Adaptive output feedback dynamic surface control of stochastic nonlinear systems with state and input unmodeled dynamics

In this paper, an adaptive neural output feedback control scheme is investigated for a class of stochastic nonlinear systems with unmeasured states and four kinds of uncertainties including uncertain nonlinear function, dynamic disturbance, input unmodeled dynamics, and stochastic inverse dynamics. The unmeasured states are estimated by K‐filters, and stochastic inverse dynamics is dealt with by constructing a changing supply function. The considered input unmodeled dynamic subsystem possesses nonlinear feature, and a dynamic normalization signal is introduced to counteract the unstable effect produced by the input unmodeled dynamics. Combining dynamic surface control technique with stochastic input‐to‐state stability, small‐gain condition, and Chebyshev's inequality, the designed robust adaptive controller can guarantee that all the signals in the closed‐loop system are bounded in probability, and the error signals are semi‐globally uniformly ultimately bounded in mean square or the sense of four‐moment. Simulation results are provided to verify the effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Mapping filtered forwarding‐based robust adaptive control for uncertain nonlinear systems with input constraint

This work develops a robust adaptive control algorithm for uncertain nonlinear systems with parametric uncertainties and external disturbances satisfying an extended matching condition. This control method is implemented in the framework of a mapping filtered forwarding‐based technique. As an attractive alternative of the adaptive backstepping method, this bottom‐up strategy forms a virtual controller and a parameter updated law at each step of the design, where Lyapunov functions and the prior knowledge of system parameters are not required. The boundedness of all signals is guaranteed by using Barbalat's lemma. According to immersion relationship, a compliant behavior of systems behaves accordingly to the lower‐order target dynamics. Furthermore, input constraints are handled by estimating a saturated scaling. A spring, mass, and damper system is used to demonstrate the controller performances via simulation results.     

Dual high‐gain‐based adaptive output‐feedback control for a class of nonlinear systems

We propose an adaptive output‐feedback controller for a general class of nonlinear triangular (strict‐feedback‐like) systems. The design is based on our recent results on a new high‐gain control design approach utilizing a dual high‐gain observer and controller architecture with a dynamic scaling. The technique provides strong robustness properties and allows the system class to contain unknown functions dependent on all states and involving unknown parameters (with no magnitude bounds required). Unlike our earlier result on this problem where a time‐varying design of the high‐gain scaling parameter was utilized, the technique proposed here achieves an autonomous dynamic controller by introducing a novel design of the observer, the scaling parameter, and the adaptation parameter. This provides a time‐invariant dynamic output‐feedback globally asymptotically stabilizing solution for the benchmark open problem proposed in our earlier work with no magnitude bounds or sign information on the unknown parameter being necessary. Copyright © 2007 John Wiley & Sons, Ltd.     

Decentralized adaptive output‐feedback control for stochastic interconnected systems with stochastic unmodeled dynamic interactions

In this paper, we consider the problem of decentralized adaptive output‐feedback regulation for stochastic nonlinear interconnected systems with unknown virtual control coefficients, stochastic unmodeled dynamic interactions. The main contributions of the paper are as follows: (1) This paper presents the first result on decentralized output‐feedback control for stochastic nonlinear systems with unknown virtual control coefficients; (2) For stochastic interconnected systems with stochastic integral input‐to‐state stable unmodeled dynamics, and more general nonlinear uncertain interconnections which depend upon the outputs of subsystems and the stochastic unmodeled dynamics, a decentralized output‐feedback controller is designed to drive the outputs and states to the origin almost surely. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust output tracking of uncertain nonlinear systems with completely unknown dead‐zone input: A self‐tuning design approach

The main purpose of this paper is to propose a direct and simple approach, called a self‐tuning design approach, to dealing with any nonsymmetric dead‐zone input nonlinearity where its information is completely unknown. In order to describe the approach, the output tracking problem is considered for a class of uncertain nonlinear systems with any nonsymmetric dead‐zone input. First, a dead‐zone input is represented as a time‐varying input‐dependent function such that the considered dynamical system with dead‐zone input can be transfered into an uncertain nonlinear dynamical system subject to a linear input with time‐varying input coefficient. Then, by making use of the self‐tuning design approach, a class of adaptive robust output tracking control schemes with a rather simple structure is synthesized. Thus, the proposed direct and simple self‐tuning design approach can be easily understood by the engineering designers, and the resulting simple adaptive robust control schemes can be well implemented in most practical engineering control problems. By combining the proposed self‐tuning design approach with other control methods, one may expect to obtain a number of interesting results for a rather large class of uncertain nonlinear dynamical systems with dead‐zone in the actuators. Finally,the simulations of some numerical examples are provided to demonstrate the validity of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Observer‐based nonlinear feedback decentralized neural adaptive dynamic surface control for large‐scale nonlinear systems

