Unknown Control Coefficients Research Articles

Adaptive Inversion-Based Fuzzy Compensation Control of Uncertain Pure-Feedback Systems With Asymmetric Actuator Backlash

This paper concerns with the problem of adaptive inverse compensation control for a class of uncertain pure-feedback nonlinear systems with asymmetric actuator backlash. By resorting to the mean-value theorem, the considered system can be transformed into the strict-feedback form with unknown state-dependent virtual control coefficients. Then, the most challenging difficulty is how to design the adaptive backlash inverse compensator in face of uncertain control gain function. To overcome this challenge, we first propose a smooth inverse model for asymmetric backlash, and based on it, a new expression of adaptive compensation error is further developed, which also paves the way to the embeddedness of fuzzy logic systems to cancel the unknown gain function. Moreover, two mutually learning mechanisms (one is for predicting unknown backlash parameters, while another is to search for optimal fuzzy weights) are further constructed such that the inverse compensator can be updated online. With the backstepping iteration design of compensator input, an adaptive fuzzy compensation controller (i.e., the compensator output) is developed to ensure the asymptotic stability of the closed-loop system. Finally, comparative simulations are conducted to validate the effectiveness and applicability of the proposed control theory.

Output feedback stabilisation for nonlinear systems with unknown output function and control coefficients and its application

ABSTRACTThis paper solves the problem of output feedback stabilisation for nonlinear systems with unknown output function and control coefficients. Since output function is Lipschitz continuous but not necessary derivable, the maximal sector region of output function is given. As long as output function belongs to the sector, an output feedback controller can be designed to render the closed-loop system globally asymptotically stable. The effectiveness of controller is demonstrated by two examples.

NN approach to state-feedback control of high-order non-linear time-delay systems with time-varying control coefficient

This paper considers the adaptive state-feedback control problem for a class of high-order non-linear systems with unknown control coefficient and time delays. By applying the neural network approximation method and the Nussbaum function approach, the restrictions on non-linear functions and the conditions on the time-varying control coefficient are largely relaxed. In addition, an adaptive neural network state-feedback controller with only one adaptive parameter is successfully constructed by introducing proper Lyapunov–Krasovskii functionals and using the backstepping technique. The proposed scheme guarantees the closed-loop system to be semi-globally uniformly ultimately bounded. Finally, a simulation example demonstrates the effectiveness of the controller.

Adaptive NN output-feedback control for stochastic time-delay nonlinear systems with unknown control coefficients and perturbations

This paper addresses the problem of adaptive output-feedback control for more general class of stochastic time-varying delay nonlinear systems with unknown control coefficients and perturbations. By using Lyapunov–Krasovskii functional, backstepping and tuning function technique, a novel adaptive neural network (NN) output-feedback controller is constructed with fewer learning parameters. The designed controller guarantees that all the signals in the closed-loop system are 4-moment (or mean square) semi-globally uniformly ultimately bounded (SGUUB). Finally, a simulation example is shown to demonstrate the effectiveness of the proposed control scheme.

Global output-feedback stabilization for high-order nonlinear systems with unknown growth rate

Summary This paper considers the global stabilization via time-varying output-feedback for a class of high-order uncertain nonlinear systems with rather weak assumptions. Essentially different from the existing literature, the systems under investigation simultaneously have more serious nonlinearities, unknowns, immeasurableness, and time-variations, which are indicated from the unknown time-varying control coefficients and the higher-order and lower-order unmeasured states dependent growth with the rate of unknown function of time and output. Recognizing that adaptive technique is quite hard to apply, a time-varying design scheme is proposed by combining time-varying approach, certainty equivalence principle and homogeneous domination approach. One key point in the design scheme is the selection of the design functions of time, in order to compensate/capture the serious unknowns and serious time-variations, and another one is the design of a time-varying observer to rebuild the unmeasured system states. With the appropriate choice of the involved design functions, the designed controller makes all the signals of the closed-loop system globally bounded and ultimately converge to zero. Copyright © 2016 John Wiley & Sons, Ltd.

