Distributed adaptive control for multiple nonholonomic systems with nonlinearly parameterized uncertainties

This paper investigates the distributed adaptive control problem for multiple nonholonomic systems with nonlinearly parameterized uncertainties. Under the assumption that the graph topology is directed and the leader is globally reachable, distributed adaptive controllers are designed recursively by using backstepping technique and algebra graph theory. It is shown that all the followers' outputs will exponentially converge to the reference output signal while all the signals of the closed‐loop system are bounded. Finally, two simulation examples are given to demonstrate the effectiveness of the control scheme.     

Robust adaptive output feedback control of nonlinearly parameterized systems

The ideas of adaptive nonlinear damping and changing supply functions were used to counteract the effects of parameter and nonlinear uncertainties, unmodeled dynamics and unknown bounded disturbances. The high-gain observer was used to estimate the state of the system. A robust adaptive output feedback control scheme was proposed for nonlinearly parameterized systems represented by input-output models. The scheme does not need to estimate the unknown parameters nor add a dynamical signal to dominate the effects of unmodeled dynamics. It is proven that the proposed control scheme guarantees that all the variables in the closed-loop system are bounded and the mean-square tracking error can be made arbitrarily small by choosing some design parameters appropriately. Simulation results have illustrated the effectiveness of the proposed robust adaptive control scheme. Translated from Journal of Sichuan University (Engineering Science Edition), 2006, 38(4): 136–140 [译自: 四川大学学报 (工程科学版)]     

Robust adaptive control of nonlinearly parameterized systems with unmodeled dynamics

Many physical systems such as biochemical processes and machines with friction are of nonlinearly parameterized systems with uncertainties. How to control such systems effectively is one of the most challenging problems. This paper presents a robust adaptive controller for a significant class of nonlinearly parameterized systems. The controller can be used in cases where there exist parameter and nonlinear uncertainties, unmodeled dynamics and unknown bounded disturbances. The design of the controller is based on the control Lyapunov function method. A dynamic signal is introduced and adaptive nonlinear damping terms are used to restrain the effects of unmodeled dynamics, nonlinear uncertainties and unknown bounded disturbances. The backstepping procedure is employed to overcome the complexity in the design. With the proposed method, the estimation of the unknown parameters of the system is not required and there is only one adaptive parameter no matter how high the order of the system is and how many unknown parameters there are. It is proved theoretically that the proposed robust adaptive control scheme guarantees the stability of nonlinearly parameterized system. Furthermore, all the states approach the equilibrium in arbitrary precision by choosing some design constants appropriately. Simulation results illustrate the effectiveness of the proposed robust adaptive controller. __________ Translated from Journal of Sichuan University (Engineering Science Edition), 2005, 37(5): 148–153 (in Chinese)     

Switched adaptive stabilization of switched nonlinearly parameterized cascade systems and its application to a two inverted pendulums

This paper studies adaptive control of switched nonlinearly parameterized cascade systems. No solvability of the adaptive control problem for subsystems is required. By exploiting the multiple Lyapunov functions method and the parameter separation technique and the tool of adding a power integrator, we develop a new switched adaptive control approach for the explicit construction of adaptive controllers of subsystems and a proper switching law that solves the adaptive stabilization problem. A key feature of the proposed adaptive controllers is its switched property, namely, each subsystem has its individual update law. A two‐inverted pendulum as a practical example is also provided to demonstrate the effectiveness of the proposed design method. Copyright © 2014 John Wiley & Sons, Ltd.     

Switched sampled output adaptive observer design for a class of switched nonlinearly parameterized systems under asynchronous switching

In this article, a switched sampled output adaptive observer for a class of switched nonlinearly parameterized systems is designed. Since the switching may occur during the sampling intervals while the sampled output only updates at sampling instants, the asynchronous switching phenomenon arises. Then, a collection of matched and mismatched corrective terms are introduced to deal with the asynchronous switching phenomenon based on sampled outputs and the designed observer. Moreover, some sufficient conditions are derived to achieve the boundedness of observation and parameter estimation errors based on an improved average dwell time method. Finally, the effectiveness of the theoretical result in this article is demonstrated through a simulation example.     