This paper presents a nonlinear gain feedback technique for observer‐based decentralized neural adaptive dynamic surface control of a class of large‐scale nonlinear systems with immeasurable states and uncertain interconnections among subsystems. Neural networks are used in the observer design to estimate the immeasurable states and thus facilitate the control design. Besides avoiding the complexity problem in traditional backstepping, the new nonlinear feedback gain method endows an automatic regulation ability into the pioneering dynamic surface control design and improvement in dynamic performance. Novel Lyapunov function is designed and rigorous stability analysis is given to show that all the closed‐loop signals are kept semiglobally uniformly ultimately bounded, and the output tracking errors can be guaranteed to converge to sufficient area around zero, with the bound values characterized by design parameters in an explicit manner. Simulation and comparative results are shown to verify effectiveness.     

Robust output tracking of uncertain nonlinear time‐delay systems with unknown dead‐zone inputs via control schemes with a simple structure

The adaptive robust output tracking control problem is considered for a class of uncertain nonlinear time‐delay systems with completely unknown dead‐zone inputs. A new design method is proposed so that some adaptive robust output tracking control schemes with a rather simple structure can be constructed. It is not necessary to know the nonlinear upper bound functions of uncertain nonlinearities. In fact, the constructed output tracking control schemes are structurally linear in the state and have a self‐tuning control gain function that is updated by an adaptation law. In this paper, the dead‐zone input is nonsymmetric, and its information is assumed to be completely unknown. In addition, a numerical example is given to describe the design procedure of the presented method, and the simulations of this numerical example are implemented to demonstrate the validity of the theoretical results.     

Adaptive fuzzy output feedback backstepping control of pure‐feedback nonlinear systems via dynamic surface control technique

In this paper, an adaptive fuzzy backstepping dynamic surface control approach is considered for a class of uncertain pure‐feedback nonlinear systems with immeasurable states. Fuzzy logic systems are first employed to approximate the unknown nonlinear functions, and then an adaptive fuzzy state observer is designed to estimate the immeasurable states. By the combination of the adaptive backstepping design with a dynamic surface control technique, an adaptive fuzzy output feedback backstepping control approach is developed. It is proven that all the signals of the resulting closed‐loop system are semi‐globally uniformly ultimately bounded, and the observer and tracking errors converge to a small neighborhood of the origin by choosing the design parameters appropriately. Simulation examples are provided to show the effectiveness of the proposed approach. Copyright © 2012 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.     

Adaptive output-feedback stabilization in prescribed time for nonlinear systems with unknown parameters coupled with unmeasured states

The prescribed-time output-feedback stabilization (ie, regulation of the state and control input to zero within a “prescribed” time picked by the control designer irrespective of the initial state) of a general class of uncertain nonlinear strict-feedback-like systems is considered. Unlike prior results, the class of systems considered in this article allows crossproducts of unknown parameters (without any required magnitude bounds on unknown parameters) and unmeasured state variables in uncertain state-dependent nonlinear functions throughout the system dynamics. We show that prescribed-time output-feedback stabilization (ie, both prescribed-time state estimation and prescribed-time regulation) is achieved through a novel output-feedback control design involving specially designed dynamics of an adaptation state variable and a high-gain scaling parameter in combination with a temporal transformation and a dual high-gain scaling based observer and controller design. While standard dynamic adaptation techniques cannot be applied due to crossproducts of unknown parameters and unmeasured states, we show that instead, the dynamics of the high-gain scaling parameter and adaptation parameter can be designed with temporal forcing terms to ensure that unknown parameters in system dynamics are dominated by a particular fractional power of the high-gain scaling parameter and the adaptation parameter after a subinterval (of unknown length) of the prescribed time interval. We show that the control law can be designed such that the system state and input are regulated to zero in the remaining subinterval of the prescribed time interval.     

Global adaptive regulation control for a class of nonlinear systems with unknown control coefficients

This paper is concerned with the global asymptotic regulation control problem for a class of nonlinear uncertain systems with unknown control coefficients. The allowed class of uncertainties include unmeasured input‐to‐state stable (ISS) and/or weaker integral ISS (iISS) inverse dynamics, parametric uncertainties, and uncertain nonlinearities. By using the Nussbaum‐type gain technique and changing the ISS/integral ISS inverse dynamics supply rates, we design a dynamic output feedback controller which could guarantee that the system states are asymptotically regulated to the origin from any initial conditions, and the other signals are bounded in closed‐loop systems. The numerical example of a simple pendulum with all unknown parameters and without velocity measurement illustrates our theoretical results. The simulation results demonstrate its efficacy. Copyright © 2015 John Wiley & Sons, Ltd.     

