An algorithm for synthesis of optimal singular adaptive observers with direct estimation of the initial state vector

An algorithmic synthesis is suggested of a new generation of adaptive observers, including optimal estimators of the initial state vector, identifiers of parameters and optimal singular (full and degenerated) observers of the current state vector, for SISO linear discrete systems. The estimation of the elements of the initial state vector is not typical for the algorithms, inherent to Luenberger's theory of observation with all due consequences. The important fact is emphasized of the dropping off of the procedure for the synthesis of systems with given poles, causing additional difficulties when Luenberger's theory of observation is used. The synthesized algorithm has features such as large-scale granularity and natural parallelism, which also allow its software and hardware interpretation on a transputer basis.     

Stable adaptive observers for nonlinear time-varying systems

An adaptive observer/identifier for single input/single output observable nonlinear systems that can be transformed to a certain observable canonical form is described. Sufficient conditions for stability of this observer are provided. These conditions are in terms of the structure of the system and canonical form, the boundedness of the parameter variations, and the sufficient richness of some signals. The scope of the canonical form and the use of the observer/identifier is motivated by the presentation of applications to time-invariant bilinear systems, nonlinear systems in phase-variable form a biotechnological process, and a robot manipulator. In each case, the specific stability conditions are presented     

Finite-dimensional adaptive observers applied to distributedparameter systems

The application of finite-dimensional adaptive observers to distributed parameter systems is addressed. Ultimate boundedness of the parameter and state errors are proved in the case of residuals which have finite energy over a finite time interval, provided the plant input is definitely exciting. In the absence of definite excitation, an error growth rate of proportional to t^1/2 is proved. The results are obtained without assuming plant stability or input boundedness     

Modeling and simulation of nonlinear and adaptive observers

This paper is concerned with methods of designing nonlinear state observers for polynomic systems, which can be modeled by state equations with linear, bilinear, and quadratic terms. The general structure of polynomic observers is introduced and simulation serves as a useful tool to determine the final observer parameters. In the case of polynomic systems and linear systems, where some of the parameters are unknown, the polynomic observer theory can also be applied for a combined estimation of states and parameters. Several examples are given to demonstrate the necessity of modeling and simulation for choosing the observer structure as well as for adjusting the observer parameters.     

On the adaptive control of robot manipulators with velocity observers

To achieve accurate tracking control of robot manipulators many schemes have been proposed. A common approach is based on adaptive control techniques, which guarantee trajectory tracking under the assumption that the robot model structure is perfectly known and linear in the unknown parameters, while joint velocities are available. Despite tracking errors tend to zero, parameter errors do not unless some persistent excitation condition is fulfilled. There are few works dealing with velocity observation in conjunction with adaptive laws. In this note, an adaptive control/observer scheme is proposed for tracking position of robot manipulators. It is shown that tracking and observation errors are ultimately bounded, with the characteristic that when a persistent excitation condition is matched then they, as well as the parameter errors, tend to zero. Simulation results are in good agreement with the developed theory.     

Robust adaptive observers for nonlinear systems with boundeddisturbances

Since existing adaptive observers for nonlinear systems may generate unbounded parameter estimates in the presence of bounded disturbances, robust adaptive observers are presented which prevent parameter estimate drift. In addition the input-to-state stability of the error dynamics with respect to disturbances and parameter time-derivatives is guaranteed by generalizing a persistency of excitation result. Asymptotic convergence of state estimation errors is still achieved for systems in adaptive observer form when disturbances are not present, by a suitable extension of Barbalat's lemma     

Redesign of adaptive observers for improved parameter identification in nonlinear systems

We propose a method for redesigning adaptive observers for nonlinear systems. The redesign uses an adaptive law that is based on delayed observers. This increases the computational burden, but gives significantly better parameter identification and robustness properties. In particular, given that a special persistency of excitation condition is satisfied, we prove uniform global asymptotic stability and semi-global exponential stability of the origin of the state and parameter estimation error, and give explicit lower bounds on the convergence rate of both the state and parameter estimation error dynamics. For initial conditions with a known upper bound, we prove tunable exponential convergence rate. To illustrate the use of the proposed method, we apply it to estimate the unmeasured flow rate and the uncertain friction parameters in a model of a managed pressure drilling system. The simulation results clearly show the improved performance of the redesigned adaptive observer compared to a traditional design.     

Continuous–discrete adaptive observers for state affine systems

The observation of a class of multi-input multi-output (MIMO) state affine systems with constant unknown parameters and discrete time output measurements is addressed. Assuming some persistent excitation conditions to hold and the sampling steps to satisfy some boundedness hypotheses, system observability is ensured and a class of global exponential observers is synthesized.     