Quasi‐passivity‐based adaptive stabilization for switched nonlinearly parameterized systems

This paper investigates the adaptive quasi‐passification‐based stabilization problem for a class of switched nonlinearly parameterized systems via average dwell time method. First, when all the subsystems have any same relative degree, the global practical stability is achieved by combining the recursive feedback quasi‐passification design technique with a switched adaptive control technique. The states and parameter estimation errors converge to the ball whose sizes can be reduced by choosing appropriate design parameters. Second, when the system states are unavailable for measurements, adaptive output feedback controllers are designed to stabilize the system using quasi‐passivity. The proposed output feedback controllers do not depend on any state observer. Finally, three examples show the effectiveness of the proposed methods.     

Adaptive finite-time tracking control for parameterized nonlinear systems with full state constraints

In this article, the issue of adaptive finite-time dynamic surface control (DSC) is discussed for a class of parameterized nonlinear systems with full state constraints. Using the property of logarithmic function, a one-to-one nonlinear mapping is constructed to transform a constrained system into an unconstrained system with the same structure. The nonlinear filter is constructed to replace the first-order linear filter in the traditional DSC, and the demand on the filter time constant is reduced. Based on finite-time stable theory and using modified DSC, the finite-time controller is designed via DSC. Theoretical analysis shows that all the signals in the closed-loop system are semiglobal practical finite-time stable. Furthermore, none of the states are outside the defined open set. In the end, simulation results are presented to demonstrate the effectiveness of the proposed control schemes with both linear filters and nonlinear filters.     

Self-triggered adaptive prescribed-time tracking control for stochastic nonlinear systems

This paper proposes a self-triggered (ST) adaptive prescribed-time tracking control method for a class of stochastic nonlinear systems. Different from the existing results, an improved ST mechanism is proposed by adding a judgment condition to reduce the negative effect of excessive design interval on system performance. Based on the one-to-one mapping and backstepping technique, an adaptive prescribed-time tracking control method is proposed, which can make the error converge to the predefined precision set within the predetermined time. Simultaneously, applying the Lyapunov stability method, the boundedness of all signals in the closed-loop system can be ensured. Finally, a detailed simulation example is provided to show the effectiveness of the proposed control strategy.     

Robust adaptive tracking control of uncertain discrete time systems

In this paper, the problem of robust adaptive tracking for uncertain discrete‐time systems is considered from the slowly varying systems point of view. The class of uncertain discrete‐time systems considered is subjected to both 𝓁_∞ to 𝓁_∞ bounded unstructured uncertainty and external additive bounded disturbances. A priori knowledge of the dynamic model of the reference signal to be tracked is not completely known. For such problem, an indirect adaptive tracking controller is obtained by frozen‐time controllers that at each time optimally robustly stabilize the estimated models of the plant and minimize the worst‐case steady‐state absolute value of the tracking error of the estimated model over the model uncertainty. Based on 𝓁_∞ to 𝓁_∞ stability and performance of slowly varying system found in the literature, the proposed adaptive tracking scheme is shown to have good robust stability. Moreover, a computable upper bound on the size of the unstructured uncertainty permitted by the adaptive system and a computable tight upper bound on asymptotic robust steady‐state tracking performance are provided. Copyright © 2005 John Wiley & Sons, Ltd.     

Robust adaptive MPC for constrained uncertain nonlinear systems

In this paper, we consider the problem of adaptive model predictive control subject to exogenous disturbances. Using a novel set‐based adaptive estimation, the problem of robust adaptive MPC is proposed and solved for a class of linearly parameterized uncertain nonlinear systems subject to state and input constraints. Two formulations of the adaptive MPC routine are proposed. A general minmax approach is considered. A Lipschitz‐based formulation is also proposed. The closed‐loop robust stability of both approaches is demonstrated. The Lipschitz‐based approach avoids the need for a minmax optimization problem and is amenable to real‐time computation. A simple chemical reactor simulation example is presented that demonstrates the effectiveness of the technique. Copyright © 2010 John Wiley & Sons, Ltd.     