Inverse optimal adaptive control for non‐linear uncertain systems with exogenous disturbances

A Lyapunov‐based inverse optimal adaptive control‐system design problem for non‐linear uncertain systems with exogenous ℒ︁₂ disturbances is considered. Specifically, an inverse optimal adaptive non‐linear control framework is developed to explicitly characterize globally stabilizing disturbance rejection adaptive controllers that minimize a nonlinear‐nonquadratic performance functional for non‐linear cascade and block cascade systems with parametric uncertainty. It is shown that the adaptive Lyapunov function guaranteeing closed‐loop stability is a solution to the Hamilton–Jacobi–Isaacs equation for the controlled system and thus guarantees both optimality and robust stability. Additionally, the adaptive Lyapunov function is dissipative with respect to a weighted input–output energy supply rate guaranteeing closed‐loop disturbance rejection. For special integrand structures of the performance functionals considered, the proposed adaptive controllers additionally guarantee robustness to multiplicative input uncertainty. In the case of linear‐quadratic control it is shown that the operations of parameter estimation and controller design are coupled illustrating the breakdown of the certainty equivalence principle for the optimal adaptive control problem. Finally, the proposed framework is used to design adaptive controllers for jet engine compression systems with uncertain system dynamics. Copyright © 2000 John Wiley & Sons, Ltd.     

Direct adaptive neural control of nonlinear strict‐feedback systems with unmodeled dynamics using small‐gain approach

In this paper, a novel direct adaptive neural control approach is presented for a class of single‐input and single‐output strict‐feedback nonlinear systems with nonlinear uncertainties, unmodeled dynamics, and dynamic disturbances. Radial basis function neural networks are used to approximate the unknown and desired control signals, and a direct adaptive neural controller is constructed by combining the backstepping technique and the property of hyperbolic tangent function. It is shown that the proposed control scheme can guarantee that all signals in the closed‐loop system are semi‐globally uniformly ultimately bounded in mean square. The main advantage of this paper is that a novel adaptive neural control scheme with only one adaptive law is developed for uncertain strict‐feedback nonlinear systems with unmodeled dynamics. Simulation results are provided to illustrate the effectiveness of the proposed scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

Observer‐based fuzzy adaptive quantized control for uncertain nonlinear multiagent systems

This paper focuses on consensus quantized control design problem for uncertain nonlinear multiagent systems with unmeasured states. Every follower can be denoted through a system with unmeasurable states, hysteretic quantized input, and unknown nonlinearities. Fuzzy state observer and Fuzzy logic systems are employed to estimate unmeasured states and approximate unknown nonlinear functions, respectively. The hysteretic quantized input can be split into two bounded nonlinear functions to avoid chattering problem. By combining adaptive backstepping and first‐order filter signals, an observer‐based fuzzy adaptive quantized control scheme is designed for each follower. All signals exist in closed‐loop systems are semiglobally uniformly ultimately bounded, and all followers can accomplish a desired consensus results. Finally, a numerical example is employed to elaborate the effectiveness of proposed control strategy.     

Decentralized output feedback controller design for nonlinear interconnected systems with unknown control direction and time‐varying delays

The decentralized output feedback control problem is considered for a class of large‐scale systems with unknown time‐varying delays. The uncertain interconnections are bounded by general nonlinear functions with unknown coefficients. The control direction parameters are unknown for each subsystem, which brings a challenging issue for decentralized controller design. To deal with this problem, we propose a new decentralized control scheme with the help of Nussbaum function. The decentralized filter is designed at first. By constructing Lyapunov–Krasovskii functional, we design the dynamic output feedback controller. It is rigorously proved that the closed‐loop system is asymptotically stable. Finally, the simulation is performed, and the results verify the effectiveness of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive backstepping neural control of state‐delayed nonlinear systems with full‐state constraints and unmodeled dynamics

In this paper, the problem of adaptive neural control is discussed for a class of strict‐feedback time‐varying delays nonlinear systems with full‐state constraints and unmodeled dynamics, as well as distributed time‐varying delays. The considered nonlinear system with full‐state constraints is transformed into a nonlinear system without state constraints by introducing a one‐to‐one asymmetric nonlinear mapping. Based on modified backstepping design and using radial basis function neural networks to approximate the unknown smooth nonlinear function and using a dynamic signal to handle dynamic uncertainties, a novel adaptive backstepping control is developed for the transformed system without state constraints. The uncertain terms produced by state time delays and distributed time delays are compensated for by constructing appropriate Lyapunov‐Krasovskii functionals. All signals in the closed‐loop system are proved to be semiglobally uniformly ultimately bounded. A numerical example is provided to illustrate the effectiveness of the proposed design scheme.     

