Fuzzy adaptive robust backstepping stabilization for SISO nonlinear systems with unknown virtual control direction

In this paper, a direct fuzzy adaptive robust control approach is proposed for a class of SISO nonlinear systems with completely unknown virtual control directions, unknown nonlinearities, unmodeled dynamics and dynamic disturbances. In the backstepping recursive design, fuzzy logic systems are employed to approximate the combined nonlinear uncertainties, a dynamic signal and Nussbaum gain technique are introduced into the control scheme to dominate the dynamic uncertainties and solve the unknown signs of virtual control directions, respectively. It is proved that the proposed robust fuzzy adaptive scheme can guarantee the all signals in the closed-loop system are semi-globally uniformly ultimately bounded. The effectiveness of the proposed approach is illustrated via three examples.     

Nonlinear adaptive stabilizing control of an anaerobic digestion model with unknown kinetics

In this paper, we consider a nonlinear model of a biological wastewater treatment process, on the basis of two microbial populations and two substrates. The model, described by a four‐dimensional dynamic system, is known to be practically validated and reliable. We propose a feedback control law for asymptotic stabilization of the closed‐loop system towards a previously chosen operating point. A numerical extremum seeking algorithm is applied to stabilize the dynamics towards an equilibrium point with maximal methane flow rate. Computer simulations are reported to illustrate the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Multiple model adaptive control for a class of nonlinear systems with unknown control directions

This study introduces an improved multiple model adaptive control (MMAC) algorithm for a class of nonlinear discrete-time systems. The controller consists of a linear direct adaptive controller, a neural network-based nonlinear direct adaptive controller and a switching mechanism. The assumption of the nonlinear term is relaxed by incorporating a parameter estimator with an augmented error. The control direction of the system is not required to be known by employing a linear direct adaptive controller with the discrete Nussbaum gain and future output predictions. The stability of the closed-loop systems applying the proposed MMAC method is proved and the improved transient performance of the system is illustrated by the simulation results.     

Universal adaptive control of nonlinear systems with unknown growth rate by output feedback

This paper investigates the problem of global stabilization by output feedback, for a family of uncertain nonlinear systems without zero dynamics. These nonlinear systems are dominated by a triangular system satisfying linear growth condition. In contrast to the previous work in the literature, the growth rate here is a positive constant but not known a priori, and therefore the problem becomes more involved and difficult. Using the idea of universal control combined with the output feedback design method developed in Qian and Lin (2002, 2003), we explicitly construct a universal-type adaptive output feedback controller which globally regulates all the states of the uncertain systems without knowing the growth rate.     

Remarks on the adaptive control of linear plants with unknown high-frequency gain

Adaptive control of first-order linear systems of the form $\text{x}\text{?}\text{= ax + bu}$ with the sign of b unknown is considered. It is shown that stabilizing adaptive controllers exist that have globally bounded gain and prespecified terminal dynamics.     

A geometric approach for adaptive estimation of unknown growth kinetics in bioreactors

This paper proposes a new approach for the estimation of unknown and time-varying specific growth rate in fed-batch bioprocess. A novel adaptive estimation technique based on the concept of invariant manifold is proposed as an effective approach to estimate growth kinetic parameters. An asymptotic nonlinear observer is used to provide simultaneous on-line estimation of biomass concentration and growth kinetic. The method is easy to implement and requires only one tuning parameter. The effectiveness of the proposed algorithm is illustrated with representative bioreactor simulation examples.     

Global adaptive stabilisation for nonlinear systems with unknown control directions and input disturbance

This paper addresses the global adaptive stabilisation via switching and learning strategies for a class of uncertain nonlinear systems. Remarkably, the systems in question simultaneously have unknown control directions, unknown input disturbance and unknown growth rate, which makes the problem in question challenging to solve and essentially different from those in the existing literature. To solve the problem, an adaptive scheme via switching and learning is proposed by skilfully integrating the techniques of backstepping design, adaptive learning and adaptive switching. One key point in the design scheme is the introduction of the learning mechanism, in order to compensate the unknown input disturbance, and the other one is the design of the switching mechanism, through tuning the design parameters online to deal with the unknown control directions, unknown bound and period of input disturbance and unknown growth rate. The designed controller guarantees that all the signals of the resulting closed-loop systems are bounded, and furthermore, the closed-loop system states globally converge to zero.     