A self-coordinating adaptive control scheme for HVDC transmission systems

The transients in a HVDC system can temporarily change line currents, voltages, and power substantially from the reference steady state values and the behavior of the system depends greatly upon the parameters of the converter controller. The DC system performances are affected by the AC system characteristics such as the short circuit ratio, and the AC system inertia. A controller which has good performance for a particular operating condition may not have sufficiently good performance under another operating condition or vice versa. Performance of the controller also depends on the impedance at the rectifier and the inverter bus, which may vary according to the operating conditions of the AC network. A controller with self-coordinating adaptive capability can perform better in various situations. The proposed controller is tested at a very low SCR, the most critical value for system performance evaluation, and at the low inertia of the AC system. Simulation results are compared between proposed controller, fuzzy tuned controller, gain scheduling controller, and fixed-parameter controller. All simulations are conducted using MATLAB/SIMULINK software package.     

An indirect adaptive control for fully feedback linearizable discrete-time non-linear systems

An indirect adaptive control for a discrete-time non-linear system that is fully input–output linearizable is developed. The unknown parameters of the system are identified by using a multi-output RLS algorithm. Based on the certainty equivalence principle, the estimated parameters are then utilized in the controller design. Stability of the adaptively controlled closed-loop system is shown by using the Lyapunov method. Numerical simulations are included to illustrated the performance of the proposed strategy. © 1997 John Wiley & Sons, Ltd.     

Adaptive interconnection and damping assignment passivity-based control for linearly parameterized discrete-time port controlled Hamiltonian systems via I&I approach

In this paper, discrete-time adaptive control of linearly parameterized fully actuated Port-controlled Hamiltonian systems with parameter uncertainties in energy function is considered. A discrete-time adaptive interconnection and damping assignment passivity-based control (IDA-PBC) method, utilizing the immersion and invariance (I&I) approach, for the considered uncertain Hamiltonian system, is presented. A discrete-time parameter estimator based on the immersion and invariance approach is derived to obtain an automatic tuning mechanism for the IDA-PBC controller. The stability analysis for the estimator and the closed-loop system is done using the Lyapunov theory. The proposed method is applied to two fully actuated physical systems and its performance is tested by simulations. Simulation results show that the proposed I&I-based adaptive IDA-PBC controller successfully preserves the performance of the IDA-PBC controller designed with true parameters under a large amount of uncertainty.     

Sampled‐data adaptive control of a class of nonlinear systems

The paper considers the discrete‐time implementation of a class of backstepping adaptive controllers for uncertain nonlinear systems in the parametric strict‐feedback form. The stability of the resultant sampled‐data system cannot be guaranteed when the direct discretization of the continuous‐time backstepping controller is applied to the same system via a sampling and hold device. Therefore, the paper has presented a sampled‐data control scheme which involves first modifying the existing continuous‐time controller and then discretizing it using the forward Euler method. It has been shown that the proposed control guarantees in a semi‐global sense the boundedness of all the variables of the overall sampled‐data system under some conditions. Particularly, the state of the nonlinear system to be controlled can converge to any arbitrarily small neighbourhood of the origin. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust adaptive stabilization for time-varying systems with unmodelled dynamics and disturbances

In this paper, robust adaptive stabilization is discussed for time-varying discrete time systems with disturbances and unmodelled dynamics. Both bounded and unbounded stochastic disturbances are considered. It is assumed that the parameters of the nominal model belong to a bounded convex set and that the ‘frozen time’ nominal model is stabilizable for all possible parameter values. Requiring neither external excitation nor stable invertibility of the nominal model, an adaptive regulator is constructed on the basis of the solution to a finite time Riccati equation and a projected gradient estimator. It is shown that the closed-loop system is stable if both the time average of the parameter variations and the model error are sufficiently small.     