Control of a Segway with unknown control coefficient and input constraint

This paper proposes a control method of the Segway with unknown control coefficient and input saturation. To design a simple controller for the Segway with the model uncertainty, the prescribed performance function is used. Furthermore, an auxiliary variable is introduced to deal with unknown time-varying control coefficient and input saturation problem. Due to the auxiliary variable, function approximators are not used in this paper although all model uncertainties are unknown. Thus, the controller can be simple. From the Lyapunov stability theory, it is proved that all errors of the proposed control system remain within the prescribed performance bounds. Finally, the simulation results are presented to demonstrate the performance of the proposed scheme.

Robust Control for the Segway with Unknown Control Coefficient and Model Uncertainties.

The Segway, which is a popular vehicle nowadays, is an uncertain nonlinear system and has an unknown time-varying control coefficient. Thus, we should consider the unknown time-varying control coefficient and model uncertainties to design the controller. Motivated by this observation, we propose a robust control for the Segway with unknown control coefficient and model uncertainties. To deal with the time-varying unknown control coefficient, we employ the Nussbaum gain technique. We introduce an auxiliary variable to solve the underactuated problem. Due to the prescribed performance control technique, the proposed controller does not require the adaptive technique, neural network, and fuzzy logic to compensate the uncertainties. Therefore, it can be simple. From the Lyapunov stability theory, we prove that all signals in the closed-loop system are bounded. Finally, we provide the simulation results to demonstrate the effectiveness of the proposed control scheme.

Nonlinear feedback design for fixed-time tracking of a class of nonlinear systems

ABSTRACTFixed-time control is more preferable than finite-time control in practical applications since the settling time is independent of the system initial condition in a fixed-time control problem. Moreover, systems in real world usually suffer from unfavourable factors, such as unknown control coefficients and external disturbance. In this paper, we consider the fixed-time tracking control for a class of nonlinear systems by considering the aforementioned two points. A strategy for specifying the control input is established by the method of adding a power integrator. The designed control law guarantees that the reference signal can be followed in a fixed time. As an application, the bank-to-turn missile system is used to show the efficiency of the proposed fixed-time tracking scheme.

Online identifier–actor–critic algorithm for optimal control of nonlinear systems

SummaryIn this paper, a novel identifier–actor–critic optimal control scheme is developed for discrete‐time affine nonlinear systems with uncertainties. In contrast to traditional adaptive dynamic programming methodology, which requires at least partial knowledge of the system dynamics, a neural‐network identifier is employed to learn the unknown control coefficient matrix working together with actor–critic‐based scheme to solve the optimal control online. The critic network learns the approximate value function at each step. The actor network attempts to improve the current policy based on the approximate value function. The weights of all neural networks are updated at each sampling instant. Lyapunov theory is utilized to prove the stability of closed‐loop system. It shows that system states and neural network weights are uniformly ultimately bounded. Finally, simulations are provided to illustrate the effectiveness of the developed method. Copyright © 2016 John Wiley & Sons, Ltd.

A unified time-varying feedback approach and its applications in adaptive stabilization of high-order uncertain nonlinear systems

We are concerned with two key problems of adaptive control design: one is to find the feasible conditions and the valid boundary of the time-varying feedback scheme; another one lies in the improved generalization of the homogeneous idea in the global adaptive stabilization of high-order uncertain nonlinear systems. The distinguished feature of the system to be investigated is the serious coexistence between unknown time-varying parameters and unknown time-varying control coefficients. Design procedures of the continuous controller are provided based on the sign function technique and the delicate search of the time-varying function and a Lyapunov function. Finally, the control of uncertain single-link robotic manipulator demonstrates the application of design scheme.

Adaptive Neural Control of Uncertain MIMO Nonlinear Systems With State and Input Constraints.

