Tuning of Gaussian stochastic control systems

A closed-loop system consisting of a control system and an adaptive controller is called tuning for a specified control objective if the real system and the ideal system defined below achieve the same value for the control objective. The real system is the system consisting of the unknown control system in closed loop with the adaptive controller in which the parameters of the adaptive controller have been determined by identification under feedback or in closed loop. The ideal system is the system consisting of the unknown control system in closed loop with a controller in which the controller has been synthesized with knowledge of the unknown control system and such that the closed-loop system satisfies the control objective. Both the Gaussian stochastic control system with full observations and with partial observations are considered. The approach to the problem is based on stochastic realization theory for Gaussian systems. The control objectives of minimum variance control and pole placement are also given. Necessary conditions for tuning are discussed     

An approach to stable indirect adaptive control

Stable indirect adaptive control of minimum and nonminimum phase plants is established for cases where a priori bounds on the unknown plant parameters are known and where for each set of parameter values within these bounds the plant has no unstable pole-zero cancellation. By incorporating this partial parameter knowledge in the adaptive law and using a nonminimal representation of the plant, it is shown that the adaptive closed loop control system can be written as an exponentially stable system driven by the identification error. The stability of the adaptive control system is then shown using techniques similar to those known from the model reference adaptive control approach.     

交会对接模拟系统姿态位置耦合有限时间控制

针对航天器交会对接模拟系统的姿态同步和位置跟踪控制问题,在存在外界扰动和系统不确定性的情况下,基于改进的快速非奇异终端滑模面和改进的自适应律,采用双闭环控制结构分别设计内环和外环有限时间姿态位置耦合控制器.所提出的自适应律不仅能有效地抑制扰动和不确定性且能保证控制器是连续的.李雅普诺夫理论推导和仿真结果表明,所提出的控制方法能保证系统内环和外环跟踪误差的有限时间稳定性和准确收敛性.     

Stability and operating constraints of adaptive LMS-based feedback control

The filtered-X LMS algorithm has enjoyed widespread usage in both adaptive feedforward and feedback controller architectures. For feedforward controller designs the filtered-X LMS algorithm has been shown to exhibit unstable divergence for plant estimation errors in excess of ±90°. Typical implementations of this algorithm in adaptive feedback controllers such as filtered-U and filtered-E have previously been assumed to conform to these same identification constraints. Here we present two instability mechanisms that can arise in filtered-E control that violate the 90° error assumption: feedback loop instabilities and LMS algorithm divergence. Analysis of the adaptive feedback system indicates that the conventionally interpreted plant estimation error can be arbitrarily small yet induce algorithm divergence; while other cases may have very large estimation errors and feedback loops cause controller instability. These analytical observations are supported by simulations. The implications of the actual plant estimation error, calculated here for the filtered-E controller, are extended to practical constraints placed on applications including filtered-U, on-line system identification, and self-excited system control.     

Adaptive architectures for control of uncertain dynamical systems with actuator and unmodeled dynamics

In adaptive control of uncertain dynamical systems, it is well known that the presence of actuator and/or unmodeled dynamics in feedback loops can yield to unstable closed‐loop system trajectories. Motivated by this standpoint, this paper focuses on the analysis and synthesis of multiple adaptive architectures for control of uncertain dynamical systems with both actuator and unmodeled dynamics. Specifically, we first analyze model reference adaptive control architectures with standard, hedging‐based, and expanded reference models for this class of uncertain dynamical systems and develop sufficient stability conditions. We then synthesize a robustifying term for the latter architecture and analytically show that this term can allow for a relaxed sufficient stability condition. The proposed theoretical treatments involve Lyapunov stability theory, linear matrix inequalities, and matrix mathematics. Finally, we compare the resulting sufficient stability conditions of the considered adaptive control architectures on a benchmark mechanical system subject to actuator and unmodeled dynamics.     