A switching periodic adaptive control approach for time‐varying parameters with unknown periodicity

Periodic variations are encountered in many real systems, which can exist in the system parameters, as a disturbance or as the tracking objective. However, there exist a great number of situations where the periodicity is not known in advance. Hence, how to compensate for the effects of time‐varying parameters with unknown periodicity remains a challenge for the controller design. In this paper, we proposed a switching periodic adaptive control approach for continuous‐time nonlinear parametric systems with periodic uncertainties in which the period and bound are not known in advance. We utilized a fully saturated periodic adaptation law to identify the unknown periodic parameters in a pointwise manner. In addition, we provided a logic‐based switching scheme to estimate the unknown period and bound online simultaneously. By virtue of Lyapunov stability analysis, we show that the asymptotic convergence can be guaranteed irrespective of the initial conditions. Finally, we carried out numerical simulations to demonstrate the efficacy of the switching periodic adaptive control algorithm. The proposed approach can be applied to parametric nonlinear systems with time‐varying parameters of unknown periodicity irrespective of the types of periodic uncertainties. Copyright © 2015 John Wiley & Sons, Ltd.     

A decoupled adaptive control algorithm for global state feedback stabilization of a class of nonlinear systems

A decoupled adaptive control algorithm, namely the combined dynamic gain and adaptive homogeneous domination approach, is introduced to solve the global state feedback stabilization problem for a class of uncertain nonlinear systems. Compared with the conventional adaptive backstepping/tuning functions approach, the algorithm differs in the way of constructing the estimator and handling the nonlinear drifts, and allows the adaptive control law that is decoupled via a dynamic gain to be designed only by choosing some appropriate constants. The proposed adaptive controller guarantees that all the states of the closed‐loop system are globally bounded and the system solutions converge to zero asymptotically. Both physical and academic examples are provided to demonstrate the validness of the theory. Copyright © 2014 John Wiley & Sons, Ltd.     

A small‐gain approach for adaptive output‐feedback NN control of switched pure‐feedback nonlinear systems

This paper investigates the problem of adaptive output‐feedback neural network (NN) control for a class of switched pure‐feedback uncertain nonlinear systems. A switched observer is first constructed to estimate the unmeasurable states. Next, with the help of an NN to approximate the unknown nonlinear terms, a switched small‐gain technique‐based adaptive output‐feedback NN control scheme is developed by exploiting the backstepping recursive design scheme, input‐to‐state stability analysis, the common Lyapunov function method, and the average dwell time (ADT) method. In the recursive design, the difficulty of constructing an overall Lyapunov function for the switched closed‐loop system is dealt with by decomposing the switched closed‐loop system into two interconnected switched systems and constructing two Lyapunov functions for two interconnected switched systems, respectively. The proposed controllers for individual subsystems guarantee that all signals in the closed‐loop system are semiglobally, uniformly, and ultimately bounded under a class of switching signals with ADT, and finally, two examples illustrate the effectiveness of theoretical results, which include a switched RLC circuit system.     

基于神经网络的一类非线性系统自适应滑模控制

针对可以分解为标称系统和不确定系统两部分的SISO非线性系统,提出了一种基于神经网络的自适应滑模控制方案。控制器由标称控制律和补偿控制律组成,标称控制律用来控制标称系统,补偿控制律是基于Lyapunov稳定性理论设计的自适应神经滑模控制律,用来控制不确定系统,而神经网络用来逼近系统的不确定性。理论分析和计算机仿真都证明,本文提出的控制策略不但能解决这类系统的轨迹跟踪控制问题,而且可以保证闭环系统的渐近稳定性。     

Robust adaptive tracking control for nontriangular time-delay nonlinear systems with input dead-zone and multiple uncertainties

This article studies the robust adaptive tracking control problem of nontriangular nonlinear systems that are affected by multiple state delays rather than the input-delay. Different from the related studies, the considered systems involve input dead-zone and various uncertainties arising in the control coefficients, structure parameters, time delays, and disturbances. A new adaptive control strategy is presented by introducing a dynamic-gain-based Lyapunov-Krasovskii functional and by generalizing the tuning function method in the framework of time-delay system theory. All the states of the closed-loop system are bounded and the tracking error can be adjusted sufficiently small. In the simulation, the delayed chemical system is studied to demonstrate the validity of the strategy.