Algorithms for the synthesis of observers for nonlinear dynamic systems

For nonlinear dynamic systems, an approach based on cycle-by-cycle linearization is proposed to construct algorithms for state observers based on linear estimation theory. This approach makes it possible to analytically synthesize a full-rank and a reduced observer of the angular velocity of a spacecraft rotation relative to the body reference frame given the measurements of three angles determining the position of this reference frame in the inertial space. Simulation results are presented.     

On Wonham stabilizability condition in the synthesis of observers for unknown-input systems

In this correspondence a stabilizability condition of Wonham is applied to the synthesis of dynamic observers for unknown-input linear multivariable systems. This approach leads to a stabilizability test of the observer structure considered, and may also lead to computerized design algorithms instead of actual tentative procedures.     

Real-time adaptive control for haptic telemanipulation with Kalman active observers

This paper discusses robotic telemanipulation with Kalman active observers and online stiffness estimation. Operational space techniques, feedback linearization, discrete state space methods, augmented states, and stochastic design are used to control a robotic manipulator with a haptic device. Stiffness estimation only based on force data (measured, desired, and estimated forces) is proposed, avoiding explicit position information. Stability and robustness to stiffness errors are discussed, as well as real-time adaptation techniques. Telepresence is analyzed. Experiments show high performance in contact with soft and hard surfaces.     

非仿射系统的自适应观测器自抗扰控制

研究了一类单输入单输出(SISO)非仿射非线性系统的控制问题,通过微分同胚变换以及自抗扰思想将该类形式转化成含有未知非线性且控制增益未知的仿射形式.引入扩展状态自适应观测器以及Nussbaum-type增益技术,利用积分反演和调节函数技术,设计了自抗扰控制器.从理论上证明了所设计的控制器能够保证闭环系统所有信号全局一致有界,并且证明了跟踪误差渐近收敛到零点的残集内.仿真例子验证了算法的有效性.     

Correlation-spectral transformation of signals in adaptive sequential basis

A procedure for deriving a system of stochastic sequential basis functions is described. It is shown that the use of these functions for correlation and spectral analysis of stochastic signals substantially reduces and simlifies computing operations. A simple method of calculation of the spectrum of variances is given. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 159–164, May–June, 2000.     

Modal synthesis of multivariable systems with observers of specified order

The problem of pole assignment in multivariable linear systems with observers of a given order v is considered. By way of a simple proof, a very general result is established which constitutes an extension of all theorems known in the literature on pole assignment via observers. On its basis, an efficient design algorithm is worked out.     

Multiple‐model adaptive control using set‐valued observers

A multiple‐model adaptive control methodology is proposed that is able to provide stability and performance guarantees, for uncertain linear parameter‐varying plants. The identification problem is addressed by taking advantage of recent advances in model falsification using set‐valued observers (SVOs). These SVOs provide set‐valued estimates of the state of the system, according to its dynamic model. If such estimate is the empty set, the underlying dynamic model is invalidated, and a different controller is connected to the loop. The behavior of the proposed control algorithm is demonstrated in simulation, by resorting to a mass–spring–dashpot system. As a caveat, the computational burden associated with the SVOs can be prohibitive under some circumstances. Copyright © 2013 John Wiley & Sons, Ltd.     

草酸钴合成过程批次间自适应优化

本文以钴湿法冶金过程草酸钴合成为背景,研究基于多向偏最小二乘回归(MPLS)模型的草酸钴平均粒度批次间自适应优化策略.本文首先利用MPLS方法建立草酸钴平均粒度的数据模型;针对模型不确定性情况下难以获得最优操作变量的问题,提出利用批次间修正项自适应优化方法,使迭代优化结果逐渐趋向于实际最优值;本文还通过引入T2统计量软约束将优化结果限制在数据模型的有效区间之内.数值仿真表明该方法可以有效解决草酸钴合成过程的批次间自适应优化问题,且与传统两步方法和迭代学习控制相比具有更好的优化效果.     

A synthesis procedure for parameter adaptive control systems

Given a plant with differential equations characterized by a parameter vector ω which is unknown and slowly varying with time and given a corresponding feedback controller with equations characterized by an adjustable parameter vector γ, a synthesis procedure is presented which leads to a closed-loop adaptive control system for adjusting γ in the face of drift variations in ω. The steps in the synthesis procedure involve 1) the structuring of the basic control system such that model matching is possible for an optimal choice in γ corresponding to every ω,gamma^{ast} = gamma^{ast}(omega), 2) the selection of a performance indexrho(gamma, gamma^{ast})which has the properties of a metric function on every adjustment interval, and 3) the derivation of a modified gradient for updating the value of γ which can be implemented on-line during the normal course of system operation. An example of a pitch-rate orientational control system is used to illustrate the synthesis procedure, and the results of a computer simulation study of the overall adaptive system are discussed which include the effects of nonlinearities, disturbance and measurement noises, as well as time variations in the unknown ω-parameters.     

A correspondence about FDI observers

An explicit existence condition for linear FDI observers is provided. This amends an earlier result of the authors and clarifies some surrounding points.