Prescribed performance adaptive fuzzy dynamic surface control of nonaffine time‐varying delayed systems with unknown control directions and dead‐zone input

In this paper, an adaptive prescribed performance control method is presented for a class of uncertain strict feedback nonaffine nonlinear systems with the coupling effect of time‐varying delays, dead‐zone input, and unknown control directions. Owing to the universal approximation property, fuzzy logic systems are used to approximate the uncertain terms in the system. Since there is no systematic approach to determine the required upper bounds of errors in control systems, the prior selection of control parameters to have a satisfactory performance is somehow impossible. Therefore, the prescribed performance technique as a solution is applied in this study to bring satisfactory performance indices to the system such as overshoot and steady state performance within a predetermined bound. Dynamic surface control strategy is also introduced to the proposed control scheme to address the “explosion of complexity” behavior existing in conventional backstepping methods. To ease the control design, the mean‐value theorem is utilized to transform the nonaffine system into the affine one. Moreover, with the help of this theorem, the unknown dead‐zone nonlinearity is separated into the linear and nonlinear disturbance‐like bounded term. The proposed method relaxes a prior knowledge of control direction by employing Nussbaum‐type functions, and the effect of time‐varying delays are compensated by constructing the proper Lyapunov‐Krasovskii functions. The proposed controller guarantees that all the closed‐loop signals are semiglobally uniformly ultimately bounded and the error evolves within the decaying prescribed bounds. In the end, in order to demonstrate the superiority of this method, simulation examples are given.     

Robust stabilization of a class of non‐minimum‐phase nonlinear systems in a generalized output feedback canonical form

In this paper, a globally robust stabilizer for a class of uncertain non‐minimum‐phase nonlinear systems in generalized output feedback canonical form is designed. The system contains unknown parameters multiplied by output‐dependent nonlinearities and output‐dependent nonlinearities enter such a system both additively and multiplicatively. The proposed method relies on a recently developed novel parameter estimator and state observer design methodology together with a combination of backstepping and small‐gain approach. Our design has three distinct features. First, the parameter estimator and state observer do not necessarily follow the classical certainty‐equivalent principle any more. Second, the design treats unknown parameters and unmeasured states in a unified way. Third, the technique by combining standard backstepping and small‐gain theorem ensures robustness with respect to dynamic uncertainties. Finally, two numerical examples are given to show that the proposed method is effective, and that it can be applied to more general systems that do not satisfy the cascading upper diagonal dominance conditions developed in recent papers, respectively. Copyright © 2008 John Wiley & Sons, Ltd.     

Finite‐model adaptive control using an LS‐like algorithm

Adaptive control problem of a class of discrete‐time nonlinear uncertain systems, of which the internal uncertainty can be characterized by a finite set of functions, is formulated and studied by using an least squares (LS)‐like algorithm to design the feedback control law. For the finite‐model adaptive control problem, this algorithm is proposed as an extension of counterpart of traditional LS algorithm. Stability in sense of pth mean for the closed‐loop system is proved under a so‐called linear growth assumption, which is shown to be necessary in general by a counter‐example constructed in this paper. The main results have been also applied to parametric cases, which demonstrate how to bridge the non‐parametric case and parametric case. Copyright © 2006 John Wiley & Sons, Ltd.     

A combined backstepping and dynamic surface control to adaptive fuzzy state‐feedback control

This paper studies an adaptive fuzzy dynamic surface control for a class of nonlinear systems with fuzzy dead zone, unmodeled dynamics, dynamical disturbances, and unknown control gain functions. The unknown system functions are approximated by the Takagi‐Sugeno–type fuzzy logic systems. There are 3 main features for the presented systematic design scheme. First, by adopting an integrated method, a novel adaptive fuzzy controller is constructed for the nonlinear system with fuzzy dead zone. Second, only 3 online learning parameters need to be tuned, which significantly reduces the computation burden. Third, the possible controller singularity problem in some of the existing adaptive control methods with feedback linearization techniques can be avoided. On the basis of the backstepping technique and dynamic surface control, all the signals of the closed‐loop system are guaranteed to be semiglobally uniformly ultimately bounded. Finally, 2 simulation examples are provided to illustrate the effectiveness of the proposed scheme.