Robust adaptive repetitive learning control for a class of time-varying nonlinear systems with unknown control direction

A robust adaptive repetitive learning control method is proposed for a class of time-varying nonlinear systems. Nussbaum-gain method is incorporated into the control design to counteract the lack of a priori knowledge of the control direction which determines the motion direction of the system under any input. It is shown that the system state could converge to the desired trajectory asymptotically along the iteration axis through repetitive learning. Simulation is carried out to show the validity of the proposed control method.     

参数未知线性系统的直接自适应模糊广义预测控制

将自适应模糊逻辑系统引入广义预测控制，对参数未知线性系统提出一种直接自适应模糊广义预测控制方法。该方法直接利用模糊逻辑系统设计广义预测控制器，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。证明了该方法不仅能保证闭环系统输入输出有界，而且可使广义误差收敛到原点的一个小领域内。     

Robust integral control for a class of nonlinear systems with unknown control coefficients

The robust integral control problem is studied for a class of nonlinear systems with input-to-state stable (ISS)unmodeled dynamics in this paper.It does not require a priori knowledge of the control coefficients.Combining the Nussbaum-type gain technique and the backstepping design,we propose a state feedback controller,which could achieve the global asymptotic tracking for any constant reference signal,irrespective of the unmeasured dynamic disturbance.It is shown that the proposed methodology further extends the existing robust nonlinear integral control results.Simulation results verify the correctness of the theoretical analysis.     

Nonlinear control of power converters: a new adaptive backstepping approach

This paper proposes a new backstepping approach to nonlinear control of power converters which is attracting considerable attention in both theoretical research and practical applications. The main difference between the proposed algorithm and the existing classical adaptive backstepping method in the literature is that the adaptation mechanism does not follow the certainty‐equivalence principle. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Observer-based adaptive control for nonlinear input-delay systems with unknown control directions

This paper investigates the problem of adaptive control for strict-feedback nonlinear systems with input delay and unknown control directions. The Nussbaum function is utilised to deal with the unknown control directions and a novel compensation system is introduced to handle the time-varying input delay. By using neural network(NN) approximation and backstepping approaches, an adaptive NN controller is designed which can guarantee the semi-global boundedness of all the signals in the closed-loop system. Two simulation examples are also given to illustrate the effectiveness of the proposed method.     

Discrete-time switching periodic adaptive control for time-varying parameters with unknown periodicity

In this paper, we address the problem of unknown periodicity for a class of discrete-time nonlinear parametric systems without assuming any growth conditions on the nonlinearities. The unknown periodicity hides in the parametric uncertainties, which is difficult to estimate with existing techniques. By incorporating a logic-based switching mechanism, we identify the period and bound of unknown parameter simultaneously. Lyapunov-based analysis is given to demonstrate that a finite number of switchings can guarantee the asymptotic tracking for the nonlinear parametric systems. The simulation result also shows the efficacy of the proposed switching periodic adaptive control approach.     

Nonlinear adaptive speed control of a permanent magnet synchronous motor: A perturbation estimation approach

This paper presents a nonlinear adaptive control (NAC) scheme for the speed regulation of a permanent magnet synchronous motor (PMSM) based on perturbation estimation and feedback linearizing control. All PMSM system’s unknown nonlinearities, parameter uncertainties, and external disturbances including unknown time-varying load torque disturbance, are defined as lumped perturbation terms, which are estimated by designing perturbation observers. The estimates are used to adaptively compensate the real perturbations and achieve adaptive feedback linearizing control of the original nonlinear system. The proposed control scheme does not require accurate system model and full state feedback. Stability of the close-loop system with proposed NAC is investigated via Lyapunov theory, and the effectiveness of proposed NAC scheme is verified through both simulation and experimental studies. Both simulation and experimental results show that the proposed NAC scheme can provide less regulation error in speed tracking, better dynamic performance and robustness against parameter uncertainties and load torque disturbance, compared with conventional vector control and load torque estimated based control.     

Robust adaptive control of nonlinear systems with unknown time delays

In this paper, robust adaptive control is presented for a class of parametric-strict-feedback nonlinear systems with unknown time delays. Using appropriate Lyapunov-Krasovskii functionals, the uncertainties of unknown time delays are compensated for. Controller singularity problems are solved by employing practical robust control and regrouping unknown parameters. By using differentiable approximation, backstepping design can be carried out for a class of nonlinear systems in strict-feedback form. It is proved that the proposed systematic backstepping design method is able to guarantee global uniform ultimate boundedness of all the signals in the closed-loop system and the tracking error is proven to converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.     