On parameter convergence in least squares identification and adaptive control

Least squares estimation is appealing in performance and robustness improvements of adaptive control. A strict condition termed persistent excitation (PE) needs to be satisfied to achieve parameter convergence in least squares estimation. This paper proposes a least squares identification and adaptive control strategy to achieve parameter convergence without the PE condition. A modified modeling error that utilizes online historical data together with instant data is constructed as additional feedback to update parameter estimates, and an integral transformation is introduced to avoid the time derivation of plant states in the modified modeling error. On the basis of these results, a regressor filtering–free least squares estimation law is proposed to guarantee exponential parameter convergence by an interval excitation condition, which is much weaker than the PE condition. And then, an identification‐based indirect adaptive control law is proposed to establish exponential stability of the closed‐loop system under the interval excitation condition. Illustrative results considering both identification and control problems have verified the effectiveness and superiority of the proposed approach.     

Multiple model adaptive control for switched linear systems: A two‐layer switching strategy

In this paper, the multiple model adaptive control scheme is first introduced into a class of switched systems. A switched multiple model adaptive control scheme is proposed to improve the transient behavior by resetting the controller parameters. Firstly, a finite‐time parameter identification model is presented, which greatly reduces the number of identification models. Secondly, a two‐layer switching strategy is constructed. The outer layer switching mechanism is to ensure the stability of the switched systems. The inner layer switching mechanism is to improve the transient behavior. Then, by using the constructed jumping multiple Lyapunov functions, the proposed adaptive control scheme guarantees that all the closed‐loop system signals remain bounded and the state tracking error converges to a small ball whose radius can be made arbitrarily small by appropriately choosing the design parameter. Finally, a practical example about model reference adaptive control of an electrohydraulic system using multiple models is given to demonstrate the validity of the main results.     

Wavelet based control for a class of delayed nonlinear systems with input constraints

In this paper, a delay independent adaptive control strategy is presented for a class of uncertain, delayed nonlinear system subjected to actuator saturation. In proposed control scheme wavelet networks are used for approximation of unknown system dynamics as well as a wavelet based compensator is designed to deal with actuator saturation. Delayed wavelet networks are used for identification of unknown system dynamics having state delayed terms, thereby the approximation capabilities of delayed wavelet network are utilized. Adaptation laws are developed for the online tuning of wavelet parameters. Adaptation singularity problem is solved by employing a switching scheme. The stability of closed loop system and ultimate upper boundedness all closed loop signals is proved by constructing a Lyapunov–Krasovskii functional.     

Advanced methods of process computer control for industrial processes

In recent years, the requirements for the performance of multilevel process control, including feedforward and feedback control, monitoring and optimization have increased. Applying process computers and micro computers, the functions of analog equipment and hardwired logic devices cannot only be replaced. Extended or quite new methods can be realized improving the performance of multilevel process control. These advanced methods for process control are characterized by: more sophisticated, better adjusted control algorithms, forecasting of process variables, estimation of not directly measurable variables, computer aided design of algorithms and adaptive or selftuning algorithms. The basis of these advanced methods are mathematical models of the processes and their signals, often gained by the process computer itself during on-line operation.The present paper discusses first how process models in open and closed loop can be obtained by on-line identification methods. Then, based on these models, the computer aided design of control algorithms, adaptive control algorithms and adaptive steady-state on-line optimization will be regarded. Monitoring of not direct measurable variables will be mentioned. For some methods, practical results with real and simulated processes are shown. Interactive process computer software packages are used which can easily be transferred to other process computers.     

Output-feedback MRAC of networked control systems with packet dropout

In this article, a technique of output-feedback model reference adaptive control for networked control systems is developed. The key issues of networked control systems such as channel bandwidth and data-packets dropout induced by the insertion of data networks in the feedback adaptive control loops are considered. The advantage of this article over earlier ones is that the combination of different aspects in networked control systems, output-feedback model reference control of systems with unknown parameters, and unknown data-packets dropout. Error models, adaptive laws, and stability analysis are derived in the case of uncertainty due to data-packets dropout. The applicability of the approach is demonstrated in a practical numerical example of a ship-steering adaptive system.     