An adaptive neural control strategy for multiple input multiple output nonlinear systems with various constraints is presented in this paper. To deal with the nonsymmetric input nonlinearity and the constrained states, the proposed adaptive neural control is combined with the backstepping method, radial basis function neural network, barrier Lyapunov function (BLF), and disturbance observer. By ensuring the boundedness of the BLF of the closed-loop system, it is demonstrated that the output tracking is achieved with all states remaining in the constraint sets and the general assumption on nonsingularity of unknown control coefficient matrices has been eliminated. The constructed adaptive neural control has been rigorously proved that it can guarantee the semiglobally uniformly ultimate boundedness of all signals in the closed-loop system. Finally, the simulation studies on a 2-DOF robotic manipulator system indicate that the designed adaptive control is effective.

Quantisation‐based robust control of uncertain non‐strict‐feedback non‐linear systems under arbitrary switching

This study concentrates on the problem of robust quantised control for a class of switched non-strict-feedback non-linear systems under arbitrary switching. Differs from non-switched non-linear systems, the stability in switched ones (especially under arbitrary switching) is much dependent on the construction of common Lyapunov function (CLF). However, such CLF is fairly difficult to be designed in this study as the simultaneous consideration of full-states uncertainties, unknown virtual control coefficients, as well as quantisation problem. To overcome the challenge, this study presents a systematic control design method. Specifically, the neural networks with minimal learning parameter, and the boundedness property of Gaussian basis functions are combined to deal with the full-states uncertainties, while an online estimator is built by sufficiently using the special structure of virtual controllers to dispose the unknown virtual coefficients problem. Moreover, a non-linear decomposition of quantiser is further proposed, rendering that the quantisation problem can be solved independently at the last step of backstepping iteration. With these results, an adaptive control algorithm which guarantees a CLF for all subsystems is successfully established such that the tracking error is steered into an adjustable area of origin asymptotically, and meanwhile all closed-loop signals remain uniformly ultimately bounded under arbitrary switching. Lastly, the obtained conclusions are well verified by the simulated results.

Global generalised exponential/finite-time control for course-keeping of ships

ABSTRACTThis paper addresses the global generalised exponential/finite-time control of the nonlinear ship course system with an unknown control coefficient. Different from the well-known Nussbaum-gain adaptive rule, a new Lyapunov-based adaptive logic switching rule is proposed to seek the correct control direction of the ship course system. The main advantage of the proposed controller is that it guarantees the global generalised exponential/finite-time control of closed-loop systems. Theoretical analysis and simulation results show the effectiveness of the developed control method.

Adaptive control of MIMO mechanical systems with unknown actuator nonlinearities based on the Nussbaum gain approach

This paper investigates MIMO mechanical systems with unknown actuator nonlinearities. A novel Nussbaum analysis tool for MIMO systems is established such that unknown time-varying control coefficients are tackled. In contrast to existing literatures on continuous-time systems, the newly-developed Nussbaum tool focuses on extending the traditional Nussbaum result from one dimensional case to the multiple one. Specifically, not only the multiple unknown input coefficients are extended to the time-varying, but also the limitation of the prior knowledge of coefficients� upper and lower bounds is removed. Furthermore, an adaptive robust controller associated with the proposed tool is presented. The asymptotic tracking of MIMO mechanical systems is guaranteed with the help of the Lyapunov Theorem. Finally, a simulation example is provided to examine the validity of the proposed scheme.

Global adaptive finite‐time stabilization of a class of switched nonlinear systems with parametric uncertainty

SummaryThis paper investigates the global adaptive finite‐time stabilization of a class of switched nonlinear systems, whose subsystems are all in p (p≤1) normal form with unknown control coefficients and parametric uncertainties. The restrictions on the power orders and the nonlinear perturbations are relaxed. By using the parameter separation technique, the uncertain parameters are separated from nonlinear functions. A systematic design procedure for a common state feedback controller and a switching adaptive law is presented by employing the backstepping methodology. It is proved that the closed‐loop system is finite‐time stable under arbitrary switching by utilizing the common Lyapunov function. Finally, with the application to finite‐time control of chemical reactor systems, the effectiveness of the proposed method is demonstrated. Copyright © 2015 John Wiley & Sons, Ltd.

