the adaptive control system and the asymptotic regulation of the plant output to zero are ensured by an additional self-excitation generated by the adaptive controller. A novel kind of an error signal to control the magnitude of the self-excitation is obtained by suitably filtering the self-exciting signal and monitoring changes of the controller parameters as they are generated by the adaptive algorithm     

一类未知非线性离散系统的直接自适应模糊预测控制

将自适应模糊逻辑系统引入预测控制,对一类未知非线性离散系统提出了直接自适应 模糊预测控制方法.首先对被控对象提出了线性时变子模型加非线性子模型的预测模型,然后直 接利用模糊逻辑系统设计预测控制器,并基于广义误差估计值对控制器参数和广义误差估计值中 的未知向量进行自适应调整.文中证明了此方法可使广义误差估计值收敛到原点的小邻域内.     

Adaptive state feedback and tracking control of systems withactuator failures

Direct adaptive-state feedback control schemes are developed for linear time-invariant plants with actuator failures with characterizations that some of the plant inputs are stuck at some fixed or varying values which cannot be influenced by control action. Conditions and controller structures for achieving plant-model state matching in the presence of actuator failures are derived. Adaptive laws are designed for updating the controller parameters when both the plant parameters and actuator-failure parameters are unknown. Closed-loop stability and asymptotic-state tracking are ensured. Simulation results show that desired system performance is achieved with the developed adaptive actuator failure compensation control designs     

An optimal stochastic multivariable PID controller: a direct output tracking approach

This paper deals with the design of an optimal stochastic controller possessing tracking capability of any reference output trajectory in the presence of measurement noise. We consider multi-input multi-output linear time-invariant systems and a proportional-integral-derivative (PID) controller. The system under consideration needs not be stable. A recursive algorithm providing optimal time-varying PID gains is proposed for the case where the number of inputs is larger than or equal to the number of outputs. The development of the proposed algorithm aims for per-time-sample minimisation of the mean-square output error in the presence of erroneous initial conditions, measurement noise, and process noise. Necessary and sufficient conditions are provided for the convergence of the output error covariance. In addition, convergence results are presented for discretised continuous-time plants. Simulation results are included to illustrate the performance capabilities of the proposed algorithm. Performance comparison with an optimal stochastic iterative learning control scheme, an optimal PID controller, an adaptive PID controller, and a recent optimal stochastic PID controller are also included.     

Adaptive LFT control of a civil aircraft with online frequency‐domain parameter estimation

This paper describes the application of an indirect linear fractional transformation (LFT)–based state‐space adaptive control scheme to a transport aircraft, within the context of the European project REconfiguration of CONtrol in Flight for Integral Global Upset REcovery. The principle of the scheme is to design and validate off‐line a gain‐scheduled controller, depending on the plant parameters to be estimated, and to combine it online with a model estimator, so as to minimize the onboard computational time and complexity. A modal approach, very classical for the design of a flight control law, is used to directly synthesize the static output feedback LFT controller, depending on the control and stability derivatives, ie, the parameters of the linearized aerodynamic state‐space model to be estimated. Since the gain‐scheduled LFT controller online depends on the parameter estimates instead of the true values, its robustness to transient and asymptotic estimation errors needs to be assessed using μ and integral quadratic constraint analysis techniques. A primary concern being an online implementation, a fully recursive frequency‐domain estimation technique is proposed, with a low online computational burden and the capability to track time‐varying parameters. Full nonlinear simulations along a trajectory validate the good performance properties of the combined estimator and gain‐scheduled flight controller. To some extent, minimal guaranteed stability and performance properties of the adaptive scheme can be ensured by switching to a robust controller when the parameter estimates are not reliable enough, thus bypassing the Certainty Equivalence Principle.     

On the robust stability of linear time-invariant plants with unstructured uncertainty

We consider general families of linear time-invariant plants described by a nominal plant model with unstructured uncertainty. We show, under a rather weak assumption, that when a family of systems is not robustly stabilizable by any linear time-invariant feedback controller, then no nonlinear time-varying controller can robustly stabilize the given family.     

Simultaneous pole placement of M discrete-time plants using a M-periodic controller

A generic procedure for designing a M-periodic controller (sought in the controller canonical form) for the simultaneous placement of the closed-loop poles of M (=2,3,4,...) discrete, time-invariant plants is presented. The procedure is a two-stage one: first, a set of M simultaneous, linear, polynomial equations, arising out of the M given plants and the corresponding desired closed-loop pole locations, are solved via a generalized Sylvester matrix approach to obtain a set of (M+1) intermediate polynomials; and next, the controller parameters are obtained solving another set of simultaneous, linear polynomial equations that involve the above intermediate polynomials. Thus, both the computational steps are linear algebraic in nature. A list of the isolated plant configurations for which solutions do not exist is given. An example illustrates the procedure.     

Direct and indirect model reference adaptive control

The paper considers the control of an unknown linear time-invariant plant using Direct and Indirect Model Reference Adaptive Control. Employing a specific controller structure and the concept of positive realness, adaptive laws are derived using Indirect Control which are identical to those obtained in the case of Direct Control. The stability questions that arise are also shown to be the same. Simulation results using the new scheme are presented for the control of both stable and unstable plants.     

Multivariable adaptive dynamic surface control based on norm estimation of unknown parameter matrices

In this article, a novel output-feedback adaptive dynamic surface control scheme is proposed for linear time-invariant multivariable plants based on the norm estimation of unknown parameter matrices. Besides avoiding the explosion of complexity problem in traditional multivariable backstepping design, the proposed scheme has the following features: (1) only one parameter needs to be updated on-line regardless of the plant order and input–output dimension, (2) only the Hurwitz condition is required for the high-frequency gain matrix and (3) the ?_∞ performance of the tracking error can be guaranteed. It is shown that all signals of the closed-loop system are semi-globally uniformly bounded. Simulation results are given to illustrate the effectiveness of the proposed scheme.     

Stable model reference adaptive control in the presence of bounded disturbances

The adaptive control of a linear time-invariant plant in the presence of bounded disturbances is considered. In addition to the usual assumptions made regarding the plant transfer function, it is also assumed that the high-frequency gain kpof the plant and an upper bound on the magnitude of the controller parameters are known. Under these conditions the adaptive controller suggested assures the boundedness of all signals in the overall system.     

Nonlinear design of adaptive controllers for linear systems

A new approach to adaptive control of linear systems abandons the traditional certainty-equivalence concept and treats the control of linear plants with unknown parameters as a nonlinear problem. A recursive design procedure introduces at each step new design parameters and incorporates them in a novel Lyapunov function. This function encompasses all the states of the adaptive system and forces them to converge to a manifold of smallest possible dimension. Only as many controller parameters are updated as there are unknown plant parameters, and the dynamic order of the resulting controllers is no higher (and in most cases is lower) than that of traditional adaptive schemes. A simulation comparison with a standard indirect linear scheme shows that the new nonlinear scheme significantly improves transient performance without an increase in control effort