Phase and amplitude sinusoidal dither adaptive control system

In many control system applications an adaptive system is required to accommodate changes in plant dynamics. A self-adaptive system described herein adjusts two control system parameters to maintain the closed-loop response essentially constant in spite of large changes in the plant gain and pole-zero locations. The adaptive system uses a high-frequency dither frequency to interrogate the state of the control system. Two self-adaptive performance criteria (SAPC) adjust the two adaptive parameters. One SAPC is based upon the amplitude response to the dither frequency and the other is based upon the phase response. The adaptive loop associated with the amplitude SAPC adjusts the control system loop gain; the adaptive loop associated with the phase SAPC adjusts a variable compensation network. A method is developed for analyzing the stability and performance of the self-adaptive parameter adjustment loops. The stability analysis includes the interaction between these adaptive loops. This two-parameter adaptive system is applied to a specific example to illustrate the techniques developed in the paper.     

Adaptive stabilisation of networked control systems tolerant to unknown actuator failures

In this article, adaptive state feedback stabilising controllers for networked adaptive control systems with unknown actuator failures are developed. The problems of networked control systems (NCSs) such as transmission delays and data-packets dropout, induced by the insertion of data networks in the feedback adaptive control loops are also considered. The novelty of this article consists in the combination of different aspects in NCSs: state tracking control of systems with unknown parameters, unknown actuator failures, network-induced delays and data-packets dropout. Normalised adaptive laws are designed for updating the controller parameters. Sufficient conditions for Lyapunov stability are derived in the case of uncertainty due to actuator failures, delays and data-packets dropout. Simulation results are given to illustrate the effectiveness of our design approach.     

Wavelet reduced order observer based adaptive tracking control for a class of uncertain nonlinear systems using reinforcement learning

This Paper investigates the mean to design the reduced order observer and observer based controllers for a class of uncertain nonlinear system using reinforcement learning. A new design approach of wavelet based adaptive reduced order observer is proposed. The proposed wavelet adaptive reduced order observer performs the task of identification of unknown system dynamics in addition to the reconstruction of states of the system. Reinforcement learning is used via two wavelet neural networks (WNN), critic WNN and action WNN, which are combined to form an adaptive WNN controller. The “strategic” utility function is approximated by the critic WNN and is minimized by the action WNN. Owing to their superior learning capabilities, wavelet networks are employed in this work for the purpose of identification of unknown system dynamics. Using the feedback control, based on reconstructed states, the behavior of closed loop system is investigated. By Lyapunov approach, the uniformly ultimate boundedness of the closed-loop tracking error is verified. A numerical example is provided to verify the effectiveness of theoretical development.     

Detection of asymmetric control valve stiction from oscillatory data using an extended Hammerstein system identification method

The study in this paper is motivated by the detection of control valves with asymmetric stiction resulting in oscillations in feedback control loops. The joint characterization of the control valve and the controlled process is formulated as the identification of a class of extended Hammerstein systems. The input nonlinearity is described by a point-slope-based hysteretic model with two possibly asymmetric ascent and descent paths. An iterative identification method is proposed, based on the idea of separating the ascent and descent paths subject to the oscillatory input and output. The structure of the formulated extended Hammerstein system is shown to be identifiable, and the oscillatory signals in feedback control loops are proved to be informative by exploiting the cyclo-stationarity of these oscillatory signals. Numerical, experimental and industrial examples are provided to illustrate the effectiveness of the proposed identification method.     

Composite adaptive dynamic surface control using online recorded data

This paper presents an online recorded data‐based design of composite adaptive dynamic surface control for a class of uncertain parameter strict‐feedback nonlinear systems, where both tracking errors and prediction errors are applied to update parametric estimates. Differing from the traditional composite adaptation that utilizes identification models and linear filters to generate filtered modeling errors as prediction errors, the proposed composite adaptation integrates closed‐loop tracking error equations in a moving time window to generate modified modeling errors as prediction errors. The time‐interval integral operation takes full advantage of online recorded data to improve parameter convergence such that the application of both identification models and linear filters is not necessary. Semiglobal practical asymptotic stability of the closed‐loop system is rigorously established by the time‐scales separation and Lyapunov synthesis. The major contribution of this study is that composite adaptation based on online recorded data is achieved at the presence of mismatched uncertainties. Simulation results have been provided to verify the effectiveness and superiority of this approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Immersion and invariance based fault tolerant adaptive spacecraft attitude control