Extended-state-observer-based adaptive control for synchronisation of multi-agent systems with unknown nonlinearities

This paper studies the problem of synchronisation to a desired trajectory for non-linear multi-agent systems. By introducing extended state observer approach, decentralised adaptive controllers are designed for distributed systems which have non-identical unknown non-linear dynamics. The non-identical unknown non-linear dynamics allows for a tracked command dynamics which is also non-linear and unknown. State variables of agents can be obtained only in the case where leader agent and the network communication topology for multi-agent systems is strongly connected digraph network structures. A Lyapunov-function-based approach is given to show that the tracking error is ultimately bounded. Some simulation results are given to demonstrate the effectiveness of the developed techniques in this paper.     

Nonlinear unknown input observability and unknown input reconstruction: The general analytical solution

Observability is a fundamental structural property of any dynamic system and describes the possibility of reconstructing the state that characterizes the system from fusing the observations of its inputs and outputs. Despite the effort made to study this property and to introduce analytical criteria capable of verifying whether or not a dynamic system satisfies this property, there is no general analytical criterion to obtain the observability of the state when the dynamics are also driven by unknown inputs. Here, we introduce the general analytical solution of this fundamental open problem, often called the unknown input observability problem. We provide the systematic procedure, based on automatic calculation (differentiation and determination of the matrix rank), which allows us to check the observability of the state even in the presence of unknown inputs. One of the fundamental ingredients to obtain this solution is the characterization of the group of invariance of observability. We have very recently introduced this group, together with a new set of tensor fields with respect to this group of transformations (Martinelli, 2020). The analytical solution of the unknown input observability problem is expressed in terms of these tensor fields. In Martinelli (2020) we provided the solution by restricting our investigation to systems that satisfy a special assumption that is called canonicity with respect to the unknown inputs. Here, after an exhaustive characterization of the concept of canonicity, we also account for the case when this assumption is not satisfied and we provide the general solution. This solution is also provided in the form of a new algorithm. In addition, even in the canonic case dealt with in Martinelli (2020), here we provide a new fundamental result that regards the convergence properties of the solution. Finally, as a consequence of the results obtained here, we also provide the condition to reconstruct the unknown inputs, and, when this condition is not met, what can be reconstructed on the unknown inputs. We illustrate the implementation of the new algorithm by studying the observability properties of a nonlinear system in the framework of visual-inertial sensor fusion, whose dynamics are driven by two unknown inputs and one known input. In particular, for this system, we follow step by step the algorithm introduced by this paper, which solves the unknown input observability problem in the most general case.     

Event-triggered adaptive tracking control for nonlinear systems with input saturation and unknown control directions

This article is concerned with event-triggered adaptive tracking control design of strict-feedback nonlinear systems, which are subject to input saturation and unknown control directions. In the design procedure, a smooth nonlinear function is employed to approximate the saturation function so that the controller can be designed under the framework of backstepping. The Nussbaum gain technique is employed to address the issue of the unknown control directions. A predetermined time convergent performance function and a nonlinear mapping technique are introduced to guarantee that the tracking error can converge in the predetermined time with a fast convergence rate and a high accuracy. Then the event-triggered adaptive prescribed performance tracking control strategy is proposed, which not only ensures the boundedness of all the closed-loop signals and the convergence of tracking error but also reduces the communication burden from the controller to the actuator. At last, the simulation study further tests the availability of the proposed control strategy.     

控制方向未知的全状态约束非线性系统的鲁棒自适应跟踪控制

针对一类控制方向未知的含有时变不确定参数和未知时变有界扰动的全状态约束非线性系统,本文提出了一种基于障碍Lyapunov函数的反步自适应控制方法.障碍Lyapunov函数保证了系统状态在运行过程中始终保持在约束区间内;Nussbaum型函数的引入解决了系统控制方向未知的问题;光滑投影算法确保了不确定时变参数的有界性.障碍Lyapunov函数、Nussbaum型函数及光滑投影算法与反步自适应方法的有效结合首次解决了控制方向未知的全状态约束非线性系统的跟踪控制问题.所设计的自适应鲁棒控制器能在满足状态约束的前提下确保闭环系统的所有信号有界.通过恰当地选取设计参数,系统的跟踪误差将收敛于0的任意小的邻域内.仿真结果表明了控制方案的可行性.