Finite-time stabilization of a general class of nonholonomic dynamic systems via terminal sliding mode

This paper presents control strategies for finite-time stabilization of a class of nonholonomic dynamic systems with unknown virtual control coefficients and system parameters. The minimal dilation degree technique and the terminal sliding mode control scheme with finite-time convergence are used to design the controllers. The systematic control strategy development involves the introduction of state transformations and the application of recursive terminal sliding mode structure. Depending on whether the system in question can be converted into a time-invariant linear system or not, two control schemes are proposed respectively guaranteeing that system states converge to zero in finite time. The effectiveness and the robust feature of the developed control approaches are testified by two practical examples: the simplified underactuated hovercraft system and the parking problem for a mobile robot of the unicycle type.

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

SummaryThis 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.

Adaptive NN prescribed performance control for nonlinear systems with output dead zone

This paper investigates adaptive neural network (NN) prescribed performance output tracking control problem for a class of strict-feedback nonlinear systems with output dead zone. By introducing a Nussbaum function, the problem of unknown virtual control coefficient is resolved, which is caused by the nonlinearity in the output dead zone. By designing the state observer and utilizing backstepping recursive design technique, a new adaptive NN control method is proposed. It is shown that all the signals of the resulting closed-loop system are bounded and the tracking error remains an adjustable neighborhood of the origin with the predefined performance under the effect of output dead zone. Finally, a simulation example is given at the simulation part, which further demonstrate the effectiveness of proposed control method.

Observer-Based Adaptive Fuzzy Tracking Control of MIMO Stochastic Nonlinear Systems With Unknown Control Directions and Unknown Dead Zones

In this paper, an adaptive fuzzy backstepping output-feedback tracking control approach is proposed for a class of multi-input and multi-output (MIMO) stochastic nonlinear systems. The MIMO stochastic nonlinear systems under study are assumed to possess unstructured uncertainties, unknown dead-zones, and unknown control directions. By using a linear state transformation, the unknown control coefficients and the unknown slopes characteristic of the dead-zones are lumped together, and the original system is transformed to a new system on which the control design becomes feasible. Fuzzy logic systems are used to approximate the unstructured uncertainties, and a fuzzy state observer is designed to estimate the unmeasured states. By introducing a special Nussbaum gain function into the backstepping control design, a stable adaptive fuzzy output-feedback tracking control scheme is developed. The main features of the proposed adaptive control approach are that it can guarantee the stability of the closed-loop system, and the tracking errors converge to a small neighborhood of zero. Moreover, it can solve the problems of unknown control direction, unknown dead-zone, and unmeasured states simultaneously. Two simulation examples are provided to show the effectiveness of the proposed approach.

Fuzzy adaptive output feedback DSC design for SISO nonlinear stochastic systems with unknown control directions and dead-zones

In this paper, the adaptive fuzzy output feedback control problem is investigated for a class of single-input and single-output (SISO) stochastic nonlinear systems unknown dead-zones and unknown control direction. In the design, by using a linear state transformation, the unknown control coefficient and the unknown slope characteristic of the dead-zone are lumped together, and the original system is transformed to a new system. Fuzzy logic systems are employed to identified the uncertain nonlinear systems, a nonlinear fuzzy state observer is constructed to solve the problem of unmeasured states, and a special Nussbaum function is introduced into the control design to solve the unknown control direction problem, respectively. To address the problem of “explosion of complexity”, the dynamic surface control (DSC) technique is employed, a stable adaptive fuzzy output-feedback tracking control scheme is developed. The stability is proven based on Lyapnov theory, and it can guarantee that all the variables of closed-loop system are bounded in probability, and tracking error converges to a small neighborhood of zero. A numerical example is provided to verify the effectiveness of the proposed method.