In this paper, an immersion and invariance (I&I) adaptive fault tolerant satellite attitude tracking control scheme is proposed. The proposed controller is capable of track the desired trajectory in the presence of unknown actuator multiplicative faults and unknown inertial matrix. Also based on Lyapunov direct method, all closed loop signals are proven to be globally asymptotically stable. The main advantage of this controller is improving closed loop performance while maintaining stability in the presence of unknown actuator faults. This method does not rely on certainty equivalence principle so it can be used to control the transient response of overall closed loop system by means of controlling the parameter estimation behavior which is not possible in traditional adaptive control. Numerical simulations are performed to demonstrate the effectiveness of proposed control scheme.     

Liapunov redesign of model reference adaptive control systems

The model reference adaptive control system has proved very popular on account of a ready-made, but heuristically based, rule for synthesizing the adaptive loops-the so-called "M.I.T. rule." A theoretical analysis of loops so designed is generally very difficult, but analyses of quite simple systems do show that instability is possible for certain system inputs. An alternative synthesis based on Liapunov's second method is suggested here, and is applied to the redesign of adaptive loops considered by some other authors who have all used the M.I.T, rule. Derivatives of model-system error are sometimes required, but may be avoided in gain adjustment schemes if the system transfer function is "positive real," using a lemma due to Kalman. This paper amplifies and extends the work of Butchart and Shackcloth reported at the IFAC (Teddington) Symposium, September, 1965.     

Stability of digital control with computer interruptions

This note analyzes centralized digital control systems in which feedback loops are closed through a digital computer which generates the control law. Intermittent computer interruptions result in the deterioration of control quality and may even render the system unstable. A criterion that guarantees asymptotic stability under any admissible interruption pattern is presented in this note.     

Adaptive force and position control of manipulators

The article presents simple methods for the design of adaptive force and position controllers for robot manipulators within the hybrid control architecture. The force controller is composed of an adaptive PID feedback controller, an auxiliary signal, and a force feedforward term, and achieves tracking of desired force setpoints in the constraint directions. The position controller consists of adaptive feedback and feedforward controllers as well as an auxiliary signal, and accomplishes tracking of desired position trajectories in the free directions. The controllers are capable of compensating for dynamic cross-couplings that exist between the position and force control loops in the hybrid control architecture. The adaptive controllers do not require knowledge of the complex dynamic model or parameter values of the manipulator or the environment. The proposed control schemes are computationally fast and suitable for implementation in online control with high sampling rates. The methods are applied to a two-link manipulator for simultaneous force and position control. Simulation results confirm that the adaptive controllers perform remarkably well under different conditions.     

Recurrent cerebellar loops simplify adaptive control of redundant and nonlinear motor systems

We have described elsewhere an adaptive filter model of cerebellar learning in which the cerebellar microcircuit acts to decorrelate motor commands from their sensory consequences (Dean, Porrill, & Stone, 2002). Learning stability required the cerebellar microcircuit to be embedded in a recurrent loop, and this has been shown to lead to a simple and modular adaptive control architecture when applied to the linearized 3D vestibular ocular reflex (Porrill, Dean, & Stone, 2004). Here we investigate the properties of recurrent loop connectivity in the case of redundant and nonlinear motor systems and illustrate them using the example of kinematic control of a simulated two-joint robot arm. We demonstrate that (1) the learning rule does not require unavailable motor error signals or complex neural reference structures to estimate such signals (i.e., it solves the motor error problem) and (2) control of redundant systems is not subject to the nonconvexity problem in which incorrect average motor commands are learned for end-effector positions that can be accessed in more than one arm configuration. These properties suggest a central functional role for the closed cerebellar loops, which have been shown to be ubiquitous in motor systems (e.g., Kelly & Strick, 2003).